1 ELIPS-3 The Space Optical Clocks (SOC) Project Final Report S. Schiller (1) , G. M. Tino (2) , S. Bize (3) , U. Sterr (4) , A. Görlitz (1) , Ch. Lisdat (4) , M. Schioppo (2) , N. Poli (2) , A. Nevsky (1) , C. Salomon (5) , and the SOC team members (1,2,3,4) (1) Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany (2) Università di Firenze and LENS, Firenze, Italy (3) Observatoire de Paris, Paris, France (4) Physikalisch-Technische Bundesanstalt, Braunschweig, Germany (5) École Normale Supérieure, Paris, France January 2012 www.spaceopticalclocks.org
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ELIPS-3
The Space Optical Clocks (SOC) Project
Final Report
S. Schiller(1), G. M. Tino(2), S. Bize(3), U. Sterr(4),
A. Görlitz(1), Ch. Lisdat(4), M. Schioppo(2), N. Poli(2),
Optical atomic clocks use optical transitions in laser cooled neutral atoms or ions as quantum frequency
reference (QFR) (see Figure 1.1). The invention of the femtosecond frequency comb has made it possible
to precisely count frequencies in the optical domain, and to transform them into the radiofrequency
domain, where they can be used by traditional techniques.
The scientific challenges for optical atomic clocks are the establishment of techniques for reliable and
simple preparation of suitable QFRs, the control of systematic effects to a high degree of accuracy, and the
development of the required components, in particular ultrastable laser sources at the frequencies
corresponding to the clock transitions. From an application point of view, the technological challenge lies
in developing a system that is robust and whose electronic control is sufficiently sophisticated that
unattended, automatic operation is possible.
Two approaches towards optical clocks are pursued in the field of time metrology at present. The first is
based on a single ion trapped in an electrodynamic trap, where the storage time can exceed many weeks.
The second, used in this project, is based on using ensembles of tens of thousand neutral atoms trapped
for a relatively short time (seconds) in a trap formed by standing optical waves (optical lattice) delivered
by a laser. Here, a new ensemble of atoms is periodically reloaded into the trap.
Figure 1.1: Principle of an optical atomic clock. A laser, the local oscillator, interrogates an ensemble of
ultracold atoms, the QFR. In the case of a lattice optical clock (shown) the atoms are at µKelvin
temperature and trapped by laser waves The interrogation by the local oscillator results in a signal
proportional to the absorption of the laser light (frequency n), which is maximum for a light frequency n0
corresponding to the center of the atomic resonance. With a feedback control, the laser frequency n is
continuously kept tuned on the atomic resonance frequency. The resulting ultra-stable optical frequency
can be converted to an equally stable radio-frequency by means of a femtosecond laser frequency comb.
Oszillator
Atome, Moleküle oder Ionen
Detektor
Regelungs-elektronik
S
Absorptions- signal
FehlersignaldS
d
Detector Laser
Femto- second frequency comb
Cold atoms
Absorption signal
Feedback control
electronics
Oszillator
Atome, Moleküle oder Ionen
Detektor
Regelungs-elektronik
S
Absorptions- signal
FehlersignaldS
dError signal
Radio-frequency signal, 200 MHz
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Figure 1.2: Schematic of a lattice clock apparatus showing the required elements. An atomic beam is
produced by an oven and travels towards the right through a space-varying magnetic field. In it, the atoms
are slowed down by a laser beam (blue arrow) that eventually stops the atoms inside the experimental
chamber (square). The red double arrows indicate the laser beams for 2nd stage cooling and trapping in
the MOT. Orange-red: lattice laser standing-wave, yellow: clock laser wave. Inset at bottom: variation of
the potential felt by the atoms due to the lattice laser. Since the lattice is deeper than the thermal energy,
the atoms are trapped in the potential minima. The localization to well below a wavelength leads to
Doppler-free spectra, analogous to the Mössbauer effect.
The fundamental advantage of neutral atom optical clocks is that comparatively large numbers (~104) of
QFRs are used simultaneously, resulting in a high signal-to-noise ratio. This leads, in turn, to a short-term
stability which is potentially vastly better (factor 102) than that already obtained with the single-ion clocks.
Lattice optical clock with neutral atoms confine them (for several seconds) in a so-called magic-
wavelength optical lattice [Katori 2003], where the wavelength is chosen such that the energy shifts of the
lower and upper states of the clock-transition 1S0 → 3P0 are exactly equal and thus the trapping potential
exerts no shift on the clock transition. The values are 813 nm for Sr and 759 nm for Yb. The clock
transition is a singlet-to-triplet transition that is nearly forbidden and therefore exhibits an extremely
narrow (theoretical) linewidth << 1 Hz. In practice, due to a finite interrogation time, it is of the order of a
1 – 10 Hz.
The preparation of a sample of ultracold neutral atoms follows the same basic principle for all species
currently considered as optical clock candidates (Figs. 1.2, 1.3). Efficient precooling to temperatures in the
mK range is done on a spectrally broad 1S0 →
1P1 (some tens of MHz) cycling transition (refer to Fig. 1.4
for the atomic level scheme), followed by a postcooling stage, typically on the 1S0 → 3P1 intercombination
transition, which brings the temperature down into the µK range. The atoms are then transferred into an
optical lattice, formed by at least two counter-propagating laser beams of the (same) “magic” wavelength.
Theoretical investigations have shown that it should be possible to control higher order perturbations
caused by these lattice laser waves at levels allowing an inaccuracy below one part in 1017.
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Figure 1.3: Basic steps of operation of a lattice optical clock.
Top row :(a) precooling and trapping: atoms produced by an oven are slowed down, then cooled and
simultaneously trapped in a magneto-optical trap produced by two coils and six counter-propagating 1st
stage cooling laser beams (blue).(b) postcooling and trapping: Once the atoms are cold enough, the 2nd
stage cooling laser beams nearly resonant with the 1S0 →
3P1 transition are turned on, forming a 2
nd stage
MOT. The atoms are cooled further, because the transition to the 3P1 level is spectrally narrow. The
counter-propagating optical lattice laser beams (red) are also turned on. (c) intercombination transition
interrogation: when the atoms are again cooled sufficiently, the 2nd stage cooling beams are turned off,
leaving a fraction of the atoms trapped in the optical lattice. The clock laser beam is turned on for a short
time (not shown), exciting a fraction of the atoms from the 1S0 to the 3P0 state. Subsequently, a pulse of 1st
stage cooling light (blue) is applied. The ensuing fluorescence of the decay from the 1P1 state is measured;
its strength is an indication of the number of atoms that was not excited by the clock laser, and represents
the spectroscopic (clock absorption) signal also shown in Fig. 1.1. After interrogation, the atoms are lost
and the cycle is repeated, with the clock laser frequency changed by a small amount. In this way, the
resonance line is observed, that also gives an error signal for correction of the laser frequency.
Bottom: geometry of the lattice laser beams (red), produced by retro-reflection, and the superposed probe
beam (yellow). A magnetic field is applied to define a quantization axis, or, in case of a bosonic atomic
species, to induce a transition moment which allows optical excitation of the transition.
Two types of atoms can serve as a QFR. Fermionic isotopes, in which the 1S0 → 3P0 transition possesses a
finite linewidth of typically a few mHz [Porsev 2004] due to hyperfine mixing in the excited state are one
choice. However, it is also possible to use the bosonic isotopes where the strongly forbidden transition
becomes weakly allowed by admixing some 3P1 or 1P1 character to the 3P0 state, by applying a magnetic
field to the atomic sample. The availability of both bosons and fermions opens interesting possibilities and
in-depth studies of the respective advantages and disadvantages of the various species, such as density-
induced frequency shifts or line broadening. In this project, both types of particles were investigated, but
one important conclusion is that the use of a fermionic isotope is more advantageous.
Figure 1.4 shows the relevant energy diagrams of the two atomic species used in this work, Strontium and
Ytterbium.
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Figure 1.4: Level schemes for Sr (top) and Yb (bottom) showing some of the relevant transitions. Color
(grey) double arrows: transitions excited by lasers. Black single arrows: spontaneous emission loss
channels. denotes the spontaneous emission rates (the value for the Yb 556 nm transition is
1.14 x 106 s-1). The magic wavelengths for the optical lattice are not shown in this diagram.
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2 Strontium laboratory clock development at Observatoire de Paris
2.1 Introduction
As part of the development plan, we have performed studies and developed methods aimed at optimizing
the physics package of a Sr optical lattice clock (WP1.1: Sr clock physics package optimization I). We
have used an existing first generation apparatus to demonstrate and study a non-destructive detection
scheme that can lead to large improvement in the clock stability. Based on the first generation apparatus,
we have also developed a complete second generation stationary system which incorporates several
improvements. This includes a beam deflection for the Zeeman slower and an improved design for the
above non-destructive detection. We have also designed and implemented a new ultra stable reference
laser with thermal noise limited performance at the level of 6x10-16. We have also designed and
implemented a 1 dimension lattice based on semi-conductor laser. The new design is focused on important
issues for transportability and future space application, namely, the compactness and more significantly
the use of power efficient semi-conductor lasers instead of the previously used titanium:sapphire laser.
Here, we point out that we have encountered several non-trivial issues that we have investigated and
solved, and that are important to take into account in future transportable and space designs.
The second part of the work was the evaluation of the performance of Sr lattice clocks (WP1.6). This
included the measurement of the frequency stability with the new ultra stable laser. We have measured
short term instability of 3 parts in 1015 at 1 second, by locking to an atomic line with a Fourier limited
linewidth of 3 Hz and a 90% contrast. Also, we have performed a thorough investigation of lattice induced
frequency shifts, taking advantage of the comparatively deeper trap in our systems. We achieved
uncertainty for this effect is below 10-17 for a lattice depth of 150 recoil energy. We have characterized
other systematic shifts down to a total fractional frequency uncertainty of 1.4x10-16
. Taking advantage of
the availability of 2 Sr lattice clocks next to each other, we have performed frequency comparisons
between the 2 clocks. The stability between the 2 clocks decreases down below 10-16 after 1000 seconds of
integration. A first series of comparisons gave an agreement between the two clocks at the 10-16 level,
consistent with the current accuracy budget. Finally, we have performed a series of high accuracy absolute
frequency measurements against atomic fountains. The uncertainty of these measurements is now fully
limited in stability and accuracy by the microwave counterpart. These measurements have been exploited
for testing the stability of fundamental constants with time and with gravitational potential.
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2.2 Second generation Sr lattice clock
2.2.1 Vacuum system with deflected Zeeman slower
We have designed, implemented and characterized the deflection unit between the Sr oven and the
Zeeman slower. One of the purposes of this work was to keep the lattice region away from a direction
sight to the Sr oven, which can impact the blackbody radiation environment of the trapped atoms, due to
its high temperature (550°C). A second advantage is to also keep the lattice region away from the flux of
hot atoms effusing from the oven, which can cause frequency shifts and limit the lifetime of lattice trapped
atoms. A third advantage is to lower (cool) the transverse velocity of atoms in the beam, thereby limiting
the divergence of the Zeeman slowed atoms. This, in turn, improves the loading of the magneto-optic trap
(MOT) and more generally, the overall efficiency of the vacuum system. This deflection scheme is done at
a modest cost in terms of laser power, power consumption, complexity and weight.
Figure 2.1: Vacuum system of the second generation Sr lattice clock. This system incorporates a
deflection section before the Zeeman slower (grey cylinder on the right).
Figure 2.1 shows the second generation Sr lattice clock system which comprises the deflected Zeeman
slowed atomic beam. The deflection zone is made of one vertical transverse cooling beam and of two
horizontal deflection and cooling beams. The detailed geometry was described in a previous Technical
Note. It can also be found with many details in A. Lecallier, PhD thesis on Contribution à la réalisation
d’une nouvelle horloge à réseau optique à atomes piégés de Strontium, from the Université Pierre et
Marie Curie, 2010. The measurement of the deflection efficiency is shown in Figure 2.2. This figure
shows the spatial distribution of atoms in the beam at the location of the lattice trap. It is clearly seen 1-
that the peak of the atomic distribution is shifted by 20 mm, 2- that the flux of the undeflected beam (red)
at the shifted position is lowered by one order of magnitude 3- that the maximum flux of the detected
beam is significantly increased.
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Figure 2.2: Characterization of the deflection unit. The red curve is the measured transverse distribution
of the beam at the location of the lattice trap without the deflection unit. The black curve is obtained with
the deflection unit.
We have compared the MOT loading in the new generation apparatus with and without the defection unit.
In both cases, the geometry and other parameters were optimized as much as possible. We have found that
the deflection unit was increasing the loading rate of the MOT by a factor of 4. This is achieved at modest
cost in terms of laser power and complexity. Here, 24 mW of 461 nm light were used for the MOT, 20
mW for the deflection unit and 10 mW for the Zeeman slower. The light for the deflection unit was split
from the main 461 nm source. A dedicated acousto-optic modulator is necessary to optimize the frequency
of the light in the deflection.
To conclude, the deflection unit was implemented successfully. Given its positive impact on the clock and
its modest cost in laser power, in weight and complexity, it is certainly an interesting option to consider in
future developments of transportable and space devices.
2.2.2 Non-destructive detection scheme
We have implemented and characterized a non-destructive atom detection scheme. The aim of this
development is to open the possibility of reuse the atomic sample from one cycle to the next. This will
drastically reduce dead time in the probing sequence, since this dead time is largely dominated by the
MOT+lattice loading time. A large reduction of dead time will lead to large improvement in the short term
stability of the clock, which is otherwise limited by so-called Dick effect. In advanced implementations,
this non-destruction scheme can be made practical enough that it can be consider for an actual clock, and
even a transportable or space devices. Notably, this scheme in principle suppresses the need for a
cumbersome and costly high performance CCD camera or for a photomultiplier which are used for the
traditional detection schemes. Potentially, the non-destructive detection scheme can be pushed below the
standard quantum noise limit, opening ways to preparing and using spin-squeezed atomic samples for the
clock.
Figure 2.3 shows the first setup used for the non-destructive atomic detection. 461 nm light is used, which
is sensitive to atoms in the ground state of the clock transition 1S0. The light injected in the detection setup
is tuned to the resonance of the 1S0-1P1.An electro-optic modulator is used to generate sidebands, here with
a modulation frequency f=90 MHz. The modulation index is adjusted to suppress the carrier completely.
Therefore, the atomic cloud is sensed only with detuned light. This is the origin of the non-destructive
character of the method. The sidebands are phase shifted proportionally to the atom number when
propagating through the cloud. This phase shift is detected with homodyne detection by making the weak
probe beam interfere with a strong local oscillator. The signal at the modulation frequency f is mixed
down and contains the atom number information. The signal at 2f is used to stabilize the phase of the
interferometer.
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Figure 2.3: Setup for the non-destructive atomic detection.
We have measured the noise of this detection scheme. We found that for a 3ms detection duration, we
have a noise equivalent to less than 100 atoms. Therefore, for a detected atom number of 104 typical of a
Sr lattice clock, this detection is at the quantum projection noise limit. The phase shift corresponding to
104 detected atoms is ~40 mrad.
Figure 2.4: Evidence of the non-destructive character of the detection scheme of Figure 2.3. A non-
destructive detection is applied to the sample and the number of remaining atoms is detected (with the
classical fluorescence detection) as a function of the lattice trap depth.
We have characterized and modeled the non-destructive character of the scheme. A non-destructive
detection is applied to the sample and the number of remaining atoms is detected (with the classical
fluorescence detection) as a function of the lattice trap depth. The result of the measurement is shown in
Figure 2.4. Above trap depth of 250 recoil energy, more than 95% of the atoms are kept in the lattice after
the detection pulse. This is in agreement with simple model based on the assumption that spontaneously
emitted photons from the non-destructive probe do not induce recoils in the longitudinal direction (Lamb-
Dicke regime), but only in the transverse directions. The random recoils in the transverse directions heat
the atoms. The hottest atoms in the distribution can escape the lattice trap, leading to the observe losses at
low trap depth. In the case of Figure 2.4, an average number of 100 photons of the non-destructive probe
are scattered by each atom. It should be noted that with this “large” number of scattered photons per
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atoms, the detection is non-destructive only in the classical sense. Prospect for achieving the quantum
non-destructive regime are discussed in the outlook section.
The non-destructive detection scheme was successfully used to perform spectroscopy of the clock
transition and operate the clock. However, the stringent alignment required between the non-destructive
probe beam and the lattice trap turned out to be a significant obstacle to daily used to the scheme in the
usual laboratory environment. The outlook section also discusses ways to circumvent this problem and to
make the scheme practical, including for transportable or space devices.
2.2.3 New ultra stable clock laser system
At the start of this project, the short term stability of the first Sr lattice clock system was limited by the
noise of the first generation probe laser system, at the level of 3x10-14 at 1 second. We have therefore
designed, developed and characterized a new ultra stable laser system at 698 nm with state-of-the-art
performance. The mechanical design of the ultra-stable cavity assembly is shown in Figure 2.5. The
design is based on a 10 cm long horizontal ULE cavity with fused silica mirrors. We do not use the
additional ULE ring proposed and patented by PTB (see below) since we were not aware of this scheme.
Of course, in any future design, it is advisable to use this PTB scheme that minimize the temperature
sensitivity that otherwise arise from the use of fused silica mirror. Here, anticipating the increased
temperature sensitivity, we took special care to the control of the thermal environment of the cavity. We
use two nested vacuum enclosures. The inner enclosure, sitting inside vacuum is temperature stabilized of
the milliKelvin level with 2 opposing 2-stage thermo-electric coolers. Inside the innermost vacuum
enclosure, we have 3 additional gold plated thermal shields. Indium contacted BK7 windows on the
temperature stabilized enclosure are shielding the mirrors from a direct exposure to the fluctuating
external blackbody radiation. We have measured the response of the cavity frequency to a temperature
perturbation measured at the innermost vacuum enclosure (where the temperature is normally sensed and
stabilized). We found a transfer function which is well-modelled with 2 cascaded low-pass filter, one with
a time constant of less than a day and the second one with a considerably higher time constant of ~4 days.
This assembly is therefore capable of providing extremely effective reduction of temperature fluctuations
at the cavity for timescales shorter than 1000 s, which are the most relevant to the clock operation. Under
constant but normal laboratory conditions, long term tracking of the cavity frequency with the atomic
transition as shown a drift rate of the cavity frequency consistently less than 100 mHz/s with day to day
changes of no more than 10 mHz/s. The cavity is also designed (with the help of finite element modelling)
to have a low sensitivity to acceleration in all 3 directions. The cavity assembly is mounted onto a
commercial passive vibration isolation platform and inside an acoustic shielding enclosure. The overall
size of the system is approximately 70 cm x 70 cm x 70 cm. A 698 nm extended cavity laser diode is first
locked to the first generation cavity acting as a pre-stabilization cavity. The pre-stabilized light is locked
to the new cavity using an acousto-optic modulator, the cavity resonance (finesse 568000) being probed,
classically, with the Pound-Drever-Hall method.
We have measured the stability of this new ultra stable laser system against another ultra-stable laser at
1062.5 nm (laser for an Hg optical lattice clock) through a Ti:Sa optical frequency comb. The measured
stability is shown in Figure 2.6 with a linear drift removed (~100 mHz/s at 698 nm). The 1062.5 nm was
characterized independently and has a short term instability of 4x10-16 at 1 s. Here, at 1s, the measurement
noise is limited by the comb. Above 10 s, the curve is representative of the Sr laser at the time of the
measurement summed with a small contribution of the 1062.5 nm system. Later on (see below), slightly
better stability was observed around 100 s for the Sr system.
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Figure 2.5: Left: Design of the 698 nm ultra-stable laser. It is based on the 10 cm horizontal ULE cavity
with fused silica mirrors. A nested under vacuum temperature stabilized enclosure and 3 thermal shields
provide a highly effective suppression of temperature fluctuations over short timescales. Right: Picture of
the cavity supported on its supporting mechanical part.
Figure 2.6: Frequency stability between the new Sr ultra-stable laser at 698 nm and another ultra-stable
laser at 1062.5 nm, measured using a Ti.Sa optical frequency comb.
2.2.4 Semiconductor-based lattice traps
We have developed semiconductor-based lattice traps for the 2 Sr lattice clock apparatus. The aim of this
work was to demonstrate the possibility to replace the Ti:Sa laser previously used in the first generation
system with a more reliable system, capable of long term, unattended operation. It was also a crucial step
toward transportable and space devices, to show that deep lattice trapped could be realized with
semiconductor laser and to investigate the potential impact of this technology on the clock accuracy as
well as other aspects of the clock operation. The optical setup for the 2 Sr clock is shown in Figure 2.7.
The details of the setup where described in a previous technical note. Here, we summarize the non-trivial
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and unanticipated issues that were encountered when developing this system and describe how these
problems were mitigated. In future transportable or space devices, it will important to take into account
these findings in the design phase.
Figure 2.7: Optical setup of the semiconductor based optical lattices for 2 Sr optical clocks. The laser
wavelength is 813 nm, the magic wavelength for Sr lattice clocks.
The 3 main findings where the following:
- When using an extended cavity laser diode as the source of 813 nm light in combination with a
build-up cavity for the lattice light, the lifetime of atoms in the lattice trap can be severely limited
by parametric heating. This effect can be strong enough that hardly any atoms are detectable in the
lattice trap, which is obviously a major obstacle to the clock operation. This parametric heating
occurs because the relatively high frequency noise of the extended laser diode is converted into
amplitude noise by the lattice cavity. Given the high Fourier frequencies involved in the process, it
is difficult to mitigate this effect by stabilizing the extended laser diode frequency. Instead, we
successfully remove the effect in the second system by using a 5 times shorter lattice cavity (65
mm instead of 325 m). For the same finesse of the lattice build-up cavity, this reduces the effect
by a factor 54.
- When using tapered semiconductor amplifier to increase the available power at 813 nm, as
shown in Figure 2.7, the residual amplified spontaneous emission of the amplifier cause large
(several parts in 1015) and fluctuating shifts of the clock frequency. So far, we have mitigated this
effect using specifically designed narrow band (0.3 nm) low loss interference filters (IF) as seen in
Figure 2.7. With a first given tapered amplifier, it was possible to purposely increase the
spontaneous emission background, measure the impact on the clock frequency and infer an upper
limit (~10-17) for the effect is the normal situation. However, the exact mechanism for the shift and
the quantitative link between the spontaneous emission spectral density and the observed shift are
not well established. We will come back to this in the outlook section. In any case, this is most
likely an important point to consider in future transportable or space designs.
- When using a short lattice cavity, which is desirable not only to mitigate the above mentioned
heating mechanism, but also for the sake of compactness, atoms in the lattice can be exposed to
electric charges trapped at the surface of the cavity mirrors. This is effect can be tremendous: we
have observed shifts in the range of 10-13. We have reduced this effect by applying UV light in the
apparatus. In future transportable or space designs, it is certainly advisable, especially for compact
setups, for consider shielding nearby dielectric surfaces with grounded metal parts.
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2.3 Characterization of 87
Sr lattice clocks
2.3.1 Narrow line spectroscopy and short term frequency stability
With the new ultra-stable laser, it was possible to observe narrow line, highly contrasted Lamb-Dicke
spectra of the clock transition. An example of such a measurement is shown in Figure 2.8. It should be
noted that this spectrum is taken in a single scan, i.e. there is no averaging: one point corresponds to a
single measurement of the transition probably.
Figure 2.8: Spectrum of the Sr clock transition taken with the new ultra stable system. The linewidth is
Fourier limited.
By locking the probe light to this atomic line, we could estimate the short term stability of the clock and
access another test of the ultra-stable cavity behavior. The result of such a measurement is shown in
Figure 2.9. The short term stability (1 to 10 s) with a t-1/2 slope (white frequency noise) is determined by
the Dick effect (i.e. the free running probe laser noise and the duty cycle of the probe sequence). Possibly,
additional noise added to the probe during its propagation along a small amount of non-stabilized optical
paths comes into play as well. The short term stability is 3x10-15 at 1 s. The 10-16 range is reached in less
than 20 s. The behavior after 50 s is determined by the fluctuations of the ultra-stable laser frequency
around its predictable linear drift which was removed with a feed-forward scheme. For comparison, we
show our estimation of the thermal noise limit imposed by the fused silica cavity mirrors.
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Figure 2.9: Stability of a Sr lattice clocks against the ultra-stable cavity.
2.3.2 Investigation of lattice-induced frequency shifts
The combination of the improved short term stability allowed by the new ultra-stable laser and the
possibility of reach lattice depth of 1000 of recoil energy allowed us to perform a thorough investigation
of lattice induced frequency shifts for a 1D lattice. The following effects have all been quantitatively
evaluated:
- The scalar shift and the high accuracy magic wavelength determination.
- The vector shift
- The tensor shift
- The hyperpolarizability
- The M1/E2 shift
A more detailed account of these measurements was given in a previous technical note. The most
important facts are the following. The tensor shift and the M1/E2 shift where quantified for the first time.
For the tensor shift, a non-vanishing value, in agreement with expectation was measured. For the M1/E2,
the effect turned out to be much smaller than the theoretical estimation of Phys. Rev. Lett. 101, 193601
(2008), so that no effect was observed (see Figure 2.10) and an upper bound to the corresponding shift was
determined. The upper bound is consistent with the early prediction of Phys. Rev. Lett. 91, 173005 (2003).
For the other effects, large improvements over previously existing values were achieved. The possibility to
reach deep lattice configurations (1000 Er) gives a large leverage factor between the investigation of the
lattice induced shift and a typical clock operation, for instance at a depth of 150 Er. Our study establishes
that at a 150 Er depth, the overall uncertainty associated to all known lattice induced frequency shifts is
less than 10-17.
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Figure 2.10: Measurement of M1/E2 lattice frequency shift. The clock frequency is measured for several
atom temperatures, which modifies the average vibrational quantum number n, and for several trap depths.
No deviation from linear variation with the trap depth is detected.
2.3.3 High accuracy comparisons between 2 Sr lattice clocks
We have performed a large number of high accuracy comparisons between our 2 Sr lattice clocks. Early
comparisons showed tremendous shifts between the 2 clocks which we found to be associated to the
already mentioned dc Stark shift induced by residual charges on the cavity mirrors of the second system.
After this effect was controlled, we have evaluated the accuracy of both systems down to an accuracy of
1.4x10-16, which now dominated by the blackbody radiation shift, as seen as in Figure 2.11.
Figure 2.11: Accuracy budget representative of the 2 Sr lattice clocks at Observatoire de Paris.
We point out that one interesting feature of this accuracy budget is the vanishing collision shift for a
typical atom number of 104. This favourable situation is due to the loading of the lattice trap directly from
the blue MOT with the so-called drain method (spatially resolved optical pumping into the metastable
states). This method leads to a much reduced atomic density for the same atom number compared to using
a second MOT on the 1S0-3P1 transition. We have further performed a series of high accuracy comparisons
between the 2 clocks, which are summarized in Figure 2.12. The overall statistical uncertainty of this data
set is 5x10-17. The clocks are found in agreement at this level. A measurement of the stability between the
2 Sr clocks is shown in Figure 2.13. The combined instability is 4.5x10-15 at 1 s.
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Figure 2.12: Series of direct frequency comparisons between the 2 Sr lattice clocks developed at SYRTE-
Observatoire de Paris.
Figure 2.13: Frequency instability between the 2 Sr lattice clocks developed at SYRTE-Observatoire de
Paris.
2.3.4 Absolute measurements of the frequency of the Sr optical lattice clock
We have also a series of high accuracy comparisons between the Sr optical lattice clocks and 3 Cs
fountains. The measurement was made using a Ti:Sa optical frequency comb referenced to an ultra-stable
reference signal derived from the sapphire resonator cryogenic oscillator which was also measured by
atomic fountain clocks. For these comparisons, both the stability and the accuracy are limited by the
atomic fountains. Figure 2.14 give the summary of these measurements. These measurements agree with
the fully independent measurement at PTB (see below) and with other previous measurements.
Figure 2.14: Absolute frequency measurements of a Sr optical lattice clock by 3 Cs fountains at SYRTE-
Observatoire de Paris.
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2.4 Outlook
We can identify a number of a further investigation that could or needs to be done to complete this work.
- Improve the stability between the 2 Sr lattice clocks: We have performed comparisons between the
clocks with synchronized interrogation periods. Such comparisons are expected to be free of the Dick
effect and thereby to give access to much improved stability for the comparison. This improvement
was not observed. It would be important to clarify why. Already mentioned, we suspect additional
uncorrelated noise to come from the small amount of yet un-stabilized optical paths.
- Fully implement the non-destructive detection method: We mentioned that the main obstacle for
practical using the (classically) non-destructive detection method was a practical problem of
misalignment. We developed a new design that can ensure a long term stable alignment of the non-
destructive probe and the 1D lattice. The implementation was impeded by some faulty optical
components. It therefore remains to fully exploit and investigate the potential of this method to further
improve the short term stability of the clock. This study is directly relevant to transportable and space
designs, given the modest level of extra complexity required for this scheme. A further step would be
to push the method into the spin-squeezing regime.
- Improve our comprehension of the impact of spontaneous emission in tapered amplifier: We have
mentioned that a more quantitative link between the spectral density of the light and a possible shift
remains to be done. This is highly relevant to transportable and space designs. Such a quantitative
understanding would help defining specifications of amplifier for such applications. Recently,
replacing one of our tapered amplifiers seems to have induced an unexpected frequency shift between
the two clocks, further showing the importance of such a study.
- Improve the design to eliminate the risk of dc Stark shift and improve the control of the blackbody
radiation (BBR) shift. Here, it should be noted that several solutions considered for controlling the
BBR shift in stationary devices involve moving parts, cryogenic devices or other scheme typically not
suitable for transportable or space designs. A suitable design should take into account all constraints:
compactness, immunity to dc Stark shifts, controlled BBR without moving parts or otherwise complex
schemes.
- Investigate the limits of 1D lattice. The 1D lattice geometry is significantly simpler and therefore
better suited a priori for transportable and space designs. The limits of the 1D geometry remain to be
fully explored, notably in the context of a microgravity environment (no more formation of localized
Wannier-Stark states due to gravity), but also in relation with collision shifts, or effects of the
transverse motion.
21
3 Strontium lattice clock development at PTB, Braunschweig
3.1 Introduction
As part of the plan to develop transportable subsystems of a demonstrator (Figure 3.1) of an optical
strontium lattice clock, the work at PTB comprised the design, construction and test of a transportable
clock laser system for a strontium lattice clock (WP 1.3). The work package aimed to develop a complete
interrogation laser at 698 nm with performance close to the one of a laboratory system, but with a total
volume of less than 1 m3 (excluding the electronics). As a realistic test, the laser is moved to Düsseldorf
and tested with the clock laser of the local ytterbium clock (WP 3).
In second set of tasks with a stationary clock setup at PTB, tests on the system level of the performance of
a complete optical lattice clock were undertaken. This included the optimization and evaluation of a 88Sr
clock (WP 1.2), especially the loading in the optical lattice and the collisional shifts. In a final work
package the strontium lattice clock was characterized concerning short term stability, accuracy and
systematic shifts (WP 1.6). This activity included a comparison to other ultra-stable lasers, the evaluation
of the clock stability and accuracy, and a frequency measurement of the clock in comparison to a primary
cesium fountain clock.
Figure 3.1: Components of a complete (transportable) lattice clock. The subcomponents that were
developed in SOC are shown in yellow.
Figure 3.2: Simplified level scheme of strontium. Transitions relevant for cooling and spectroscopy are
indicated by arrows. In this project, compact laser systems for cooling at 461 nm and for interrogating the
clock transition at 698 nm were developed.
laser BB 1
primary
cooling
laser BB 2
secondary
cooling
laser BB 3
repumper
atomics
package
fibres clock laser
fs comb
fibres
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laser BB 4
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22
3.2 Stationary clock with 88
Sr
With the advanced development of laboratory optical lattice clocks with neutral strontium, the sources of
environmental perturbations can already be clearly identified. Precise quantification of all contributions
was achieved at a relative accuracy level of 10–16 [Ludlow 2008] and is subject of on-going experimental
work.
For optical clocks based on laser-cooled neutral strontium, both the bosonic isotope 88Sr and the fermionic 87Sr can be used. The physical difference in the application of the two is the process that enables the
excitation of the doubly forbidden, ultra-narrow clock transition 3P0 - 1S0 (see Figure 3.2).
In 88Sr, a single photon transition is totally forbidden because both states have total angular momentum
J = 0. A dipole moment transition is typically induced by magnetic mixing of the triplet states, which also
causes a quadratic Zeeman shift of the clock levels [Taichenachev 2006]. In contrast, the clock transition
in 87Sr is very weakly allowed due to hyperfine mixing [Takamoto 2003]. This reduces the laser power
required for the interrogation of the clock transition and thus leads to lower systematic ac-Stark shifts.
Figure 3.3: Setup of the optical lattice (provided by a Ti:Sa laser), into which the strontium atoms are
loaded from a magneto optical trap (MOT). The atoms are interrogated by the clock laser at 698 nm,
which is overlapped with the lattice using a dichroic mirror.
Figure 3.4: Timing of the experiment to load bosonic 88Sr atoms into the optical lattice and detect them
after interrogation with the clock laser.
F = 30 mm
HWP polarizer
F = 300 mm
pump laser 10 W
Ti:Sa 1.1 W
optical fiber
mechanicalshutter
gravity
dichroic mirror
698 nm interrogation
laser
"Blue" cooling (461 nm)
Broadband cooling (689 nm)
Optical lattice (813 nm)
200 ms
50 ms
70 ms
T ~ 2 mK , N ~ 4 107
T ~15 µK , N ~ 1 107
T ~ 3 µK , N ~ 8 106.
.
.
T ~ 3 µK , N ~ 1 106.
Detection ground state (MOT beams , 461 nm)
Blow-away (461 nm)
Repumper (679 nm, 707 nm)
Detection excited state (MOT beams , 461 nm)
Interrogation laser (698 nm)
20 ms
20 ms
20 ms
20 ms
200 ms
Cooling and trapping sequence
Spectroscopy sequence
0 ms 250 ms 500 ms 750 ms
23
However, the natural abundance of 81% favours the application of 88Sr especially in transportable clocks,
for which simple techniques to load and prepare the atoms are required. Also the laser cooling and state
preparation of 88Sr is simpler than for 87Sr. For cooling of 88Sr we use a two stage cooling process. The
atoms are initially laser cooled on the dipole-allowed transition 1P1 – 1S0 (blue arrow in Figure 3.2) to a
temperature of few millikelvin, limited by the Doppler limit for laser cooling. The second cooling stage on
the intercombination line 3P1 – 1S0 (red transition in Figure 3.2) reaches the microkelvin temperatures
required for loading the atoms deep into the optical lattice, as needed for spectroscopy experiments.
3.2.1 Setup
In the setup at PTB the 88Sr atoms are interrogated in a 1D lattice (Figure 3.3). To load the atoms into the
optical lattice we cool the strontium atoms to a few microkelvin using a two-stage cooling process (Figure
3.4). In the first cooling stage, atoms are captured from a Zeeman-slowed atomic beam and cooled to
2 mK in a magneto-optical trap (MOT) operating on the broad 1S0 – 1P1 transition at 461 nm [Katori 1999].
This MOT works with a magnetic field gradient of 7.4 mT/cm, a 1/e2
laser beam diameter of 10 mm and a
total laser intensity of 21 mW/cm2. The cooling laser is detuned 54 MHz below the 1S0 – 1P1
transition
frequency. After 200 ms, 4·107
atoms are trapped in the MOT. For further cooling, a MOT working at the
spin-forbidden 1S0 – 3P1
transition at 689 nm with a 1/e2
laser beam diameter of 5.2 mm is employed. To
cover the Doppler shift of the atoms from the first cooling stage and to compensate the limited velocity
capture range of the 689 nm MOT the laser spectrum is broadened by modulating the laser frequency at
50 kHz with a peak to peak frequency excursion of 3 MHz. For this phase of the 689 nm MOT, a magnetic
field gradient of about 0.7 mT/cm, a total intensity of 33 mW/cm2
and a detuning of 1.6 MHz below the 1S0
– 3P0
transition is used. Within a 50 ms long broadband cooling interval, the atoms are cooled down to
15 μK. Finally the frequency modulation is switched off and the cooling laser is operated at a single
frequency with 400 kHz detuning below the 1S0 – 3P1 transition. With an intensity of 440 μW/cm2 and a
70 ms long cooling interval this process leads to 8·106 atoms at a temperature of 3 μK.
During the whole cooling process the atomic cloud is super-imposed with the horizontally oriented 1D
optical lattice operated at 813 nm. At this wavelength the light shift of the 1S0 and 3P0
states cancels and the
clock transition frequency becomes independent of the laser intensity [Katori 2003]. As shown in Figure
3.3, the 1.1 W output beam of the Ti:sapphire lattice laser is coupled into a polarization maintaining
optical fibre and passes through polarization optics before being focused on the center of the atom cloud.
The horizontally directed beam is linearly polarized with its polarization oriented perpendicularly to
gravity. A dichroic mirror is used to retro-reflect the 813 nm laser beam and hence establish the 1D optical
lattice. With a beam radius of 30 μm and a power of 600 mW a trap depth of 120 μK is realized. In future,
the lattice laser can be replaced by a diode laser with tapered amplifier. Such a system will greatly
simplify the transportability of the whole experimental setup. It must be considered though, that diode
lasers typically have a broad spectral pedestal which can lead to uncontrolled frequency shifts.
Appropriate measures must be taken to purify the light spectrally. Interference filters or an optical cavity
in which the lattice is formed are thinkable. Presently, the current setup avoids these complications and
allows for easy evaluation of systematic effects. After switching off the 689 nm MOT up to 2·106
atoms at
3 μK are trapped in the lattice. This corresponds to a transfer efficiency from the first stage MOT into the
lattice of up to 5%.
The atoms in the lattice are irradiated during a variable time by light from the clock laser. The clock laser
is discussed in detail in Chapter 3.4. The laser beam has a radius of 40 μm at the position of the atoms. Up
to 2 mW are available.
The atomic population is detected in the ground and excited state after the clock excitation. For this
purpose, first the ground state population is detected by a MOT phase of 20 ms on the blue cooling
transition during which the trap fluorescence is recorded. The atoms are then blown away by a resonant
461 nm pulse (20 ms) and the population in the excited state 3P0 is optically pumped within 20 ms via the 3S1 state to the 3P1 state from which it decays rapidly into the ground state (see Figure 3.2). The atoms are
again detected by a blue MOT phase (20 ms). The time sequence, which had not been optimized for fast
detection, is given in Figure 3.4.
The lattice provides the confinement of the atoms, which is required to interrogate the atoms practically
free from perturbations due to motion (Doppler effect). To achieve this, strong confinement of the atoms is
required along the axis of interrogation by the clock laser. The axis with strongest confinement is along
the symmetry axis of the standing optical wave. The wavelength of the trap laser is fixed to the magic
wavelength by a wavelength meter (accuracy 2 MHz).
24
3.2.2 Density shifts and decoherence in 88
Sr
With the bosonic isotope 88Sr, collisions are not suppressed at low temperatures by quantum statistics, thus
theirs influence on an optical clock was studies in detail [Lisdat 2009]. Because of the efficient loading in
our setup, 3×106 atoms are trapped in the lattice (≈ 1000 atoms per site), leading to a high density in the
lattice. To induce a dipole transition matrix element on the clock transition, we apply a homogeneous
magnetic field of up to 3 mT. First, inelastic loss was observed from the decay of the atom number after an
excitation pulse. This could be described by the differential equation:
Eq. 3.1
Here the losses from inelastic collisions are given by the coefficients ee, ge. From the observed loss
curves these coefficients could be determined to ge = (5.3 ± 1.9) 10-19 m3/s and ee = (4.0 ± 2.5) 10-18 m3/s.
These numbers are relevant for the design of a clock with long interrogation times, as these losses can
limit the available times.
To describe collisional effects during the coherent optical excitation, the evolution of the atomic density
matrix was determined by solving the master equation
. Eq. 3.2
Here the coherent evolution during an excitation with Rabi frequency and detuning is described by a
2-level Hamiltonian H and the relaxation by a matrix R:
Eq. 3.3
It describes collisional dephasing through the coefficient dep and the natural decay rate through . The
dephasing was determined from a fit of Eq. 3.3 to observed Rabi-oscillations and spectra of the clock
transition. A value of and ee = (3.2 ± 1.0)×10-16 m3/s was found, which allows to estimate the minimum
linewidth at a given atomic density.
Figure 3.5: Observed density dependent shift of the 88Sr clock transition. The open symbols were
excluded from the linear fit. The inset shows the dependence of the shift on the excitation probability with
a linear fit. The diamond in the main graph bases on the data in the inset. The shift was rescaled according
to the trap parameters and atom temperature.
0.0 2.0x104
4.0x104
6.0x104
8.0x104
0
5
10
15
20
25
15 20 25 30 35
6.6
6.9
7.2
7.5
7.8
sh
ift
(Hz)
atom number difference
sh
ift
(Hz)
excitation probability (%)
25
To observe density related effects, the clock laser was locked to samples of different atom number,
alternating between the two conditions every second cycle. This allows operating two stabilizations to the
different samples effectively in parallel, and a shift can be obtained from the difference of the offset
between clock laser and reference cavity that is steered to keep the laser frequency centred to the atomic
line. During these measurements we have obtained an instability below 10-15 at an averaging time = 10 s
and scaling as -1/2
. From the observed shift as a function of atom number we were able to determine a
shift coefficient (7.2 ± 2.0)×10-17 Hz·m3.
Having quantified three collision influences, we can give guidelines for the design of a 1D-lattice clock
with bosonic 88Sr. Assuming a typical lattice depth of kB × 10 µK, an atom temperature of 3 µK, and an
available lattice laser power of 300 mW, one could choose a lattice waist of 75 µm. With an atomic cloud
size of 280 µm and at the current level of accuracy for the density shift correction of 4%, a density shift of
about 1 Hz would be tolerable to reach a fractional accuracy of 10-16, which is also the present uncertainty
due to the blackbody shift [Campbell 2008b]. This would limit the total atom number to about 2×104
distributed over about 1400 sites, a value comparable to or larger than in present lattice clocks with 87Sr.
The collisional broadening is then about 1.3 Hz. A new density shift measurement in the proposed lattice
should yield an improved correction and allows for increasing the atom number until the collisional
broadening becomes relevant. Aiming at a line width of about 10 Hz, operation with more than 105 atoms
is feasible. With a cycle time of 200 ms, the stability as limited by quantum projection noise in 1 s reads
2×10-17. To achieve this stability, however, the atom number has to be controlled to about 0.2%. At this
density, losses do not distort the observed line or limit the excitation probability. Thus 88Sr can be a
competitive candidate for a high stability clock even with a 1D lattice. As the level scheme and thus the
preparation is simpler with this isotope compared to 87Sr, this isotope remains a valid candidate for
local oscillator, MX: mixer; F: loop filter; VCO: voltage control oscillator; AOM: acoustic optical
modulator; G: driver for the AOM.
For analysis of the performance of the fiber noise compensation system we used 1064 nm light from a
Nd:YAG laser (InnoLight, Mephisto OEM 200 NE) with a linewidth of 1 kHz on a 100 ms time scale.
Figure 5.4.11 shows the power spectral density of the 100 MHz beat note between the original wave
before the fiber and the back reflected wave. The bumps around the carrier indicate a servo bandwidth of
25 kHz, consistent with the calculated servo bandwidth. The sharp and strong central peak in the spectrum
indicates that the PLL is working properly. The linewidth of the carrier is below the resolution bandwidth
of the analyzer of 1 Hz. This should be compared with the unlocked case, when the beat note is broadened
to about 360 Hz. From the measured power spectral density we obtain a root-mean-square (rms)-phase
error of rms = 263 mrad.
In Figure 5.4.11, right, the Allan deviation of the beat note is shown. At 1 s gate time the Allan deviation
is 0.19 Hz, i.e. 6.6 x 10-16 relative instability, and drops further for longer integration times. The value for
the uncompensated case is one order of magnitude worse at this integration time, and does not vary
significantly with averaging time. In the locked case we see a -1/2 variation of the deviation, implying that
the frequency noise has white spectral character. The reason for this particular - dependence is not clear
yet.
The implemented fiber link allows a frequency resolution of 50 mHz over 10 s integration time, and
contributes to the linewidth of a laser, e.g. a clock laser, a value less than 1 Hz. The fiber link will be
operated at the relevant Yb wavelengths 1156 nm or 578 nm, where we expect similar performance. This
performance is compatible with the milestones for the stability and accuracy of the Yb clock.
68
Figure 5.4.11: Left: Power spectral density of the rf signal produced by the beat between the probe beam
before the fiber and the back reflected beam, measured on the photodiode PD. The spectrum was
composed from eight individual measurements of different resolution bandwidth, shown in colour. Central
narrow peak at 100 MHz is the carrier. The fractional power contained in the carrier is 93.3 %. Inset:
close-in of the carrier, showing the noise pedestal.
Right: Allan deviation of the beat note between the probe beam at the input and the light back reflected
through the fiber, in lock (blue) and free running (black). is the integration time. A small peak is seen on
the time scale of the laboratory temperature variations, which have approximately 1 K amplitude. These
variations have some influence because a fiber section of several ten meters in length and the analog lock
electronics are located in the laboratory and are exposed to them.
69
5.5 Observation of the clock transition in Yb in a magneto-optical trap
As a first test for the eventual realization of an optical lattice clock in our project we have performed a
brief investigation of the optical clock transition (1S0 -> 3P0) in 171Yb in a MOT. This investigation was
carried out in our stationary apparatus using a “green” MOT operating on the 1S0 ->
3P1 cooling transition
at 555,8 nm that was continuously loaded from a Zeeman slower [Nemitz2009]. If the atoms in the MOT
are exposed to light from the clock an atom loss is induced if the clock laser is on resonance as it transfers
atoms from the 1S0 ground state to the 3P0 excited state where they do no longer interact with the MOT
light. With a power on the order of 1mW the steady state atom number in the MOT can thus be reduced by
90%.
Figure 5.9: Observation of the clock transition in 171Yb in a continuously loaded MOT. Depicted is the
fluorescence of the MOT as a function of the clock laser frequency.
A spectrum of the clock transition which was taken by the procedure described above is depicted in
Fig. 5.9. The obtained line is fitted by a Gaussian in order to determine the line center and the width.
While it is not clear that a Gaussian is the correct line shape, at the current level of accuracy we regard
it as sufficient for a first evaluation of the clock transition.
The line center of the clock transition spectrum determined from the spectrum shown in Figure 5.9 is at
f0 = 518 295 836 906 ±5 kHz. This frequency is shifted by 315 kHz to the blue side of the unperturbed
resonance at funperturbed = 518 295 836 590.8652 kHz [Lemke2009]. The observed shift can readily be
attributed to a light shift of the clock transition due to the MOT light, which lowers the energy of the 1S0 state as the MOT light is tuned close to the red side of the 1S0 ==> 3P1 transition.
The observation of the clock transition which is described here was merely intended to demonstrate the
feasibility to perform spectroscopy of the clock transition in atomic Yb in our lab. All future
investigations will be performed with Yb atoms trapped in an optical lattice.
70
5.6 Conclusion and Outlook
Although many more groups are investigating the use of strontium for optical lattice clocks, Yb still
presents a valid option for future developments of transportable and space optical clocks. In particular, the
group of C. Oates at NIST [Lemke2009, Lemke2011, Ludlow2011, Sherman2011] has demonstrated the
potential of Yb optical lattice clocks to reach an inaccuracy and instability in the 10-18 range.
In our own compact setup for a transportable optical lattice clock the current status is that ultracold
bosonic (174Yb) and fermionic (171Yb) atoms can be efficiently loaded into a 1D optical lattice, the clock
laser system and corresponding frequency metrology has been set up, and the system is being prepared for
a spectroscopic investigation of the clock transition of 171Yb in a 1D optical lattice. We anticipate that a
first complete characterization of the clock transition will be completed within the year 2012. We
anticipate that the characterization will be simplified by the capability of our system to store a large
number of atoms in a magic wavelength optical lattice. Since the results obtained by the NIST group
indicate that the isotope 171Yb is the best choice for an Yb optical lattice clock we will initially concentrate
our efforts on the investigation of this isotope while comparisons with other bosonic and fermionic
isotopes are intended at a later stage.
The work on the transportable optical lattice clock will be continued after the completion of the ESA-
funded project Space Optical Clocks in the framework of the EU-funded project Space Optical Clocks 2
(SOC2). Within this follow-up project it is planned to move the transportable clock temporarily to INRIM
(Torino, Italy) to compare it to microwave frequency standards and possibly also to a stationary Yb optical
lattice clock which is currently under development. This will be the first true test of the transportability of
our apparatus and the validity of our approach towards space operation of an Yb optical lattice clock.
In the course of the SOC project we have already identified several possible improvements to the Yb
optical clock apparatus which will lead to a better performance and transportability. These are:
Improvement of the resonator-based setup for the optical lattice: It is planned to extend the
current system to a 2D lattice. A possibility for future developments is to use Zerodur or ULE
for the resonator mounting structure since those materials have better thermal and magnetic
properties than the currently used invar steel.
Improvement of cooling laser systems: We will further investigate interference-filter-based
ECDLs at 399 nm with the goal to compactify the precooling laser system. The postcooling
laser system at 556 nm will be replaced by a compact frequency-doubled fiber laser which is
developed by the company Menlo Systems.
Implementation of a repumping laser at 1388nm for clock interrogation: The repumping laser
will be required in order to optimize the signal to noise of clock interrogation.
Frequency stabilization of cooling and trapping lasers: The robustness of the stabilization
system could be significantly improved by stabilizing all lasers to a frequency stabilization unit
based on a stable optical resonator.
Improvements to the vacuum system: Within the project Space Optical Clocks 2 our colleagues
at the University of Birmingham will investigate the use of light-weight materials and UHV-
compatible glues for the design of compact transportable vacuum chambers. If successful, we
will incorporate their results in the design of a next generation vacuum system for the
transportable Yb optical lattice clock.
Improvements to the clock laser: Within the project Space Optical Clocks 2 we aim at
developing a more compact and higher-performance clock laser for the interrogation of Yb at
578 nm.
Finally, we mention that the Yb clock laser developed within this project has been successfully used in
high-resolution spectroscopy of Europium ions in an oxide crystal, cooled to cryogenic temperature [Chen
2011].
71
6 Synthesis and design concept of the space optical clock
6.1 Synthesis of state-of-the-art
On the basis of the results achieved so far both within SOC (see above) and outside SOC, two main
conclusions can be drawn:
1. The development of neutral atom clocks with a performance close to the goal performance for the SOC
mission appears feasible within several years. The most critical required performance improvement is
accuracy, as the stability of the Sr and the Yb clocks are already close to the goal level. Neutral atom clock
breadboards with an inaccuracy at the level of 2.5 10-17 appears possible within the year 2015, and
1.5 10-17 by 2016, provided sufficient funding is available.
Table 6.1 presents an overview of the systematic effects affecting the accuracy of a Strontium clock based
on the isotope 87Sr. It shows the current status of characterizations in a stationary 87Sr lattice clock, the
expected near-future improvement in stationary clocks and expected performance of a near-future
transportable clock. The latter is assumed to use the present technology, developed in part in SOC, and to
benefit from improvements of the knowledge and control of systematic frequency shifts that are currently
investigated with stationary clocks. Also, the current developments of narrow linewidth clock lasers, using
low thermal noise cavities will decrease the uncertainty. A 87Sr clock, with a spin polarized atomic sample
in a 1D optical lattice is considered.
For the case of Ytterbium, it is expected that similar performance can be achieved. Table 6.2 reports the
current performance limits of the NIST Yb clock.
2. A neutral atom clock demonstrator with physical parameters (volume, mass, power) significantly
reduced compared to a laboratory clock and nearing the requirements of a clock on the ISS is feasible.
10 Tunneling lattice depth U <1·10–17 1.6·10–17 -- 1·10–18 1·10–18
TOTAL 1.4·10–16
1.5·10–16
1.4·10–16
5·10–18
1.2·10–17
Table 6.1: Parameters that affect the uncertainty of a Strontium-87 optical lattice clock and corresponding
contributions to the uncertainty of the clock frequency. Not shown is the tensor light shift as it is
negligible. ER is the recoil energy of the Sr atom, U is the lattice depth, T is the temperature of the
environment. A: present stationary clock at JILA [Campbell 2008a], B: present stationary clock at PTB
[Falke 2011], C: present stationary clock at Observatoire de Paris (to be published), D: Near future
laboratory clock (5 years), E: Transportable near future clocks.
Comments (referring to the respective line of the table): 1. Currently measurements are under way to measure the blackbody shift in a cryogenic environment. There, the shift can be
reduced to a few times 10-18. With this measurement, also room-temperature clocks can be corrected to a large degree,
provided the temperature at the position of the atoms is known with sufficiently small uncertainty. A transportable clock can
be calibrated for its blackbody shift by comparison to a laboratory clock. Then at 300 K temperature, a modest remaining
0.1 K uncertainty of the average temperature would lead to a fractional uncertainty of 7·10–18 (see [Middelmann 2010]).
2. Lattice wavelength can be set to the magic wavelength by comparison with stationary clocks and variation of the lattice
depth over a large range. In a transportable clock the effect can be calibrated with respect to a stationary clock, or (as in case
of the SOC mission scenario) with respect to the clock transitions wavelength using a frequency comb or a stable reference
cavity
3. Collisions: For Fermions, the collisional shift appears due to inhomogeneous excitation and p-wave contributions. Can be
suppressed by 2 D lattice [Swallows 2010] and precise alignment of clock laser. Recent results at PTB and SYRTE indicate,
that with a well-defined optical setup for excitation this shift is below 2×10-17 and controllable to lower levels even in a 1D
geometry. For future clocks operation at lower density and a better characterization of the shift is anticipated.
4. Servo Error: depends on the variations of the cavity frequency and drift over time. With better temperature control of the
cavity and operating at the zero crossing of its CTE this influence can be further reduced in future clocks. A performance of
a transportable interrogation laser a factor of 3 above a lab system is assumed.
5. Hyperpolarizability sets a maximum lattice depth, while the minimum depth at zero g is set by the tunneling. From new
measurements by the SYRTE group, a 125 ER deep lattice leads to (2.3 ± 1.6) mHz shift, i.e. 4∙10-18 uncertainty. At lower
lattice depth smaller shifts are estimated.
6. The AC Stark shift from the probe laser can be reduced by using longer interrogation pulses with reduced intensity, which
will become possible with low thermal noise cavities currently under construction. A poorer performance of a transportable
interrogation laser system is assumed.
7. The first-order Zeeman effect enters when the magnetic field fluctuates during the probing of the Zeeman components. It
can be reduced by better shielding or active stabilization.
8. Line pulling from other Zeeman components can be largely avoided by using good spin polarization, purification pulses and
small resolved linewidth of the clock transition, possible with improved clock lasers.
9. The second-order Zeeman effect can be calibrated with stationary clocks to high accuracy.
10. Tunnelling: at zero g; the atom tunnelling at 125 ER leads to a width of the lowest band of 0.2 mHz, so a possible shift is
below 10-18. On Earth tunnelling can be suppressed by tilting the lattice.
Table 6.2: Parameters that affect the uncertainty of a ytterbium-171 optical lattice clock and current status
of experimental uncertainties in a stationary clock [Lemke2009].
Comments: (referring to the respective line of the table): 1. While the calculated blackbody shift in ytterbium is smaller than in strontium, the uncertainty on the calculation which is
limiting the present value is larger [Porsev2006]. The uncertainty in the blackbody shift can be improved by a direct
measurement of the atomic polarizability or by performing a reference measurement at cryogenic temperature.
2. The effect of the lattice can be reduced by a better determination of the magic wavelength and/or use of a shallower lattice.
At a lattice depth of 100 ER, the frequency accuracy of the lattice laser required in order to have a 5×10-18 uncertainty
contribution is approx. 1 MHz. See also comment for 87Sr. Since 171Yb has a spin of 1/2, there is no tensor light shift.
3. For Fermions, the collisional shift is due to inhomogeneous excitation. It can be suppressed in higher dimensional lattices
[Swallows 2010, Chin2001].
4. At a lattice depth of 200 ER the uncertainty in the hyperpolarizability implies a frequency uncertainty of 10-17 [Barber2008].
5. See comment for 87Sr
6. See comment for 87Sr
7. Important only for uncertainties below 10-17
8. Important only for uncertainties below 10-17; coefficient is a factor of 3 smaller than in Sr.
74
6.2 Design of the space clock
In the technical note TN 4, the design of a neutral atom space clock is given in detail. We summarize here
the overall concept.
The system has a total volume of ca. 540 liter, a mass of ca. 300 kg, and a power requirement of approx.
300W, plus 100 W for the two optical links. Details of the distribution of volume, mass on the individual
subsystems are shown in Table 6.3. For comparison, ACES uses 1000 liter, 270 kg, 450 W.
The basic clock concept is modular. The various subsystems can be developed and tested separately. The
main subsystems are shown in Fig. 6.1 and are:
(i) Atomics package
(ii) Atom manipulation laser systems
(iii) Frequency stabilization system (FSS)
(iv) Microwave-optical local oscillator, including clock laser (MOLO)
(v) Control electronics:
Laser frequency or phase locking units (CE-1, CE-2, CE-3, CE-5) for FSS, MOLO, Optical link
(vi) Clock operation computer (CE-4)
(vii) Frequency comparison and distribution package (FCDP)
(viii) Optical link
(ix) Microwave link (MWL)
(x) Payload computer (XPLC), GNSS receiver
75
Figure 6.1: Overview of the complete experimental payload for the SOC mission, broken down into
subsystems and their connections.
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Subsystem Volume (liter) Mass (kg)
Atom manipulation laser systems 63 49
Atomics Package 72 30
Control Electronics (partial: CE-1, CE-4, CE-5) 54 22.5
Microwave-optical local oscillator
Frequency comb 43 22.5
CE-2, CE-3, beat detection units, AOM 10 10
698 nm clock laser 24 15Reference cavity 61 15
Frequency stabilization system (incl. Wavemeter) 12 6
Frequency distribution package (FCDP, incl. USO) 7 8
Microwave link (MWL) 14 14
GNSS receiver 2 5
Control system and data storage (XPLC) 2 4
Structure and harness 20 60
Optical link 80 25
Optional: 2nd optical link 80 25
Sum (incl. Option) 544 311
Table 6.3: Estimated physical parameters of the clock and link subsystems. Parameters of the optical link
are based on the TESAT LCT.
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7 Future plans
7.1 EU-FP-7 project “Development of high-performance transportable and breadboard
optical clocks and advanced subsystems” (SOC2)
This project is a continuation of the present project. It is run by a consortium of 16 European partners,
including all major European metrology laboratories (coordination: S. Schiller) has started on March 1,
2011, and lasts for four years. Its EU funding envelope is 2 M€. Some information can be found at the
website www.soc2.eu.
The goals of the project are twofold:
1.) Develop two transportable engineering confidence optical clock demonstrators with performance
Instability < 1×10-15/ 1/2
Inaccuracy < 5×10-17
This goal performance is better than the best microwave cold atom clock by a factor 100 and approx. 10,
in instability and inaccuracy, respectively and is a significant step towards the SOC mission requirements.
The two systems are to be brought to TRL4 (validation in a laboratory environment). Figure 7.1 shows a
conceptual schematic of one of the systems.
2.) Develop the corresponding laser systems (adapted in terms of power, linewidth, frequency stability,
long-term reliability), atomic package systems with control of systematic (magnetic fields, black-body
radiation, atom number), and an electronic and computer control system, where novel solutions with
reduced space, power and mass requirements will be implemented. Some of the laser systems will be
developed to 2nd generation level with emphasis on even higher compactness and robustness. Also, some
laser components will be tested at TRL 5 level (validation in relevant environment).
As a result of the SOC2 project, it will become feasible to test and validate the breadboards under different
conditions.
The components of and the completed breadboards shall be characterized and optimized both during and
after their development phase. These characterizations shall include the effect of transport (vibrations),
temperature, and aging. They shall be done with respect to stationary optical clocks available in different
metrology laboratories.
A scientific use as well as technology demonstration of the prototype and breadboards shall be done by
using them as ground stations during the 2013-2015 ACES mission. For this purpose, each clock must be
complemented with a transportable frequency comb of suitable performance (to be developed in the SOC2
project) and an ACES microwave ground station. The clocks can be operated at several locations during
the ACES mission, including locations of particular geophysical interest, thereby demonstrating
relativistic geodesy with high-performance mobile clocks.
Test experiments with optical clocks separated in altitude could be performed starting in 2013. These
experiments will represent a demonstration of clock performance under non-laboratory conditions and first
studies of the gravitational redshift of clocks and of Local Position Invariance in Earth’s gravitational
field. They will be complementary to already ongoing tests performed in the Sun’s field with laboratory
clocks. In order of increasing difficulty, they may include:
(i) Comparison of two clocks located at top and bottom of a high tower (e.g. a television tower), with ~
100 m height difference, and linked by stabilized optical fiber.
(ii) Comparison of clocks operated near top and bottom of a high mountain (height difference ~ 2 km) and
linked by optical fiber or microwave link;
(iii) Comparison of an optical clock operated on a high-altitude (40 km) balloon with a transportable
ground clock via MWL or optical link.
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Figure 7.1: Overview of the modular strontium lattice clock to be developed in the SOC2
project (subsystems in color).
laser BB 1
primary
cooling
laser BB 2
secondary
cooling
laser BB 3
repumper
atomics
package
fibres clock laser
fs comb
fibres
Users /
Comparisons
Linkrf
internal M&C
LAN
diagnostics
operator consoleMinicomputer
laser BB 4
dipole trap
79
7.2 GSTP project “Development of Core Technological Elements in Preparation for
Future Optical Atomic Frequency Standards and Clocks in Space” (AO/1-
6530/10/NL/NA)
Members of project SOC are participating in the initial phase project, lasting approximately till mid-2012
and can bring in their expertise gained during SOC and SOC2.
It is hoped that the detailed design activities of the GSTP project will be beneficial towards establishing a
baseline design for the SOC mission on the ISS.
7.3 ESA candidate mission “STE-QUEST”
Within the studies for this mission, a demonstrator of an ultrastable laser plus frequency comb and
microwave generation will be developed by U. Düsseldorf and PTB Braunschweig, for use as a “clock
oscillator” for a cold atom microwave clock.
This development is closely related to the clock laser for the SOC mission and will therefore be an
important contribution.
7.4 Proposed roadmap for the SOC mission
2012-15: Technology and Engineering Model Development
Engineering models (TRL 6) of critical components and subsystems shall be developed in this activity.
The specifications shall be compatible with a clock of <1 × 10-17 inaccuracy, < 1 × 10-16 instability (at
1000 s), with physical parameters (for operation with a single atomic species) consistent with Table I.
o Part 1: (2012-2014)
Taking into account that a number of laser and optics technologies have already been
developed to EM or FM level for other missions (ACES, LISA-PF, PROBA-2, etc.), crucial
components to be developed here are those that have not been space qualified previously, e.g.
laser diodes for the specific wavelengths, nonlinear crystals for blue, green and yellow light