1 Atomic Clocks in Ion Traps Helen Margolis Winter School on Physics with Trapped Charged Particles, Les Houches, 16 th January 2012 Outline • Introduction to time and frequency metrology • Basic principles of trapped ion optical clocks – Trapping and cooling the ion – Observation of the reference transition – Probe laser stabilization – Measurement of the clock transition frequency • Systems studied and state-of-the-art performance – Stability – Systematic frequency shifts • Tests of fundamental physics H. S. Margolis, “Frequency metrology and clocks”, J. Phys. B 42, 154017 (2009) H. S. Margolis, “Optical frequency standards and clocks”, Contemp. Phys. 51, 37 (2010)
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Atomic Clocks in Ion Traps
Helen Margolis
Winter School on Physics with Trapped Charged Particles, Les Houches, 16th January 2012
Outline
• Introduction to time and frequency metrology
• Basic principles of trapped ion optical clocks
– Trapping and cooling the ion
– Observation of the reference transition
– Probe laser stabilization
– Measurement of the clock transition frequency
• Systems studied and state-of-the-art performance
– Stability
– Systematic frequency shifts
• Tests of fundamental physics
H. S. Margolis, “Frequency metrology and clocks”, J. Phys. B 42, 154017 (2009)H. S. Margolis, “Optical frequency standards and clocks”, Contemp. Phys. 51, 37 (2010)
2
Introduction to time and frequency metrology
Introduction of atomic time
First caesium atomic clock developed at NPL
by Essen & Parry, accurate to 1 part in 1010
1955
The second is the duration of 9 192 631 770 periods
of the radiation corresponding to the transition
between the two hyperfine levels of
the ground state of the caesium-133 atom.
1967
0.0
0.2
0.4
0.6
0.8
1.0
-80 -60 -40 -20 0 20 40 60 80
microwave frequency - 9192631770 [Hz]
tra
ns
itio
n p
rob
ab
ility
The best caesium fountain atomic clocks
now have accuracies of a few parts in 1016
2012
0.0
0.2
0.4
0.6
0.8
1.0
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
1 Hz
3
Performance of a frequency standard
Stability
How much the frequency varies over some period of time.
Reproducibility
How well similar devices produce the same frequency.
How well its frequency has been measured relative to the definition of the SI unit of time.
Accuracy
Allan variance and Allan deviation
log σy(τ)τ -1
τ 1/2τ -1/2
τ 0
white phase,
flicker phase
white
frequencyflicker
frequency
random
walk
log τ
Fractional frequency instability as a function of averaging time τ
( ) ( )2
1
2
2
1kky yy −= −τσ ∫
+−=
τ
τ
k
k
t
t
k tf
ftfy d
)(
0
01where
σy2(τ) = Allan variance
σy(τ) = Allan deviation
4
Advantage of optical clocks
• Based on forbidden optical transitions in ions or atoms
• Natural linewidth ~ 1 Hz (less for some systems)
• Frequencies ~ 1015 Hz
• Q-factor ~ 1015 (or even higher)
Optical clocks are:
Theoretically achievable fractional frequency instability:y(τ) =
ηQ (S/N)
τ –1/2 Q = f0
∆f= line quality factor
(S/N) = signal-to-noise ratio for
1Hz detection bandwidth
τ = averaging time in seconds
η ~ 1 (depends on shape of resonance
and method used to determine f0)
Components of an optical clock
Oscillator
(Ultra-stable laser)
+
Counter
(Femtosecond comb)
+
Reference
(narrow optical transition
in an ion or atom)
5
Basic principles oftrapped ion optical clocks
Trapped ion optical clocks
• No 1st-order Doppler shift
• Minimum 2nd-order Doppler shift
• Field perturbations minimised at trap centre
• Background collision rate low
Low perturbation environment:
coolingtransition
reference (“clock”) transition
τ ∼10 ns
τ ∼1 s
groundstate
• Based on “forbidden” (e.g. E2) transitions in single trapped ions(Q ~ 1015)
• Long interrogation times possible
6
Principles of ion trapping
Quadrupole potential:
)2( )(),,( 22 zrtAtzr −=φ
Radiofrequency voltage appliedto ring electrode
→ ion trapped in time-averaged pseudopotential minimum
• Carry out frequency measurements for 3 orthogonal magnetic field directions
• Average quadrupole shift is zero
( )1cos 312
35 22 −
−=∆ βνj
mA
Method 2: [Dubé et al., Phys. Rev. Lett. 95, 033001 (2005)]
• Carry out frequency measurements for Zeeman components corresponding to all different possible |mj| values
• Average quadrupole shift is zero independent of magnetic field direction
Method 3: [Roos et al., Nature 443, 316 (2006)]
• Use an entangled state specifically designed to cancel the quadrupole shift by averaging over states with different |mj|.
Second-order Doppler shifts
Thermal (secular) motion
Micromotion
First-order Doppler shifts are eliminated by laser cooling the ion to the
Lamb-Dicke regime.
Second-order Doppler shifts arise from two sources:
• Ion cooled to close to the Doppler cooling limit (typically ~ 1 mK)
• Shift approaches the 10-18 level
• Careful minimization in three dimensions vital for reduction below 10-17
21
Stark shifts
Motionally-induced Stark shift
• Motion leads to average displacement from trap centre
• Ion experiences a time-averaged non-zero electric field
• Shift can be reduced to a few parts in 1018
Blackbody Stark shift
• Typically 100 – 500 mHz at room temperature, but reasonably constant
• Large uncertainty in absolute value of correction
(typical 30% uncertainty in Stark shift coefficients)
• 1S0 – 3P0 transition in 27Al+ has lowest known shift of –8(3) x 10-18 @ 300K
AC Stark shifts
AC Stark shifts
• High extinction of cooling (and repumper) beams is vital
• Negligible shift due to probe laser at typical intensities used
• Current exception is 467 nm electric octupole transition in 171Yb+
(but shift will reduce as probe laser linewidth is improved)
0 1 2 3 4 50
1000
2000
3000
4000
5000
(fre
qu
ency
- 64
21
214
96
772
00
0 H
z)
/ H
z
power / mW
Measurements of the 467 nm electric octupole transition in 171Yb+ (NPL)
22
Improvements in optical frequency standards
1.0E-18
1.0E-17
1.0E-16
1.0E-15
1.0E-14
1.0E-13
1.0E-12
1.0E-11
1.0E-10
1.0E-09
1950 1960 1970 1980 1990 2000 2010
Year
Fra
ctional un
cert
ain
ty
Essen’s Cs clock
Cs redefinition of the second
Cs fountain clocks
Hg+
Al+Sr
Hg+
Sr+ YbHg+,Yb+,CaH
H
HCa
Iodine-stabilised HeNe
Femtosecond combs
Microwave
Optical (absolute frequency measurements)
Optical (estimated systematic uncertainty)
Sr
Al+
Yb+
Tests of fundamental physics
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Do fundamental constants vary with time?
Any optical transition frequency can be written as ( ) cRFCf ∞= α
Rate of change with time is ( )cRtt
Aft
∞∂∂+
∂∂=
∂∂
lnln ln α
( )αα
ln
ln
∂∂= F
Awhere Ion Clock transition A
Sr+ 2S1/2 –2D5/2 0.43
Yb+ 2S1/2 –2D3/2 0.88
Yb+ 2S1/2 –2F7/2 -5.95
Hg+ 2S1/2 –2D5/2 -2.94
In+ 1S0 – 3P0 0.18
Al+ 1S0 – 3P0 0.008
Frequency ratios between dissimilar optical clocks depend on the fine structure constant α.
Calculations:
Dzuba et al., Phys. Rev. A 59, 230 (1999) Dzuba et al., Phys. Rev. A 68, 022506 (2003)Angstmann et al., Phys. Rev. A 70, 014102 (2004) Dzuba et al, Phys. Rev. A 77, 012515 (2008)
If local position invariance holds, then fundamental physical constants should be constant in time.
Status of laboratory tests
= 1.052 871 833 148 990 438 (55)fAl+
fHg+
Relative uncertainty 5.2 x 10-17
4.3 x 10-17 statistics
1.9 x 10-17 Hg+ systematics
2.3 x 10-17 Al+ systematics
Rosenband et al., Science 319, 1808 (2008)
Repeated measurements over 1 year:
year/10)3.26.1( 17−×±−=αα&
Comparison between 199Hg+ and 27Al+ optical clocks at NIST:
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Frequency ratio measurements in 171Yb+
Ion Clock transition A
Sr+ 2S1/2 –2D5/2 0.43
Yb+ 2S1/2 –2D3/2 0.88
Yb+ 2S1/2 –2F7/2 -5.95
Hg+ 2S1/2 –2D5/2 -2.94
In+ 1S0 – 3P0 0.18
Al+ 1S0 – 3P0 0.008
436 nm (E2)
467 nm (E3)
F = 1
F = 0
2S1/2
F = 1
F = 0
2P1/2
F = 2
F = 12D3/2
3D[3/2]1/2
F = 0
F = 1
1D[5/2]5/2
2F7/2
F = 2
F = 3
F = 4
F = 3
Interleaved interrogation of two optical clock transitions in the same ion in the same environment
common-mode rejection / reduction of some(but not all) systematic frequency shifts
S. N. Lea, Rep. Prog. Phys. 70, 1473 (2007)
Gravitational redshift measurements
Frequency shift2
)1(c
U
f
fZ
∆′+=∆≡ α
non-zero if local position
invariance is not valid
∆U = gravitational potential
difference between clocks
Effect in the laboratory is very small but detectable with the best clocks
Chou et al., Science 329, 1630 (2010)
One clock moved up by ∆h = 33 cm
Comparison of two Al+ clocks at NISTg = local
acceleration due to gravity
corresponding to
Measured
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High precision measurement of the gravitational redshift
Gravitational redshift was tested at the 70 ppm level by Gravity Probe A (comparison of ground & space-borne H-masers).
Space environment offers advantages of
• large changes in gravitational potential
• freedom from Earth seismic noise
Proposed STE-QUEST mission (advanced scenario including an optical clock) would provide a test at the 18 ppb level.
http://sci.esa.int/ste-quest
Time & Frequency group at NPL
Patrick Gill
Geoff Barwood Witold Chalupczak Anne CurtisJohn Davis Chris Edwards Jeff Flowers Rachel Godun Guilong Huang Luke JohnsonDhiren Kara Hugh Klein Stephen LeaGiuseppe Marra Yuri Ovchinnikov Setnam ShemarKrzysztof Szymaniec Giuseppe Tandoi Stephen WebsterPeter Whibberley
Liz Bridge, Steven King University of OxfordIan Hill Imperial CollegeMaurice Lessing University of St AndrewsBen Parker UCLVeronika Tsatourian Heriot-Watt University