Principles and brief history of Cavity QED S.Haroche, 1 st specialized Solvay Lecture, June 4 2010 From the Bohr-Einstein photon box thought experiment… …to the super-high Q cavities of today’s real experiments…. …exploring the quantum dynamics of atoms and photons in a confined space has progressed a lot…
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S.Haroche- Principles and brief history of Cavity QED
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Principles and brief history ofCavity QED
S.Haroche,1st specialized Solvay Lecture,
June 4 2010
From the Bohr-Einstein photonbox thought experiment…
…to the super-high Q cavities oftoday’s real experiments….
…exploring the quantum dynamicsof atoms and photons in a confined
space has progressed a lot…
…and its «realization»by Gamov…
Bohr’s draft of a box storing andreleasing a photon to test quantumlaws…
1
Early History of Cavity QED:controlling spontaneous emission
Early History: Tailoring spontaneous emissionin a confined space
Spontaneous processes are random. Only their rate can be predicted and,in the case of photon emission, estimated by classical arguments based on
Maxwell’s equations
The spontaneous emission rate of an excited state depends on the atom’sstate, but also on the structure of the surrounding vacuum, which
determines the density of modes into which photons are emitted: an atomwithin boundaries does not radiate as in free space.
Similar effects in beta decay: a neutron lives longer in a nucleus than infree space!
Spontaneous emissionenhancement predicted byE.Purcell in 1945…
…and the possibility to inhibitspontaneous emission in atoms
suggested by D.Kleppner in 1981
Emissioninhibited
Emissionenhanced
When gap is increased to l = l/2, modedensity jumps and undergoesresonances for larger l values
100-1000
or larger
2l/!
Antennae radiating near reflecting surfaces
Dispersive effects:cavity Lamb shifts,
Casimir effect l/!
Free-spacemode
density
Modedensity in
cavity (peakincreaseswith Q)
"c/"
In close-spaced gap, field
modes with polarization \\ to
mirrors are suppressed
Dipole \\
to mirror
and
image
cancell
Dipole #
to mirror
and
image
add up
"c/"
When mirrors are curved,focusing effects enhancethe resonances, leading to
huge emissionenhancement factors
First demonstration of Purcell effect on atoms
Rydberg atoms prepared instate 23S in a cavity (V=70mm3)
resonant with transition 23S-
22P (!=340 GHz).
Ionization signal in a ramped electric field applied
to the atoms after they leave the cavity.
The 22P state ionizes in a larger field, thus at a
later time than 23S.
Ionization of 22P
Ionization of 23S
Signals corresponding to anaverage of N atoms crossing
together the cavity: N = 3.5, 2
and 1.3 for traces a,b,c
respectively. Cavity on
resonance (solid line) or off-
resonance (dashed line).Enhancement factor:
! = "at
C/"(23S#22P ) = 530
P.Goy, J-M.Raimond, M.Gross et S.Haroche, PRL 50, 1903 (1983)
Inhibiting the spontaneous emission of circularRydberg atoms
Atom prepared in circularRydberg state n=22
(orbit parallel to metal plates)
Ionisation
detector
Atomic transmission versus "/2L: " is
swept by Stark effect, L being kept
constant. The sharp signal increase for"/2L=1 demonstrates the inhibition of s.e.
of the Rydberg atom which survives
longer in its initial state.
microwave transition
Inhibited transition n=22 # n’=21 at " = 0.45mm
! / 2L
R.G.Hulet, E.S.Hilfer et D.Kleppner,PRL 55, 2137 (1985).
Many enhancement and inhibition experiments in microwave,infrared and optical part of spectrum realized since these
pionneering studies…
Collective emission in cavity: from Purcell to Dicke
Atoms located at equivalent nodal positions incavity are symetrically coupled to field: they
evolve during emission in a subspace invariant byatomic permutation. There is no way to know
which atom has emitted when a photon is lost…
Strong correlations with entanglement spontaneously build up betweenatoms, making collective dipole larger than when atoms radiate
independently
Superradiance rate proportional to number N of atoms
Due to this correlation, the spontaneous emission occurs faster than forsingle atom: this is Dicke superradiance
Purcell factor: ~ number ofimages in cavity wall collectively
emitting with one atom
Number of atomsradiating collectively
together
A double enhancement effect: !C(N ) ="N!
0
e,e ! "S =1
2e,g + ge( ) ! g,gTwo atoms:
Observation of Dicke superradiance in a cavity
Sample of N=3200 Sodium atoms prepared
in Rydberg state 29S, emitting collectively in
a cavity resonant with 29S-28P transition at!= 162 GHz. The single atom spontaneous
emission rate in free space on this transitionis $0 =43s-1. Purcell factor: % = $at
C / $0 ~ 70.
The atom-cavity coupling is switched-off after variable
time by applying an electric field in cavity (Stark
effect). For each interaction time t , we measure thenumber of atoms in states 29S and 28P after cavity
exit. From an ensemble of 900 realizations of
experiment, we reconstruct the histograms of the
number Ne of excited atoms as a function of t (in unitsof tD ~ %N/$0 = 460 ns).
Agreement between experimental histograms andtheory (solid lines in black)
Chapman (Georgia Tech), Vuletic (MIT),Orozco (Maryland), Blatt (Insbruck),Meschede (Bonn), Lange (Sussex)…
Cavity QED in optical domain:the atom-cavity «!molecule!»
The transmission spectrum of thecavity is split into two componentswhen cavity contains a single atom
(from atomic beam or dropped froma MOT).
Fourier transform of time-dependent Rabi oscillation
Thompson et al, PRL, 68, 1132 (1992)
Single atom detection by cavity field
transmission
Depending on laser frequency, a single atom
transit across cavity is signaled by a dip or a
peak.
A 100% efficient atom detector which can count
one by one atoms in the cavity
a
a
b b
J.McKeever et al, PRL 93, 143601 (2004)
Using CQED as single atom counter to studyatom-laser statistics
similarity with optical laser (Glauber theory)
Second order atom
correlation (BEC atom-laser)
Histogram of number of
atoms in time-bin (Poisson)
Second order atom
correlation for thermal
atom beam
A.Öttl et al, PRL, 95, 090404 (2005)
Conversely, the atom modifies the cavityfrequency, which changes its response to the
field. From an analysis of this fieldtransmission, the position of the atom inside
the cavity can be obtained in real time:an atom-cavity microscope tracking atoms.
Feed back procedures to improve thetrapping have been implemented.
C.J.Hood et al, Science, 287, 1457
(2000) .T.Fischer et al, PRL 88, 163002
(2002)
Trapping force of a single photon in acavity
The atom-cavity dressed energies are atomic
position dependent. Their spatialderivative corresponds to a light-force
exerted on average by one photon!This force can attract atom inside the
cavity.
Garching group (similar films by Caltech group)
The CQED photon pistol:releasing photons one by one on demand
A Raman process on a single atom converts
triggering pulses into photons escaping one
by one from the cavityi
frepumping
Experiment performed
with flying atoms, then
with trapped atoms in
cavity
Kuhn et al, PRL, 89, 067901 (2002) J.McKeeveret al, Science, 303, 1992 (2004)M. Hijlkema et al,arXiv:quant-ph/0702034 (2007)
The escaping light isanalysed after beam
splitting by correlation.Coincidence rate measured
as a function of delaybetween the two output
channels.
Missing central peak isevidence of single photon
emission(a photon cannot be
«!split!»)
Analyzing the photon pistol output
Single atom-non linear optics:the photon blockade effect in optical CQED
Once a photon is resonant with theatom-cavity system, a second photon isoff-resonant: only one photon at a timecan be transmitted by cavity atresonance!
The transmitted light isantibunched
Birnbaum et al, Nature 436, 87 (2005).
4. Entanglement experiments in microwave
CQED
Two essential ingredients
Circular Rydberg atoms
Large circular orbit
Strong coupling to microwaves
Long radiative lifetimes (30ms)
Level tunability by Stark effect
Easy state selective detection
Quasi two-level systems
n = 51
n = 50
Superconducting microwave cavity
Gaussian field mode with 6mm waist
Large field per photon
Long photon life time improved by ring around mirrors (1ms)
Easy tunability
Possibility to prepare Fock or coherent states with controlled
mean photon number
e
g
The
spring
The
spin
Oven Circular Rydberg
state preparation
Cavity
Microwave source
(coherent state)
Auxiliary microwave
(atom manipulation)
State selective
detection
Artist’s view of the Paris microwave CQED
set-up (2001-2005 version)
Raimond, Brune and Haroche RMP, 73, 565 (2001)
The route to circular states: a 53 photon adiabatic process
Rubidium level scheme with transitions
implied in the selective depumping and
repumping of one velocity class in the
F=3 hyperfine state
In green, velocity distribution before
pumping, in red velocity distribution of
atoms pumped in F=3, before being excited
in circular Rydberg state
Controlling the atom-cavity interaction time: atomic velocity
selection by optical pumping
0 30 60 900.0
0.2
0.4
0.6
0.8
Pe(t
)
time ( ? s)
51 (level e)
50 (level g)
51.1 GHz
Hagley et al, PRL 79, 1 (97)
Initial state
|e,0>
$ / 2 pulse
Creates atom-cavity
entanglement
|e,0> % |e,0> + |g,1>
µ
Useful Rabi pulses
( quantum knitting)
e,0 ! cos"t
2
#$%
&'(e,0 + sin
"t
2
#$%
&'(g,1
EPR pairs in CQED
0 30 60 900.0
0.2
0.4
0.6
0.8
Pe(t
)
time ( ? s)
51 (level e)
50 (level g)
51.1 GHz
Maître et al, PRL 79, 769 (97)
|e,0> % |g,1>
|g,1>% |e,0>
|g,0> % |g,0>
(|e> +|g>)|0> % |g> (|1> +|0>)
µ
e,0 ! cos"t
2
#$%
&'(e,0 + sin
"t
2
#$%
&'(g,1
$ pulse maps
atomic state on
field and back
0 30 60 900.0
0.2
0.4
0.6
0.8
Pe(t
)
time ( ? s)
51 (level e)
50 (level g)
51.1 GHz
Nogues et al, Nature, 400, 239 (1999); Rauschenbeutel et al, PRL, 83, 5166 (1999)
2$ pulse: phase gate and
quantum logic operations
|e,0> % - |e,0>
|g,1> % - |g,1>
|g,0> % |g,0>
µ
e,0 ! cos"t
2
#$%
&'(e,0 + sin
"t
2
#$%
&'(g,1
V(t)
e1g2
Entangled atom-atom pair mediated by real photon exchange
Electric field F(t) used to
tune atoms #1 and #2 in
resonance with C for a
determined time t realizing
)/2 or ) Rabi pulse
conditions
Hagley et al, P.R.L. 79,1 (1997)
+
+
Direct entanglementof two atoms via
virtual photonexchange:
a cavity-assistedcontrolled collision(after S.B.Zeng and G.C.Guo, PRL 85,
2392 (2000)).
Relatively insensitive to cavity Q and thermal photons
! = 10"6#eg
1
$1
+1
$2
%
&'
(
)*
Two modes:1/*#1/* 1 +1/*2
A thought experiment about complementarity
– Microscopic slit: set in motion when deflecting particle.Which path information and no fringes
– Macroscopic slit: impervious to interfering particle.No which path information and fringes
– Wave and particle are complementary aspects of the quantum object.