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)

J-M Raimond, P.Goy, M.Gross, C.Fabre et S.Haroche, Phys.Rev.Lett. 49, 1924 (1982)

2.

The strong coupling regime of CQED intime-domain:

Rydberg-atom microwave experiments

From Purcell to Rabi:the strong coupling regime of Cavity QED

Spontaneous emission in acontinuum of cavity modes of

width &c = '/Q imparts toatomic excited state a width $c

inversely proportional to &c.

&c$c

(

!c="2

#c

<< #c

From Purcell to Rabi:

the strong coupling regime of Cavity QED

As cavity Q factor increases, thecavity spectral width &c='/Q

decreases and the rate ofemission $c shoots up. The

perturbative treatment of the

Purcell effect breaks down when

these two widths become equal.

&c$c

(

!c="2

#c

$ #c

! =da .E0

h= da

"

2h#0Vc

$ %c ="

Q

Atomicdipole

Vacuumfluctuations in

Cavity

Strong coupling

regime:

large dipole, small cavityvolume and very large Q

factor

VacuumRabi

frequency

e

gThe spin:

2-level atom

From Purcell to Rabi:the strong coupling regime of Cavity QED is

a story about a spin and a spring

0

1

2

The spring:

Cavity mode

H =h!

eg

2e e " g g#$ %&+ h!a†a " i

h'

2a e g " a† g e#$ %&

(Jaynes Cummings Hamitonian)

e,0 !"! cos#t

2

$

%&

'

() e,0 + sin

#t

2

$

%&

'

() g,1

Vacuum Rabi oscillation:(reversible spontaneous emission)

e,n !"! cos# n +1t

2

$

%&

'

() e,n + sin

# n +1t

2

$

%&

'

() g,n +1

Rabi oscillation sped-up in n

photons (stimulated emission)

(

n

p(n)

0 1 2 3

Rabi oscillation in vacuum or in small coherent field:direct test of photon graininess

Pe(t) = p(n)cos

2 ! n +1t

2

"

#$

%

&'

n

( ; p(n) = e)n n

n

n!

n = 0 (nth = 0.06)

n = 0.40 (±0.02)

n = 0.85 (±0.04)

n = 1.77 (±0.15)

Pe(t) signal Fourier transform Inferred p(n)

Brune et al,PRL,76,1800,1996.

First strong coupling experiment in CQED:the micromaser (1985)

Herbert Walther

1935-2006Meschede et al, PRL 54, 551 (1985)

Rydberg atoms cross one at a time a

high Q cavity and build up a many-

photon field in it by cumulative Rabi

oscillations:

the ultimate maser-laser

The ideal micromaser: a quantum machine todeliver photons in a box

!n = 0

!n = +1

j = 0 j =1

Probabilities given by Rabi:

Pj(n) = cos

2 ! n +1t + j"

2

#

$%

&

'(

Photon numberconverges to n0

Simulations:n undergoes

staircase-likeevolution, varying

randomlybetweendifferent

realizations

Solid line:ensemble average

If trapping

condition

fulfilled, all

trajectories

converge to n0

(here n0=10) Photon nber histograms at increasing times

! n0+1t = 2p"

# Pj=1(n0 ) = 0

Trapping states

l

t = l / v

The two-photon micromaser:cavity tuned at half-frequency of transition between same parity levels

!n = 0

Emits photons by pairsSingle photon emission towards intermediate level is inhibited by CQED

M.Brune et al, PRL 59, 1899 (1987)

!n = +2

J.McKeever et al, Nature, 425, 268 (2003).

Lasing of a single

atom trapped in a

cavity

(Caltech group)

Microlasers in optical CQED

The optical version of the micromaser:

field builds up from « kicks » produced

by atoms crossing one by one the cavity

K.An et al, PRL, 73, 3375 (1994).

3.

The strong coupling regime of atomic-CQED in optical experiments

H.J.Kimble (Caltech), G.Rempe (Garching),T.Esslinger (ETH-Zurich)

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.

Particle/slit

entanglement

Einstein-Bohr

discussionat Solvay

1927

A “modern” version of Bohr’s proposal

with a Mach-Zehnder interferometer

_

_

D

•Interference between two well-separated paths.

• Getting a which-path

information?

&

A “modern” version of Bohr’s proposal:

Mach-Zehnder with a moving beam-splitter

• Massive beam splitter: negligible motion, no which- path information, fringes

• Microscopic beam splitter: which path information and no fringes

_

_

D&

Complementarity and entanglement

• A more general analyzis of Bohr’s experiment

– Initial beam-splitter state

– Final state for path b

– Particle/beam-splitter state

– Particle/beam-splitter entanglement

– (an EPR pair if states orthogonal)

– Final fringes signal

• Small mass, large kick

NO FRINGES

• Large mass, small kick

FRINGES

0

!

0a b

!" = " + "

0a b

!" "

0 0! =

0 1! =

_

O

B1

B2

M

M'

a

b

P

D

_&

Complementarity and decoherence

Entanglement with another system destroys interference

• explicit detector (beam-splitter/ external)

• uncontrolled measurement by the environment (decoherence)

_

_

D

Complementarity, decoherence and entanglement intimately linked

&

A more realistic system: Ramsey interferometry• Two resonant $/2 classical pulses on an atomic transition e/g

_B2

B1

M

M'

a

b

D

Which path information?

Atom emits one photon in R1 or R2

Ordinary macroscopic fields

(heavy beam-splitter)

Field state not appreciably affected. No "which path" information

FRINGES

Mesoscopic Ramsey field

(light beam-splitter)

Addition of one photon changes the field. "which path" info

NO FRINGES

R1 R2

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Pg

Fréquence relative (kHz)

&

An object at the quantum/classical boundary

Coherent field in a cavity

• State produced by a classicalsource coupled for finite time tothe cavity mode: field defined by

complex amplitude '

• A picture in phase space(Fresnel plane)

From quantum to classical

• Vacuum or

small field:• Large quantum fluctuations. A field at the

single-photon level is a quantum object

• Large field

• Small quantum fluctuations. A field withmore than 10 photons is almost aclassical object.

a

!'

Bohr’s experiment with a Ramsey interferometerStore one Ramsey field in a high Q cavity

Initial cavity state

– Intermediate atom-cavity state

• Ramsey fringes contrast

– Large field

• FRINGES

– Small field

NO FRINGE

D

S

R1R2

e

g

C

__

!

( )1, ,

2e ge g! !" = +

e g! !

e g! ! !" "

0 , 1e g

! != =

Atom-cavity interaction timeTuned for $/2 pulse

Possible even if C empty

From

quantum to

classicalclassical

&

Quantum/classical limit for an interferometer

Fringes contrast versus photon number N in first Ramsey field

Fringes vanish for quantum

field

photon number plays

the role of the beam-

splitter's "mass"

An illustration of the (N()

uncertainty relation :

• Ramsey fringes reveal

field pulses phase

correlations.

• Small quantum field: large

phase uncertainty and low

fringe contrast

Not a trivial blurring of the

fringes by a classical noise:

atom/cavity entanglement

can be erasedNature, 411, 166 (2001)

0 2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Fringes c

ontr

ast

N

An elementary quantum eraser

• Another thought experiment

_

_

D

Two interactions with the same beamsplitter assembly erase the which path information

and restore the interference fringes

&

Ramsey “quantum eraser”

• A second interaction with the mode erases the which path info

Ramsey fringes without fields !

– Quantum interference fringes without external field

– A good tool for quantum manipulations

_,0e

( )1

,0 ,12e g+

,0e

10 12 14 16 18 20 22 24

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Pe

|g,1>

Atom found in g: one photon in C

whatever the path:no info and fringes

&

A conditional quantum

eraser: new perspective

on EPR