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Hanbury Brown and Twiss and other correlations: from photon to atom quantum optics
Alain Aspect - Groupe d’Optique AtomiqueInstitut d’Optique – Palaiseau
http://www.lcf.institutoptique.fr/atomoptic
Sao Carlos, June 4, 2011
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The Hanbury Brown and Twiss effect and other landmarks in quantum optics:
from photons to atoms•The Hanbury Brown and Twiss photon-photon correlation experiment: a landmark in quantum optics•Atomic HBT with He*•Pairs of quantum correlated atoms in spontaneous 4-wave mixing of matter waves
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The Hanbury Brown and Twiss effect and other landmarks in quantum optics:
from photons to atoms•The Hanbury Brown and Twiss photon-photon correlation experiment: a landmark in quantum optics•Atomic HBT with He*•Pairs of quantum correlated atoms in spontaneous 4-wave mixing of matter waves
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The HB&T experiment: correlations in light?
Measurement of the correlation function of the photocurrents at two different points and times
1 2(2)1 2
1 2
(r , ) (r , )(r , r ; )
(r , ) (r , )i t i t
gi t i t
Semi-classical model of the photodetection (classical em field, quantized detector):
Measure of the correlation function of the light intensity:
2(r, ) (r, ) (r, )i t I t t E
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The HB&T effect: correlations in light!Light from incoherent source: time and space correlations
Mj
P1
P2
(2)1 2(r , r ; )g
(2)1 2
(2)1 2 c c
(r r ; 0) 2
(r r ; ) 1
g
g L
A measurement of g(2) 1 vs. and r1
r2 yields the coherence volume
(2)1 2(r r ; ) 1g
c
• time coherence
c 1/ • space coherence
c /L
1
2
(2)2 1(r r ; 0) 1g
Lc
r1 – r2
1
2P1
P2
P1
P2
g(2)(r1, r2;)
P1
P2
P1
P2
g(2)(r1, r2;)
(2)1 2(r , r ; 0)g
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The HB&T stellar interferometer: an astronomy tool
Measure of the coherence area angular diameter of a star
LcCL
LC L
L
1 1(2)
1 2
(r , ) (r , )( ;0)
(r , ) (r , )Li t i t
g Li t i t
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The HB&T stellar interferometer: an astronomy tool
Measure of the coherence area angular diameter of a star
Equivalent to the Michelson stellar interferometer ?
r1 r2
Visibility of fringes
1 2(1)1 2 1/ 2 1/ 22 2
1 2
(r , ) (r , )(r , r ; )
(r , ) (r , )
t tg
t t
E EE E
LcCL
LC L
L
1 1(2)
1 2
(r , ) (r , )( ;0)
(r , ) (r , )Li t i t
g Li t i t
r
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The HB&T stellar interferometer: an astronomy tool
Measure of the coherence area angular diameter of a star
Equivalent to the Michelson stellar interferometer ?
r1 r2
Visibility of fringes
1 2(1)1 2 1/ 2 1/ 22 2
1 2
(r , ) (r , )(r , r ; )
(r , ) (r , )
t tg
t t
E EE E
LcCL
LC
HB&T insensitive to atmospheric fluctuations!
L
L
1 1(2)
1 2
(r , ) (r , )( ;0)
(r , ) (r , )Li t i t
g Li t i t
r
Not the same correlation function: g(2) vs g(1)
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HBT and Michelson stellar interferometers yield the same quantity
Mj
P1
P2
(2)1 2(r , r ; )g
( , ) exp jj j j j
j
P t a M P tc
E
Many independent random emitters: complex electric field = sum of many independent random processes
Central limit theorem Gaussian random process
2(2) (1)1 2 1 2(r , r ; ) 1 (r , r ; )g g
*1 2(1)
1 2 1/ 2 1/ 22 21 2
(r , ) (r , )(r , r ; )
(r , ) (r , )
t tg
t t t
E EE E
* *1 1 2 21 2(2)
1 2 2 21 2 1 2
(r , ) (r , ) (r , ) (r , )(r , ) (r , )(r , r ; )
(r , ) (r , ) (r , ) (r , )
t t t ti t i tg
i t i t t t
E E E EE E
HBT Stellar Interferometer
Michelson Stellar Interferometer
Same width: star size
Incoherent source
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The HB&T stellar interferometer:it works!
The installation at Narrabri (Australia): it works!
HB et al., 1967
HBT intensity correlations: classical or quantum?
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HBT correlations were predicted, observed, and used to measure star angular diameters, 50 years ago. Why bother?
The question of their interpretation, classical vs. quantum, provoked a debate that prompted the emergence of modern quantum optics!
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Classical wave explanation for HB&T correlations (1): Gaussian intensity fluctuations in incoherent light
Mj
P1
P2
(2)1 2(r , r ; )g
Many independent random emitters: complex electric field fluctuates intensity fluctuates
Gaussian random process 2(1)
1 2(2)
1 2 1 (r(r , r ; ) , r ; )gg
22 (2)1 1( ) ( ) ( , ;0) 1I t I t g r r
For an incoherent source, intensity fluctuations (second order coherence function) are related to first order coherence function
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Classical wave explanation for HB&T correlations (2): optical speckle in light from an incoherent source
( , ) exp jj j j j
j
P t a M P tc
E
Many independent random emitters: complex electric field = sum of many independent random processes
Gaussian random process 2(2) (1)
1 2 1 2(r , r ; ) 1 (r , r ; )g g
Intensity pattern (speckle) in the observation plane:
• Correlation radius Lc /
• Changes after c 1 /
Mj
P1
P2
(2)1 2(r , r ; )g
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The HB&T effect with photons: a hot debateStrong negative reactions to the HB&T proposal (1955)
g(2)(0) = 2 probability to find two photons at the same place larger than the product of simple probabilities: bunching
In term of photon counting
1 2(2)1 2
1 2
(r , r ; , )(r , r ; )
(r , ) (r , )t t
gt t
joint detection probability
single detection probabilities
For independent detection events g(2) = 1
How might independent particles be bunched ?
M jP1
P2
(2)1 2(r , r ; )g
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The HB&T effect with photons: a hot debateStrong negative reactions to the HB&T proposal (1955)
g(2)(0) > 1 photon bunching How might photons emitted from distant points in an incoherent source not be statistically independent?
HB&T answers
• Light is both wave and particles. Uncorrelated detections easily understood as independent particles
(shot noise)Correlations (excess noise) due to beat notes of random waves
2(2) (1)1 2 1 2(r , r ; ) 1 (r , r ; )g g
cf . Einstein’s discussion of wave particle duality in Salzburg (1909), about black body radiation fluctuations
M jP1
P2
(2)1 2(r , r ; )g
• Experimental demonstration!
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The HB&T effect with photons: Fano-Glauber quantum interpretation
E1 D1
E2 D2
Two photon emitters, two detectors
Initial state:•Emitters excited•Detectors in ground state
E1
D1
E2
D2
Final state:•Emitters in ground state•Detectors ionized
Two paths to go from THE initial state to THE final state
Amplitudes of the two process interfere
1 2 1 2(r , r , ) (r , ) (r , )t t t Incoherent addition of many interferences: factor of 2 (Gaussian process)
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The HB&T effect with particles: a non trivial quantum effect
Two paths to go from one initial state to one final state: quantum interference of two-photon amplitudes
Two photon interference effect: quantum weirdness•happens in configuration space, not in real space•A precursor of entanglement (violation of Bell inequalities), HOM,
etc…Lack of statistical independence (bunching) although no “real” interactioncf. Bose-Einstein Condensation (letter from Einstein to Schrödinger, 1924)Two entangled particles interference effect, and the ability to prepare and observe individual pairs, is at the root of the second quantum revolution**AA: “John Bell and the second quantum revolution” foreword of “Speakable and Unspeakable in Quantum Mechanics” , J.S. Bell (Cambridge University Press 2004); http://www.lcf.institutoptique.fr/Groupes-de-recherche/Optique-atomique/Membres/
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1960: invention of the laser (Maiman, Ruby laser)• 1961: Mandel & Wolf: HB&T bunching effect should be easy
to observe with a laser: many photons per mode• 1963: Glauber: laser light should NOT be
bunched: quantum theory of coherence• 1965: Armstrong: experiment with single mode AsGa laser: no bunching well above threshold; bunching below threshold
• 1966: Arecchi: similar with He Ne laser: plot of g(2)()
Intensity correlations in laser light? yet more hot discussions!
Simple classical model for laser light:
0 0 n n 0exp{ }E i t e e E E
(8 Juillet 1960, New York Times)(8 Juillet 1960, New York Times)
Phys Rev Lett 1963
Quantum description identical by use of Glauber-Sudarshan P representation (coherent states )
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The Hanbury Brown and Twiss effect: a landmark in quantum optics
•Easy to understand if light is described as an electromagnetic wave•Subtle quantum effect if light is described as made of photons
Intriguing quantum effect for particles*
Hanbury Brown and Twiss effect with atoms?
* See G. Baym, Acta Physica Polonica (1998) for HBT with high energy particles
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Atomic Hanbury Brown and Twiss and other quantum atom optics effects
•The Hanbury Brown and Twiss photon-photon correlation experiment: a landmark in quantum optics•Atom atom correlation experiments: He* fantastic•Pairs of quantum correlated atoms by spontaneous non-linear mixing of 4 de Broglie waves
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The HB&T effect with atoms: Yasuda and Shimizu, 1996
• Cold neon atoms in a MOT (100 mK) continuously pumped into an untrapped (falling) metastable stateSingle atom detection (metastable atom)Narrow source (<100mm): coherence volume
as large as detector viewed through diverging lens: no reduction of the visibility of the bump
Effect clearly seen• Bump disappears
when detector size >> LC
• Coherence time as predicted:
/ 0.2 sE m
Totally analogous to HB&T: continuous atomic beam
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Atomic density correlation (“noise correlation”): a new tool to investigate quantum gases
Interaction energy of a sample of cold atoms• for a thermal gas (MIT, 1997)• for a quasicondensate (Institut d’Optique, 2003)
3 atoms collision rate enhancement in a thermal gas, compared to a BEC• Factor of 6 ( ) observed (JILA, 1997) as predicted by
Kagan, Svistunov, Shlyapnikov, JETP lett (1985)
22 (r) 2 (r)n n22 (r) (r)n n
• Correlations in a quasicondensate (Ertmer, Hannover 2003)• Correlations in the atom density fluctuations of cold atomic samples
Atoms released from a Mott phase (I Bloch, Mainz, 2005)Molecules dissociation (D Jin et al., Boulder, 2005) Fluctuations on an atom chip (J. Estève et al.,Institut d’Optique, 2005)… (Inguscio, …)
Noise correlation in absorption images of a sample of cold atoms (as proposed by Altmann, Demler and Lukin, 2004)
33(r) 3! (r)n n
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Atomic density correlation (“noise correlation”): a new tool to investigate quantum gases
Interaction energy of a sample of cold atoms• for a thermal gas (MIT, 1997)• for a quasicondensate (Institut d’Optique, 2003)
3 atoms collision rate enhancement in a thermal gas, compared to a BEC• Factor of 6 ( ) observed (JILA, 1997) as predicted by
Kagan, Svistunov, Shlyapnikov, JETP lett (1985)
22 (r) 2 (r)n n22 (r) (r)n n
Noise correlation in absorption images of a sample of cold atoms (as proposed by Altmann, Demler and Lukin, 2004)
33(r) 3! (r)n n
What about individual atoms correlation function measurements?
Measurements of atomic density averaged over small volumes
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The Hanbury Brown and Twiss effect and other landmarks in quantum optics:
from photons to atoms
•The Hanbury Brown and Twiss photon-photon correlation experiment: a landmark in quantum optics•Atomic HBT with He*•Pairs of quantum correlated atoms in spontaneous 4-wave mixing of matter waves
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Metastable Helium 2 3S1
An unique atomic species• Triplet () 2 3S1 cannot radiatively decay
to singlet () 1 1S0 (lifetime 9000 s)
• Laser manipulation on closed transition 2 3S1 2 3P2 at 1.08 mm (lifetime 100 ns)
• Large electronic energy stored in He*Þ ionization of colliding atoms or
molecules
Þ extraction of electron from metal: single atom detection with Micro Channel Plate detector
1 1S0
2 3S1
2 3P2
1.08 mm
19.8 eV
Similar techniques in Canberra, Amsterdam, ENS
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He* laser cooling and trapping, and MCP detection: unique tools
Single atom detection of He*
He* on the Micro Channel Plate detector: an electron is extracted multiplication observable pulse
Clover leaf trap@ 240 A : B0 : 0.3 to 200 G ;
B’ = 90 G / cm ; B’’= 200 G / cm2
z / 2 = 50 Hz ; / 2 = 1800 Hz
Tools crucial to the discovery of He* BEC (Institut d’Optique, 2000)Analogue of single photon counting development, in the early 50’s
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Position and time resolved detector:a tool for atom correlation experiments
Delay lines + Time to digital converters: detection events localized in time and position
• Time resolution better than 1 ns
• Dead time : 30 ns • Local flux limited by MCP
saturation • Position resolution (limited
by TDC): 200 mm
105 single atom detectors working in parallel !
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Atom atom correlations in an ultra-cold atom cloud
• Cool the trapped sample to a chosen temperature (above BEC transition)
• Release onto the detector• Monitor and record each detection
event n:Pixel number in (coordinates x, y)Time of detection tn (coordinate z)
1 1, ,... , ,... = a re rd con ni t i t 1 1, ,... , ,..n ni t i t
of the atom positions in a single cloud
Cold sample
Detector
Pulsed experiment: 3 dimensions are equivalent ≠ Shimizu experiment
x
z
y
Repeat many times (accumulate records) at same temperature
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g(2) correlation function: 4He* thermal sample (above TBEC)
(2) ( 0; )g x y z • For a given record (ensemble of detection events for a given released sample), evaluate probability of a pair of atoms separated by x, y, z.
[(2)(x, y, z)]i • Average over many records (at
same temperature)• Normalize by the autocorrelation
of average (over all records)(2) ( , , )g x y z
1.3 mK
Bump visibility = 5 x 10-2
Agreement with prediction (resolution)
HBT bump around x = y = z = 0
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Resolution (200 mm) sufficient along y and z but insufficient along x. Expected reduction factor of 15
The detector resolution issue
c fallsource2xL t
M x
If the detector resolution xdet is larger than the HBT
bump width Lcx
then the height of the HB&T bump is reduced:
(2) C
det
1 1L
gx
At 1 mK,
• ysource = zsource 4 mm Lcy = Lcz =500 mm • xsource 150 mm Lcy = 13 mm
NB: vertical resolution is more than sufficient: zdet V t 1 nm
xdet
xz
y
(2) ( , , )g x y z
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x,y correlation function (thermal 4He*)
1.3 mK
g(2)(Dx, Dx, Dx) : pancake perpendicular to x (long dimension of the source)
( 2) ( ; ; 0)g x y
Dx Dy
x
0.55 mK
1.0 mK
1.35 mK
x y
Various source sizes
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g(2) correlation function in a Bose Einstein Condensate of 4He* (T < Tc)
No bunching: analogous to laser light
(see also Öttl et al.; PRL 95,090404Truscott, Baldwin et al., 2010)
(2) (0;0;0) 1g
Decrease the atomic cloud temperature:
phase transition to BEC
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Atoms are as fun as photons?
They can be more!
In contrast to photons, atoms can come not only as bosons (most frequently), but also as fermions, e.g. 3He, 6Li, 40K...
Possibility to look for pure effects of quantum statistics• No perturbation by a strong “ordinary” interaction (Coulomb
repulsion of electrons)• Comparison of two isotopes of the same element (3He vs 4He).
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The HB&T effect with fermions: antibunching
Two paths to go from one initial state to one final state: quantum interference
Two particles interference effect: quantum weirdness, lack of statistical independence although no real interaction
… no classical interpretation22( ) ( )n t n t
Amplitudes added with opposite signs: antibunching
impossible for classical densities
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The HB&T effect with fermions: antibunching
Two paths to go from one initial state to one final state: quantum interference
Two particles interference effect: quantum weirdness, lack of statistical independence although no real interaction
… no classical interpretation22( ) ( )n t n t
Amplitudes added with opposite signs: antibunching
impossible for classical densities
Not to be confused with antibunching for a single particle (boson or fermion): a single particle cannot be detected simultaneously at two places
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Evidence of fermionic HB&T antibunching
Electrons in solids or in a beam: M. Henny et al., (1999); W. D. Oliver et al.(1999); H. Kiesel et al. (2002).
Neutrons in a beam: Iannuzi et al. (2006)
Heroic experiments, tiny signals !
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HB&T with 3He* and 4He*an almost ideal fermion vs boson comparison
Samples of 3He* and 4He* at same temperature (0.5 mK, sympathetic cooling) in the trap :
same size (same trapping potential)Þ Coherence volume scales as the atomic
masses (de Broglie wavelengths)Þ ratio of 4 / 3 expected for the HB&T widths
Collaboration with VU Amsterdam (W Vassen et al.)
Neutral atoms: interactions negligible
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HB&T with 3He* and 4He*fermion versus bosons
Direct comparison: • same apparatus• same temperature
3He*
4He*
Collaboration with VU Amsterdam (W Vassen et al.)
Ratio of about 4 / 3 found for HB&T signals widths (mass ratio, ie de Broglie wavelengths ratio)
Pure quantum statistics effect
Fermion anticorrelation also seen in Mainz : Rom et al. Nature 444, 733–736 (2006)
Jeltes et al. Nature 445, 402–405 (2007) (Institut d’Optique-VU)
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The Hanbury Brown and Twiss effect and other landmarks in quantum optics:
from photons to atoms
•The Hanbury Brown and Twiss photon-photon correlation experiment: a landmark in quantum optics•Atomic HBT with He*•Pairs of quantum correlated atoms in spontaneous 4-wave mixing of matter waves
From quantum photon optics to quantum atom optics
Photon counting (1950): start of modern qu. optics: photon corr. functions: HBT
Single atom detection, resolved in time and space (2005-)Atom correlation functions: atomic HBT, Fermions and bosons
Correlations in atomic cascade photon pairs (1967)Entanglement, Bell in. tests (1972,1982)
Correlations in atom pairs from molecular dissociation (D Jin)
1970: photon pairs in non-linear crystal 1987: entanglement easier to obtain
No equivalent to fermions
No entanglement observed yet
An equivalent in non-linear atom optics?
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Non linear mixing of matter waves(4-wave mixing)
(3) non-linear atom optics process (NIST, MIT)
p1 p2
p4p3
p1p2
p33 colliding BEC’s
2 1p p
3 1 2p p p
Appearance of a daughter BEC
4 3p p
Amplification of probe 3
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(3) non-linear mixing of matter waves (4-wave mixing)
Stimulated process : appearance of a daughter BEC observed (NIST, MIT)
p1 p2
p4p3
p1p2
p33 colliding BEC’s
2 1p p
3 1 2p p p
daughter BEC
4 3p p
Amplification of 3
Spontaneous process: appearance of pairs predicted (Meystre, Cirac-Zoller, Drummond, Kurisky, Moelmer…)
p1 p2
p4
p1p2
p32 colliding BEC’s
2 1p p
1 2p p
spontaneous atom pairs
4 3p p
p’3
p’44 3 1 2p p p p
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Observation of spontaneous 4-wave mixing in collision of two 4He* BEC’s
4 3 1 2p p p p
p reconstruction by elementary kinematics
(free fall)
p1 p2
p4
p1p2
p32 colliding BEC’s
2 1p p
1 2p p
p’3
p’4
p1 p2
p4
p1p2
p32 colliding BEC’s
2 1p p
1 2p p
p’3
p’4
Observation of the full s-wave scattering spherical shell
s-wave collision halo ( cf. MIT, Penn state, Amsterdam)
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Observation of correlated 4He* pairs
p1 p2
p4
p3 Colliding BEC’s 2 1p p
4 3
3 4
p p
p p const
Momentum correlation in scattered atoms
Correlation of antipodes on
momentum sphereAtoms in pairs of
opposite momenta
(2)1 2( )g V V
(2)1 2( )g V V
Are there other correlations in the momentum distribution?
A. Perrin et al. PRL 2007
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HBT correlations in the s-wave collision halo
HBT correlations observed for (almost) collinear atoms!
g(2)(V1 V1)Theory far from trivial (coll. K Moelmer, K. Keruntsyan)
How can we get a chaotic statistics (HBT) from a collision between coherent ensembles of atoms (BEC’s)?
p1 p2
p4
p3
Correlation between atoms of two different pairs: trace over the partners yields Gaussian statistics.Recently observed with photons
Summary: progress in quantum atom opticsHB&T observed with bosons and fermions
Observation of pairs of atoms obtained in a spontaneous non-linear atom optics processFully quantum process: • back to back correlations = particle image;• HBT = 2 particle quantum amplitudes (or classical waves)• Number difference squeezing observed (JC Jaskula, PRL 2010) A tool for atom interferometry below the quantum standard limit
(Bouyer & Kasevich, Dunningham, Burnett, Barnett)
p1 p2
p4
p3
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Summary: progress in quantum atom opticsHB&T observed with bosons and fermions
Do we have entangled atom pairs?
Entanglement in momentum space: 3 3 3 3p , p p , p
Observation of pairs of atoms obtained in a spontaneous non-linear atom optics processFully quantum process: • back to back correlations = particle image;• HBT = 2 particle quantum amplitudes (or classical waves)• Number difference squeezing observed (JC Jaskula, PRL 2010) A tool for atom interferometry below the quantum standard limit
(Bouyer & Kasevich, Dunningham, Burnett, Barnett)
p1 p2
p4
p3
To be distinguished from incoherent mixture of 3 3 3 3p , p and p , p
Simplified model, in analogy to quantum photon optics: yes!
p4
p3p’3
p’4
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Demonstration of momentum entanglement A possible scheme
p3
p4p’3
p’4
a b
With photonsProposal: Horne, Shimony, Zeilinger: PRL 1989Expt: Rarity, Tapster, PRL 1990
3 4 3 41 p ,p p ,p2
How to show entanglement in ?
Recombine p3 and p’3 , p4 and p’4 , and look for a modulation of
coincidence rates N++ , N+ , N+ , N , vs a b
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Demonstration of momentum entanglement A possible scheme
With atoms, experiments are going to be hard, but a similar scheme to test Bell’s inequalities seems possible… Might be used to test non-trivial BCS like states with cold atoms
(T. Kitagawa, M. Greiner, AA, E. Demler, PRL 2011)
p3
p4p’3
p’4
a b
With photonsProposal: Horne, Shimony, Zeilinger: PRL 1989Expt: Rarity, Tapster, PRL 1990
3 4 3 41 p ,p p ,p2
How to show entanglement in ?
Recombine p3 and p’3 , p4 and p’4 , and look for a modulation of
coincidence rates N++ , N+ , N+ , N , vs a b
hopefully before 2024!
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Groupe d’Optique Atomique duLaboratoire Charles Fabry de l’Institut d’Optique
Philippe Bouyer
ELECTRONICS André Villing
Frédéric Moron
ATOM CHIP BECIsabelle BouchouleJean-Baptiste TrebiaCarlos Garrido Alzar
He* BECDenis Boiron
A. PerrinV Krachmalnicoff
Hong ChangVanessa Leung
1 D BEC ATOM LASER
Vincent Josse David Clément
Juliette BillyWilliam Guérin
Chris VoZhanchun Zuo
Fermions Bosons mixtures
Thomas BourdelGaël Varoquaux
Jean-François ClémentThierry BotterJ.-P. BrantutRob Nyman
BIOPHOTONICSKaren Perronet
David Dulin
THEORY L. Sanchez-Palencia
Pierre Lugan
Nathalie Wesbrook
Chris Westbrook
OPTO-ATOMIC CHIPKarim el Amili
Sébastien Gleyzes
The He* team
C. Westbrook D. Boiron V. KrachmalnicoffA. Perrin
J.C. Jaskula G. PartridgeM. Bonneau
