1 / 50

Hanbury Brown and Twiss and other correlations: from photon to atom quantum optics

Hanbury Brown and Twiss and other correlations: from photon to atom quantum optics. Sao Carlos, June 4, 2011. Alain Aspect - Groupe d’Optique Atomique Institut d’Optique – Palaiseau http://www.lcf.institutoptique.fr/atomoptic.

kale
Download Presentation

Hanbury Brown and Twiss and other correlations: from photon to atom quantum optics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. HanburyBrown and Twiss and other correlations: from photon to atom quantum optics Sao Carlos, June 4, 2011 Alain Aspect - Grouped’OptiqueAtomique Institut d’Optique– Palaiseau http://www.lcf.institutoptique.fr/atomoptic

  2. 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

  3. 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

  4. The HB&T experiment: correlations in light? Measurement of the correlation function of the photocurrents at two different points and times Semi-classical model of the photodetection (classical em field, quantized detector): Measure of the correlation function of the light intensity:

  5. The HB&T effect: correlations in light! 2 Lc 1 r1 – r2 tc Light from incoherent source: time and space correlations a 2 1 • time coherence • space coherence A measurement of g(2) -1vs. tand r1-r2yields the coherence volume

  6. The HB&T stellar interferometer: an astronomy tool Measure of the coherence area  angular diameter of a star a  LC L L Lc

  7. The HB&T stellar interferometer: an astronomy tool Measure of the coherence area  angular diameter of a star a  LC L L Lc Equivalent to the Michelson stellar interferometer ? Visibility of fringes r1 r2 r

  8. The HB&T stellar interferometer: an astronomy tool Measure of the coherence area  angular diameter of a star a  LC L L Lc Not the samecorrelationfunction:g(2) vs g(1) HB&T insensitive to atmospheric fluctuations! Equivalent to the Michelson stellar interferometer ? Visibility of fringes r1 r2 r

  9. HBT and Michelson stellar interferometers yield the same quantity Many independent random emitters: complex electric field = sum of many independent random processes Incoherent source Central limit theorem  Gaussian random process Samewidth:  star size Michelson StellarInterferometer HBT StellarInterferometer

  10. The HB&T stellar interferometer:it works! The installation at Narrabri (Australia): it works! HB et al., 1967

  11. HBT intensity correlations: classical or quantum? 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!

  12. Classical wave explanation for HB&T correlations (1): Gaussian intensity fluctuations in incoherent light Gaussian random process  Many independent random emitters: complex electric field fluctuates intensity fluctuates For an incoherent source, intensity fluctuations (second ordercoherencefunction) are related to first ordercoherencefunction

  13. Classical wave explanation for HB&T correlations (2): optical speckle in light from an incoherent source Many independent random emitters: complex electric field = sum of many independent random processes Gaussian random process  • Intensity pattern (speckle) in the observation plane: • Correlation radius Lc l / a • Changes after tc 1 / Dw

  14. The HB&T effect with photons: a hot debate P M 1 j P 2 Strong negative reactions to the HB&T proposal (1955) In term of photon counting joint detection probability single detection probabilities For independent detection events g(2) = 1 g(2)(0) = 2  probability to find two photons at the same placelargerthan the product of simple probabilities:bunching How might independent particles be bunched ?

  15. The HB&T effect with photons: a hot debate P M 1 j P 2 Strong 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 • Experimental demonstration! • 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 cf . Einstein’s discussion of wave particle duality in Salzburg (1909), about black body radiation fluctuations

  16. The HB&T effect with photons: Fano-Glauber quantum interpretation Two photon emitters, two detectors D1 E1 E1 D1  D2 E2 E2 D2  • Initial state: • Emitters excited • Detectors in ground state • 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  Incoherent addition of manyinterferences: factor of 2 (Gaussianprocess)

  17. 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” interaction cf. Bose-Einstein Condensation (letter from Einstein to Schrödinger, 1924) Twoentangledparticlesinterferenceeffect, and the ability to prepare and observe individual pairs, isat 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/

  18. Intensity correlations in laser light? yet more hot discussions! Phys Rev Lett 1963 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)(t) Quantum description identical by use of Glauber-Sudarshan P representation (coherent states ) Simple classical model for laser light:

  19. 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

  20. 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

  21. 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 state • Single 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: Totally analogous to HB&T: continuous atomic beam

  22. Atomic density correlation (“noise correlation”): a new tool to investigate quantum gases • 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) Interaction energy of a sample of cold atoms • for a thermal gas (MIT, 1997) • for a quasicondensate (Institut d’Optique, 2003) Noise correlation in absorption images of a sample of cold atoms (as proposed by Altmann, Demler and Lukin, 2004) • 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.,Institutd’Optique, 2005) • … (Inguscio, …)

  23. Atomic density correlation (“noise correlation”): a new tool to investigate quantum gases • 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) Interaction energy of a sample of cold atoms • for a thermal gas (MIT, 1997) • for a quasicondensate (Institut d’Optique, 2003) Noise correlation in absorption images of a sample of cold atoms (as proposed by Altmann, Demler and Lukin, 2004) Measurements of atomicdensityaveraged over small volumes What about individual atoms correlation function measurements?

  24. 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

  25. Metastable Helium 2 3S1An unique atomic species • Triplet () 2 3S1cannot 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) 2 3P2 1.08 mm 2 3S1 • Large electronic energy stored in He* • ionization of colliding atoms or molecules • extraction of electron from metal:single atom detection with Micro Channel Plate detector 19.8 eV 1 1S0 Similar techniques in Canberra, Amsterdam, ENS

  26. He* laser cooling and trapping, and MCP detection: unique tools 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 He* on the Micro Channel Plate detector: an electron is extracted  multiplication  observable pulse Single atom detection of He* Analogue of single photon countingdevelopment, in the early 50’s Tools crucial to the discovery of He* BEC (Institut d’Optique, 2000)

  27. 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 !      

  28. 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) y x Cold sample z Detector of the atom positions in a single cloud Repeat many times (accumulate records) at same temperature Pulsed experiment: 3 dimensions are equivalent ≠ Shimizu experiment

  29. g(2) correlation function: 4He* thermal sample (above TBEC) • For a given record (ensemble of detection events for a given released sample), evaluate probability of a pair of atoms separated by Dx, Dy, Dz. •  [p(2)(Dx, Dy, Dz)]i • Average over many records (at same temperature) • Normalize by the autocorrelation of average (over all records) 1.3 mK Bump visibility = 5 x 10-2 Agreement with prediction (resolution)  HBT bumparoundDx =Dy =Dz = 0

  30. The detector resolution issue y x z Dxdet If the detector resolutionDxdet is larger than the HBT bump width Lcx then the height of the HB&T bump is reduced: • Dysource=Dzsource 4 mm  Lcy = Lcz =500mm • Dxsource 150 mm  Lcy = 13mm At 1 mK, Resolution (200 mm) sufficientalongy and zbut insufficientalongx. Expected reduction factor of 15 NB: vertical resolution is more than sufficient: Dzdet  V Dt  1 nm 

  31. x,y correlation function (thermal 4He*) Various source sizes 0.55 mK 1.3 mK Dx Dy 1.0 mK Dx Dy g(2)(Dx,Dx,Dx) : pancake perpendicular to x (long dimension of the source) 1.35 mK x

  32. g(2) correlation function in a Bose Einstein Condensate of 4He* (T < Tc) Decrease the atomiccloudtemperature: phase transition to BEC No bunching:analogous to laser light (see also Öttl et al.; PRL 95,090404 Truscott, Baldwin et al., 2010)

  33. 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 vs4He).

  34. The HB&T effect with fermions: antibunching Two paths to go from one initial state to one final state: quantum interference Amplitudes added with opposite signs: antibunching Two particles interference effect: quantum weirdness, lack of statistical independence although no real interaction … no classical interpretation impossible for classical densities

  35. The HB&T effect with fermions: antibunching Two paths to go from one initial state to one final state: quantum interference Amplitudes added with opposite signs: antibunching Two particles interference effect: quantum weirdness, lack of statistical independence although no real interaction … no classical interpretation 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

  36. 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 !

  37. HB&T with 3He* and 4He*an almost ideal fermion vs boson comparison Neutral atoms: interactions negligible • Samples of 3He* and 4He*at same temperature (0.5 mK, sympathetic cooling) in the trap : •  same size (same trapping potential) • Coherence volume scales as the atomic masses (de Broglie wavelengths) • ratio of 4 / 3 expectedfor the HB&T widths Collaboration with VU Amsterdam (W Vassen et al.)

  38. HB&T with 3He* and 4He*fermion versus bosons Jeltes et al. Nature 445, 402–405 (2007) (Institut d’Optique-VU) • Direct comparison: • same apparatus • same temperature 4He* Ratio of about 4 / 3 found for HB&T signals widths (mass ratio, ie de Broglie wavelengths ratio) 3He* Pure quantum statistics effect Collaboration with VU Amsterdam (W Vassen et al.) Fermion anticorrelation also seen in Mainz : Rom et al. Nature 444, 733–736 (2006)

  39. 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

  40. 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 No equivalent to fermions Correlations in atomic cascade photon pairs (1967)Entanglement, Bell in. tests (1972,1982) Correlations in atom pairs from molecular dissociation (D Jin) No entanglementobservedyet 1970: photon pairs in non-linear crystal 1987: entanglement easier to obtain An equivalent in non-linear atom optics?

  41. Non linear mixing of matter waves(4-wave mixing) (3) non-linear atom optics process (NIST, MIT) Appearance of a daughter BEC p3 3 colliding BEC’s p1 p2 p2 p1 Amplification of probe 3 p3 p4

  42. (3) non-linear mixing of matter waves (4-wave mixing) Stimulated process : appearance of a daughter BEC observed (NIST, MIT) daughter BEC p3 3 colliding BEC’s p1 p2 p2 p1 Amplification of 3 p3 p4 Spontaneous process: appearance of pairs predicted (Meystre, Cirac-Zoller, Drummond, Kurisky, Moelmer…) p3 spontaneous atom pairs p’3 2 colliding BEC’s p1 p2 p2 p1 p’4 p4

  43. Observation of spontaneous 4-wave mixing in collision of two 4He* BEC’s p reconstruction by elementary kinematics (free fall) Observation of the full s-wave scattering spherical shell s-wave collision halo ( cf. MIT, Penn state, Amsterdam)

  44. Observation of correlated 4He* pairs p3 Colliding BEC’s p1 p2 p4 Momentum correlation in scattered atoms Correlation of antipodes on momentum sphere Atoms in pairs of opposite momenta A. Perrin et al. PRL 2007 Are there other correlations in the momentum distribution?

  45. 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)? Correlation between atoms of two different pairs: trace over the partners yields Gaussian statistics. Recently observed with photons

  46. Summary: progress in quantum atom optics HB&T observed with bosons and fermions Observation of pairs of atoms obtained in a spontaneous non-linear atom optics process • Fully 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)

  47. Summary: progress in quantum atom optics HB&T observed with bosons and fermions Observation of pairs of atoms obtained in a spontaneous non-linear atom optics process • Fully 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) Do we have entangled atom pairs? Simplified model, in analogy to quantum photon optics: yes! Entanglement in momentum space: To be distinguished from incoherent mixture of

  48. Demonstration of momentum entanglement A possible scheme 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--, vsfa - fb With photons Proposal: Horne, Shimony, Zeilinger: PRL 1989 Expt: Rarity, Tapster, PRL 1990

  49. Demonstration of momentum entanglement A possible scheme 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--, vsfa - fb With photons Proposal: Horne, Shimony, Zeilinger: PRL 1989 Expt: Rarity, Tapster, PRL 1990 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) hopefully before 2024!

  50. Groupe d’Optique Atomique duLaboratoire Charles Fabry de l’Institut d’Optique Chris Westbrook Philippe Bouyer V. Krachmalnicoff A. Perrin C. Westbrook D. Boiron Fermions Bosons mixtures He* BEC Denis Boiron A. Perrin V Krachmalnicoff Hong ChangVanessa Leung Thomas BourdelGaël Varoquaux Jean-François ClémentThierry BotterJ.-P. Brantut Rob Nyman 1 D BEC ATOM LASER Vincent JosseDavid Clément Juliette Billy William GuérinChris VoZhanchun Zuo ATOM CHIP BEC BIOPHOTONICS Isabelle Bouchoule Jean-Baptiste TrebiaCarlos Garrido Alzar Karen PerronetDavid Dulin The He* team Nathalie Wesbrook THEORYL. Sanchez-PalenciaPierre Lugan OPTO-ATOMIC CHIP ELECTRONICSAndré Villing Frédéric Moron Karim el AmiliSébastien Gleyzes M. Bonneau J.C. Jaskula G. Partridge

More Related