Nonclassical atom pairs in collisions of BECs: from squeezing to Bell test proposals

Transcription

1 Nonclassical atom pairs in collisions of BECs: from squeezing to Bell test proposals Piotr Deuar Institute of Physics, Polish Academy of Sciences, Warsaw, Poland With particular thanks to: Chris Westbrook, Denis Boiron, J-C Jaskula, Alain Aspect, Marie Bonneau, Valentina Krachmalnicoff, Vanessa Leung Institut d'optique, Palaiseau, France Andrew Truscott, Ken Baldwin, Bryce Henson, Roman Khakimov Australian National University, Canberra, Australia Karen Kheruntsyan, Robert Lewis-Swan University of Queensland, Brisbane, Australia Marek Trippenbach, Jan Chwedeńczuk, Paweł Ziń, Tomasz Wasak University of Warsaw, Poland

2 Outline (ambitious version) The Palaiseau He* experiments Numerical description (STAB method) Number difference squeezing Cauchy-Schwartz inequality violation Hong-Ou-Mandel dip Towards Bell inequality violation by positions of massive particles 2/31

3 The Palaiseau He* experiments 3/31

4 BEC collision with He* makes pairs, detects single atoms Multi channel plate short time momentum distribution = long time position distribution Single-atom tomography E ~ 20eV 4 He in metastable state Single atom detection efficiency η ~ 12% Supersonic collision t=0 Bragg pulse t=0.3 s expansion momentum distribution Perrin, Chang, Krachmalnicoff, Schellekens, Boiron, Aspect, Westbrook, PRL 99, (2007) 4/31

5 Two body collisions in the halo Above the speed of sound behaves as a superfluid a condensate no longer k-space density BEC k BEC -k PD, Ziń, Chwedeńczuk, Trippenbach, EPJD 65, 19 (2011) BEC width in k-space is Scattered atoms well separated from BEC 5/31

6 Bogoliubov pair creation Assume small BEC incoherent part scattered atoms K.E. + trap Potential from BEC For scattered atoms Pair creation cf. nondegenerate parametric down conversion 6/31

7 Experiment - correlations Kheruntsyan, Jaskula, PD, Bonneau, Partridge, Ruaudel, Boiron, Lopes, Westbrook, PRL 108, (2012) Cross-correlation (pair creation) k m z ism atc h Self-correlation (Hanbury Brown-Twiss) m k xy y k m z ism atc h k y z m is ch t a z 7/31 m xy m is ch t a

8 Quantum nonlocality Bell's theorem: Any hidden variable theory consistent with relativity cannot describe all the phenomena of quantum mechanics 1935 EPR paradox quantum mechanics is incomplete 1964 Bell's inequality either quantum mechanics or local realism Experiments: Freedman & Clauser Aspect [photons] looks like it's quantum mechanics Zeilinger (closed locality loophole) Wineland (closed detection loophole) [ion internal states] Zeilinger (ruled out Leggett-type non-local realism) Martinis [solid state qubits] -... Now consider separated entangled atomic pairs: - entangled position of massive particles 8/31

9 Nonclassical atom optics in the Palaiseau experiment 2005 single atom measurements, HBT Schellekens, Hoppeler, Perrin, Viana Gomes, Boiron, Aspect, Westbrook, Science 310, 648 (2005) 2007 Observation of correlations across halo Perrin, Chang, Krachmanicoff, Schellekens, Boiron, Aspect, Westbrook, PRL 99, (2007) 2010 sub-poissonian fluctuations of number difference across halo (cf. antibunching) Jaskula, Bonneau, Partridge, Krachmalnicoff, PD, Kheruntsyan, Aspect, Boiron, Westbrook, PRL 105, (2010) 2012 Cauchy-Schwartz inequality violation Kheruntsyan, Jaskula, PD, Bonneau, Partridge, Ruaudel, Lopes, Boiron, Westbrook, PRL 108, (2012) 2015 Hong-Ou-Mandel effect Lopes, Imanaliev, Aspect, Cheneau, Boiron, Westbrook, Nature 520, 66 (2015) 9/31

10 Numerical description (STAB) 10/31

11 Theory: Bogoliubov equations for the scattered field Evolution equations: Initial condition: 11/31

12 Bogoliubov hurdles Looks like a linear problem, so why not just diagonalize and have everything, but The numerical lattice might be too large ( points in a 3D calculation) (note also the human time bottleneck!) 2. BEC evolves parallel to the Bogoliubov field would have to re-diagonalize at each time step (boooo...) Diagonalization can be avoided by using the positive-p representation 12/31

13 Positive-P representation Drummond, Gardiner, J Phys A 13, 2353 (1980) Drummond, Gardiner J. Phys. A 13, 2353 (1980) Hilbert space dimension nm Probability distribution of bra & ket coherent fields The distribution P is positive & real Density matrix distribution P for the fields random samples of the fields From nm variables we get samples x M n = Hilbert space dimension at one point M = numerical lattice size 13/31

14 Simulation - STAB method PD, Chwedeńczuk, Ziń, Trippenbach, PRA 83, (2011) Bogoliubov GPE mean field quantum noise Bogoliubov-de Gennes form Can use plane wave basis ---> no diagonalizing of 107 X 107 matrices :) Gaussian real white noise 14/31

15 Evolution single realization 15/31

16 Number difference squeezing 16/31

17 Experiment number squeezing Jaskula, Bonneau, Partridge, Krachmalnicoff, PD, Kheruntsyan, Aspect, Boiron, Westbrook, PRL 105, (2010) Number difference squeezing between opposite regions of the halo.(sub-poissonian fluctuations) 17/31

18 Cauchy-Schwarz inequality 18/31

19 Cauchy-Schwartz inequality For vectors: Limit on allowed fluctuations of random variables: Obeyed by classically understood field intensities. Simplest test of stronger-than-classical correlation Precursor, necessary condition of Bell tests etc. Violated in the past in quantum optics: - Clauser, Phys. Rev. D 9, 853 (1974) - Kimble Dagenais, Mandel, PRL 39, 691 (1997) - Zou, Wang, Mandel, Opt. Commun. 84, 351 (1991) - Marino, Boyer, Lett, PRL 100, (2008) 19/31

20 Cauchy-Schwartz quantum formulation Consider 2 boson modes e.g. small bins in k-space and simultaneous detection of two particles: - coincidence rate for ~ two particles in mode 1: - coincidence counts for one particle in each mode: ~ If these came from classical field amplitudes, they would obey the Cauchy-Schwartz inequality: For classical fields 20/31

21 Multimode Cauchy-Schwartz violation Kheruntsyan, Jaskula, PD, Bonneau, Partridge, Ruaudel, Boiron, Lopes, Westbrook, PRL 108, (2012) Consider two bins in k-space, rather than modes Bin averaged correlations Opposing zones simulation Neighbour zones CLASSICAL REGION compare 21/31

22 Hong Ou Mandel demonstration 22/31

23 Hong Ou Mandel effect Two indistinguishable particles on beam splitter Top reflected Source: Wikipedia Pass through Both reflected Bottom reflected destructively interefere -1 phase shift due to unitarity 23/31

24 HOM experiment Lopes, Imanaliev, Aspect, Cheneau, Boiron, Westbrook, Nature 520, 66 (2015) 24/31

25 HOM violation Lopes, Imanaliev, Aspect, Cheneau, Boiron, Westbrook, Nature 520, 66 (2015) 25/31

26 Towards Bell inequality violation 26/31

27 The dream: Rarity-Tapster Bell inequality experiment Bell inequality violation due to a different distribution of particles, not internal states down-converted pair collision Precursor: Rarity-Tapster Experiment σ screen Bell inequality violation beam splitter down-converted pair With local realism Bragg pulses Rarity & Tapster, PRL 64, 2495 (1990) Coincidence rate coincidence counting 27/31

28 The dream: Rarity-Tapster Bell inequality experiment Lewis-Swan, Kheruntsyan, PRA 91, (2015) ATOMS PHOTONS 28/31

29 Simulations using the STAB method look promising k-space Lewis-Swan, Kheruntsyan, PRA 91, (2015) BUT... Requires very low density to avoid double occupation of counting bins. Number of experimental runs needed scales as density^2 Quantum efficiency ~ 10% 29/31

30 Wrap-up Supersonic disturbances in ultracold atomic clouds produce correlated fewatom states similar to few-photon states Quantum atom optics Many nonclassical phenomena have already been seen Sub-Poissonian number fluctuations Cauchy-Schwartz inequality violation Hong-Ou-Mandel effect Long-time aim: Bell inequality violation via differing mass distributions Thank you! 30/31

31 Thank you Collaboration IF PAN Igor Nowicki Joanna Pietraszewicz Institut d'optique Chris Westbrook Denis Boiron Alain Aspect Vanessa Leung Jean-Christophe Jaskula Valentina Krachmalnicoff Marie Bonneau Josselin Ruaudel Raphael Lopes Australian National University Andrew Truscott Ken Baldwin Bryce Henson Roman Khakimov Funding Warsaw University Marek Trippenbach Jan Chwedeńczuk Pawel Ziń Tomasz Wasak Swinburne University of Technology Peter Drummond University of Queensland Karen Kheruntsyan Tod Wright 31/31

32 32/31

33 New experimental setup in moving lattice Bonneau, Ruaudel, Lopes, Jaskula, Aspect, Boiron, Westbrook, PRA 87, (R) (2013) Dispersion relation Number squeezing between bins covering k and k peaks 0 33/31 2

34 He* BEC collisions (T=0) Frequency doubling Coherent Energy stolen from mf(t) Main halo k, -k pairs Energy resonant Mean-field Induced halo k0± δk pairs Energy stolen from mf(t) end of collision k As per experiment: Krachmalnicoff, Jaskula, Bonneau, Leung, Partridge, Boiron, Westbrook, PD, Zin, Trippenbach, Kheruntsyan, PRL 104, (2010) BEC 34/31