Correlated atom pairs in collisions of BECs: from nonclassical states to Bell test proposals

Transcription

1 Correlated atom pairs in collisions of BECs: from nonclassical states to Bell test proposals Piotr Deuar Institute of Physics, Polish Academy of Sciences, Warsaw Experiment Chris Westbrook (Palaiaseau): Denis Boiron Jean-Christophe Jaskula Marie Bonneau Guthrie Partridge Josselin Ruaudel Raphael Lopes + Alain Aspect Theory Piotr Deuar (IF PAN) Karen Kheruntsyan (Uni. Queensland) Marek Trippenbach (UW) Paweł Ziń Jan Chwedeńczuk Tomasz Wasak

2 Outline 1. Atomic pair creation 2. Palaiseau He* experiment 3. Quantum nonlocality experiments + Bell test proposal 4. Tradeoffs for avoiding degradation of quantum correlations 5. New experimental setup in lattice 2/24

3 Atom pair creation 4 wave mixing Vogels, Xu, Ketterle, PRL 89, (2002) Spin dynamics RuGway, Hodgman, Dall, Johnsson, Truscott, PRL 107, (2011) Dissociation of molecular BEC Pair emission from a 1D gas Bucker, Grond, Manz, Berrada, Betz, Koller, Hohenster, Schumm, Perrin, Schmiedmayer, Nature Phys. 7, 608 (2011) Greiner, Regal, Stewart, Jin, PRL 94, (2005) Lücke, Scherer, Kruse, Pezzé, Deuretzbacher, Hyllus,Topic, Peise, Ertmer, Arlt, Santos, Smerzi, Klempt, Science 334, 773 (2011) 3/24

4 BEC collision Palaiseau experiment Single-atom tomography t=0 Bragg pulse t=0.3 s expansion momentum distribution E ~ 20eV 4 He in metastable state Perrin, Chang, Krachmalnicoff, Schellekens, Boiron, Aspect, Westbrook, PRL 99, (2007) Single atom detection efficiency η ~ 12% 4/24

5 BEC collision 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 5/24

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 6/24

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 m is ch t a k xy y k z mis ma t ch k y z z 7/24 m xy m is ch t a

8 Simulation - t-dependent Bogoliubov approx. PD, Chwedeńczuk, Ziń, Trippenbach, PRA 83, (2011) Useful to see what's going on (only have access to the final distribution in experiment) condensate Bogoliubov fluctuation field MUST BE small Bogoliubov is easily solvable. However, 3D simulation: 107 spatial grid points. H = x matrix? Did not try to diagonalize Treat only using positive-p representation See also Wigner treatment: Sinatra, Castin & Lobo J. Mod Opt 47, GP mean field Can use plane wave basis ---> no diagonalizing of 107 X 107 matrices :) 8/24

9 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 mass - objects with internal structure 9/24

10 So far in Palaiseau 2005 single atom measurements, HBT M. Schellekens et al, Science 310, 648 (2005) 2007 Observation of correlations across halo A. Perrin et al, PRL 99, (2007) 2010 sub-poissonian fluctuations of number difference across halo (cf. antibunching) J.C. Jaskula et al, PRL 105, (2010) 2012 Cauchy-Schwartz inequality violation K. V. Kheruntsyan et al, PRL 108, (2012) 10/24

11 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) 11/24

12 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) 12/24

13 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 13/24

14 (half-) collision started by Bragg pulse Experiment setup, bins Small time BEC BIN halo BIN BEC short time momentum distribution = long time position distribution MCP 14/24

15 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 15/24

16 Rarity-Tapster Bell test A similar concept with He* Rarity-Tapster experiment σ Bell inequality violation collision down-converted pair screen Bragg pulses down-converted pair Rarity & Tapster, PRL 64, 2495 (1990) beam splitter coincidence counting 16/24

17 Tradeoffs for quantum effects : simple model PD, Wasak, Zin, Chwedeńczuk, Trippenbach, PRA 88, (2013) Gaussian ansatz for correlations Multimode relationships for number squeezing : LARGE BIN Green: simple model Blue, red: full simulation long t w SMALL BIN short t w V: 17/24

18 Tests with a simplified system We simulated a simplified model with spherical initial condensates of various particle numbers 1 shot to extract the generic behaviour BIN SIZE 18/24

19 Degradation of squeezing PD, Wasak, Zin, Chwedeńczuk, Trippenbach, PRA 88, (2013) Full calculation Squeezing still destroyed Reduced model (RBM) Halo: free flight + pair production only Condensates: stiff movement 19/24

20 Monochromatic source PD, Wasak, Zin, Chwedeńczuk, Trippenbach, PRA 88, (2013) Full calculation Monochromatic source (plane waves) Full calculation Reduced model (RBM) RBM Squeezing becomes almost perfect, even with all extra Bogoliubov effects 20/24

21 Dense vs. dilute halos PD, Wasak, Zin, Chwedeńczuk, Trippenbach, PRA 88, (2013) High density Low density Many particles per bin 1 or 0 particles per bin Good signal Poor signal Strong degradation Little degradation 21/24

22 Degradation: summary Degradation of squeezing can be traced back to the non-monochromaticity of the mother clouds. Spatial extent of phase grains mediates the appearance of stray atoms in opposite bins. (via a number of processes). Sensitivity to the non-monochromatic source grows with halo density. Low density halos are advantageous because the probability of having some uncorrelated pairs in the opposite bin is low, since the neighboring bins are mostly empty. 22/24

23 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 23/24 2

24 Summary Collisions of BECs produce strongly correlated atom pairs Similar to non-degenerate parametric down-conversion Cauchy-Schwartz violation with massive, separated particles Simplest non-classicality test Precursor of Bell tests on entanglement of mass Outlook: Bell inequality tests Rarity-Tapster scheme Non-monochromatic nature of clouds mediates degradation Through the presence of stray pairs Badness can be dodged at the cost of poor SNR 24/24