Quantum atom optics with Bose-Einstein condensates

Transcription

1 Quantum atom optics with Bose-Einstein condensates 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 Basic ultracold Bose gas [thinking of He*] Discretize lattice, but take 0 Bose-Hubbard ^_^ 2/22

3 Correlated pair creation Bogoliubov approximation Assume small BEC incoherent part scattered atoms K.E. + trap Potential from BEC For scattered atoms Pair creation 3/22

4 BEC collision with He* makes pairs, detects single atoms Supersonic collision Palaiseau experiment Chris Westbrook group 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% 4/22

5 Theory: try Bogoliubov equations for the scattered field Evolution equations: Initial condition: 5/22

6 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...) 3. Assumption of small may fail Diagonalization can be avoided by using the positive-p representation 6/22

7 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 7/22

8 Schrodinger Langevin equations Evolution of diffusive evolution of P (Fokker-Planck equation) random walk of samples of Observables Expectation values of observables moments of P stochastic averages of samples As samples we get better precision 8/22

9 Bare positive-p equations PD, Drummond PRL 98, (2007) PD, Drummond, PRL 98, (2007) Mean field GP equation Rest of quantum mechanics Gaussian real white noise trouble: noise amplification Deuar, PRL 103, (2009) 9/22

10 Solution: Bogoliubov positive-p equations (STAB method) PD, Chwedeńczuk, Ziń, Trippenbach, PRA 83, (2011) PD, Chwedeńczuk, Trippenbach, Ziń, PRA 83, (2011) condensate Treat only Bogoliubov fluctuation field MUST BE small using positive-p representation Mean field Now equations are linear > no blow-up of noise :) Can use plane wave basis ---> no diagonalizing of 106 X 106 matrices :) ---> less human time used! :) 10/22

11 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) 11/22

12 The dream: Rarity-Tapster Bell inequality experiment Bell inequality violation due to a different distribution of particles, not internal states Rarity-Tapster experiment σ Bell inequality violation Precursor: A similar concept with He* Atomic HOM collision experiment down-converted pair screen Lopes et al., Nature 520, 66 (2015) Bragg pulses down-converted pair Rarity & Tapster, PRL 64, 2495 (1990) With local realism beam splitter Coincidence rate coincidence counting 12/22

13 The dream: Rarity-Tapster Bell inequality experiment Lewis-Swan, Kheruntsyan, PRA 91, (2015) ATOMS PHOTONS 13/22

14 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% 14/22

15 Canberra He* Experiment Truscott group - Very stable system, nice counting statistics - Measured up to 6th order correlations Dall, Manning, Hodgman, RuGway, Kheruntsyan, Truscott, Nature Phys. 9, 341 (2013) g(2)( z) g(3)( z) g(4)( z) g(5)( z) g(6)( z) 15/22

16 Phase grains - Single-shot effect - Four-wave mixing, but spontaneously seeded Spontaneous 4WM + Bose enhancement Seeded 4WM: seed Norrie, Ballagh, Gardiner, PRA 73 Deng, Hagley, Wen, Trippenbach, Band, Julienne, Simsarian, Helmerson, Rolston, Phillips, Nature 398, 218 (1999) PD, Wasak, Ziń, Chwedeńczuk, Trippenbach, PRA 88, (2013) 16/22

17 Evolution (single realization) in x space STAB simulation 17/22

18 Evolution (single realization) in k space STAB simulation 18/22

19 Seeking phase grains in the ANU experiment: simulations 19/22

20 Seeking phase grains: simulated particle positions Looks like nice phase grains present. 20/22

21 Not so visible with 10% detection efficiency.. 21/22

22 Wrap-up Supersonic disturbances in ultracold atomic clouds produce correlated few-atom states similar to few-photon states Quantum atom optics Examples of interesting phenomena include: Nonclassical atom pairs Spontaneous growth of phase grains - mini-condensates many more... Long-time aim: Bell inequalities using mass distributions Still trying... Poor detection efficiency seems to be the main hurdle Useful to incorporate this in simulations Thank you! 22/22