Bogoliubov theory for atom scattering into separate regions

Abstract

We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein Condensate into two well-separated regions. We find the full dynamics of the pair-production process, calculate the first and second order correlation functions and show that the system is ideally number-squeezed. We calculate the Fisher information to show how the entanglement between the atoms from the two regions changes in time. We also provide a simple expression for the lower bound of the useful entanglement in the system in terms of the average number of scattered atoms and the number of modes they occupy. We then apply our theory to a recent "twin-beam" experiment [R. Bücker {\it et al.}, Nat. Phys. {\bf 7}, 608 (2011)]. The only numerical step of our semi-analytical description can be easily solved and does not require implementation of any stochastic methods.

11 pages, 6 figures

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• Nonlinear atom interferometer surpasses classical precision limit
• Squeezing and entanglement in a Bose-Einstein condensate
• Twin matter waves for interferometry beyond the classical limit
• Observation of atom pairs in spontaneous four wave mixing of two colliding Bose-Einstein Condensates
• Violation of the Cauchy-Schwarz inequality with matter waves
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• Violation of the Cauchy-Schwarz Inequality in the Macroscopic Regime
• Paired atom laser beams created via four-wave mixing
• Dynamics of parametric matter wave amplification
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Cited by in corpus (13)

• Collective emission of matter-wave jets from driven Bose-Einstein condensates
• On the observation of nonclassical excitations in Bose-Einstein condensates
• Bell inequality, Einstein-Podolsky-Rosen steering and quantum metrology with spinor Bose-Einstein condensates
• Characterization of the stimulated excitation in a driven Bose-Einstein condensate
• Inflationary preheating dynamics with ultracold atoms
• Four-wave mixing in spin-orbit coupled Bose-Einstein condensates
• Pair correlation of atoms scattered from colliding Bose-Einstein quasicondensates
• Emission of particles from a parametrically driven condensate in a one-dimensional lattice
• The influence of the interaction between quasiparticles on parametric resonance in Bose-Einstein quasicondensates
• The influence of interaction between quasiparticles on parametric resonance process in Bose-Einstein condensates
• Atomic twin-beams and violation of a motional-state Bell inequality from a phase-fluctuating quasi-condensate source
• Properties of atomic pairs produced in the collision of Bose-Einstein condensates
• Quantum interferometry in multi-mode systems