Quantum dynamics in ultra-cold atomic physics

Abstract

We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially large. These phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum EPR entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorp- tion, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.

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Cited by in corpus (9)

• Functional Wigner representation of BEC quantum dynamics
• Center-of-mass motion as a sensitive convergence test for variational multi-mode quantum dynamics
• Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below $\hslash$
• Many-body quantum dynamics of an asymmetric bosonic Josephson junction
• Effective two-mode description of a few ultra-cold bosons in a double-well potential
• Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction
• Bose-Einstein condensate fluctuations versus an interparticle interaction
• Grassmann phase-space methods for fermions: uncovering classical probability structure
• Coherent functional expansions in quantum field theory