Quantum dynamics in ultra-cold atomic physics

TL;DR

This paper reviews advanced phase-space methods for analyzing quantum dynamics in ultra-cold atomic systems, covering both theoretical frameworks and practical applications like entanglement, quantum collisions, and interferometry.

Contribution

It introduces recent developments in phase-space representations, including non-classical approaches with higher dimensionality, for complex quantum systems in ultra-cold atomic physics.

Findings

Demonstrates quantum EPR entanglement in a four-mode BEC

Analyzes quantum collisions with up to 106 modes and 105 particles

Explores quantum entropy and variational optimization in phase-space

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.