Phase space manipulations of many-body wavefunctions

TL;DR

This paper develops a theoretical framework using the Wigner function to manipulate many-body wavefunctions in phase space, enabling operations like squeezing, rotation, and time reversal, with applications in cooling and robustness enhancement.

Contribution

It introduces a unified approach to phase space manipulation of many-body wavefunctions, including novel techniques for cooling and robustness improvements.

Findings

Squeezing and rotation can be used for cooling in quantum gases.

Optical analogies help understand phase space manipulations.

Spin-echo techniques improve robustness of velocity dispersion reduction.

Abstract

We explore the manipulation in phase space of many-body wavefunctions that exhibit self-similar dynamics, under the application of sudden force and/or in the presence of a constant acceleration field. For this purpose, we work out a common theoretical framework based on the Wigner function. We discuss squeezing in position space, phase space rotation and its implications in cooling for both non-interacting and interacting gases, and time reversal operation. We discuss various optical analogies and calculate the role of spherical-like aberration in cooling protocols. We also present the equivalent of a spin-echo technique to improve the robustness of velocity dispersion reduction protocols.