Symplectic tomography of ultracold gases in tight-waveguides

TL;DR

This paper introduces symplectic tomography for ultracold gases in tight-waveguides, providing a method to measure and reconstruct quantum states from density and momentum data during various dynamical evolutions.

Contribution

It presents a novel operational approach to measure the reduced single-particle symplectic tomogram and reconstruct the one-body density matrix in ultracold quantum gases.

Findings

RSPST can be obtained from time evolution of density profiles.

Method applicable during free expansion, gravity fall, and harmonic oscillations.

Allows reconstruction of the one-body density matrix.

Abstract

The phase space is the natural ground to smoothly extrapolate between local and non-local correlation functions. With this objective, we introduce the symplectic tomography of many-body quantum gases in tight-waveguides, and concentrate on the reduced single-particle symplectic tomogram (RSPST) whose marginals are the density profile and momentum distribution. We present an operational approach to measure the RSPST from the time evolution of the density profile after shutting off the interactions in a variety of relevant situations: free expansion, fall under gravity, and oscillations in a harmonic trap. From the RSPST, the one-body density matrix of the trapped state can be reconstructed.