Tomographic reconstruction of quantum correlations in excited Bose-Einstein condensates

TL;DR

This paper demonstrates how quantum tomography can effectively characterize and distinguish different quantum states of perturbed Bose-Einstein condensates, providing accurate predictions of their second moments and correlations.

Contribution

It introduces a method to reconstruct the quantum state of a BEC using tomography, enabling detailed analysis of correlations and state distinctions under various conditions.

Findings

Reconstructed density operator predicts second moments accurately for states described by Gross-Pitaevskii.

Including momentum distribution improves predictions for mixed states.

Observation of anomalous second moments allows reliable predictions for amplitude squeezed states.

Abstract

We propose to use quantum tomography to characterize the state of a perturbed Bose-Einstein condensate. We assume knowledge of the number of particles in the zero-wave number mode and of density distributions in space at different times, and we treat the condensate in the Bogoliubov approximation. For states that can be treated with the Gross-Pitaevskii equation, we find that the reconstructed density operator gives excellent predictions of the second moments of the atomic creation- and annihilation operators, including the one-body density matrix. Additional inclusion of the momentum distribution at one point of time enables somewhat reliable predictions to be made for the second moments for mixed states, making it possible to distinguish between coherent and thermal perturbations of the condensate. Finally, we find that with observation of the zero-wave number mode's anomalous second moment the reconstructed density operator gives reliable predictions of the second moments of locally amplitude squeezed states.