Images of a Bose-Einstein condensate: diagonal dynamical Bogoliubov vacuum

TL;DR

This paper demonstrates that any time-dependent Bogoliubov vacuum state of a Bose-Einstein condensate can be diagonalized in a suitable basis, facilitating simulations of quantum measurements on excited condensates.

Contribution

It proves the diagonalization of time-dependent Bogoliubov vacua in a dynamic basis, enabling improved simulation methods for quantum measurement processes.

Findings

Diagonal form of Bogoliubov vacuum is achievable in a time-dependent basis.

Application demonstrated through phase imprinting and density measurement of a dark soliton.

Method enhances simulation accuracy of quantum measurements on excited condensates.

Abstract

Evolution of a Bose-Einstein condensate subject to a time-dependent external perturbation can be described by a time-dependent Bogoliubov theory: a condensate initially in its ground state Bogoliubov vacuum evolves into a time-dependent excited state which can be formally written as a time-dependent Bogoliubov vacuum annihilated by time-dependent quasiparticle annihilation operators. We prove that any Bogoliubov vacuum can be brought to a diagonal form in a time-dependent orthonormal basis. This diagonal form is tailored for simulations of quantum measurements on an excited condensate. As an example we work out phase imprinting of a dark soliton followed by a density measurement.