Time-dependent quantum many-body theory of identical bosons in a double well: Early time ballistic interferences of fragmented and number entangled states

TL;DR

This paper develops a time-dependent multiconfigurational theory to model the complex many-body dynamics of bosonic gases in traps, revealing distinct interference patterns for different quantum states upon expansion.

Contribution

It introduces a novel, self-consistent dynamical framework that captures atomic correlations and mean-field effects in bosonic many-body systems from first principles.

Findings

Different interference patterns for fragmented and entangled states

Atomic correlations significantly influence expansion dynamics

Efficient numerical implementation of the theory

Abstract

A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states.