Quantum Field Theoretical Analysis on Unstable Behavior of Bose-Einstein Condensates in Optical Lattices

TL;DR

This paper uses quantum field theory to analyze the unstable behavior of Bose-Einstein condensates in optical lattices, focusing on dynamical instability and complex eigenmodes, with results aligning with nonlinear Schrödinger equation predictions.

Contribution

It introduces a quantum field theoretical framework to diagonalize the Hamiltonian of unstable Bose-Einstein condensates, providing a consistent formulation for analyzing their dynamics.

Findings

Identification of complex eigenmodes causing instability

Consistent formulation of the Hamiltonian with physical states

Numerical results matching discrete nonlinear Schrödinger equation

Abstract

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows a unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consitent with as those given by the discrete nonlinear Schrodinger equation.