Two-component Bose gas in an optical lattice at single-particle filling

TL;DR

This paper investigates a two-component Bose gas in an optical lattice at single-particle filling, deriving an effective Hamiltonian and analyzing its ground state, revealing a transition between Mott insulator and phase-fluctuating states.

Contribution

It introduces a continued-fraction approach to derive an effective Hamiltonian for a two-component Bose gas in an optical lattice and studies its ground state properties.

Findings

Dimerized mean-field state corresponds to a Mott insulator.

Unmodulated lattice exhibits long-range phase fluctuations.

Comparison with single-component Bose gas highlights unique phase behavior.

Abstract

The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly-occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose.