Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond

TL;DR

This paper explores the behavior of one-dimensional bosons in optical lattices of varying depths, connecting the Bose-Hubbard and sine-Gordon models, and provides a comprehensive phase diagram relevant for experiments.

Contribution

It extends the phase diagram of 1D bosons in optical lattices from deep to shallow regimes using Bose-Fermi mapping, bridging Bose-Hubbard and sine-Gordon models.

Findings

Derived the phase diagram across different lattice depths.

Analyzed equations of state and energy gaps.

Explored density profiles in harmonic traps.

Abstract

We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the sine-Gordon regime of weak lattices, to the complete absence of a lattice. Using the Bose-Fermi mapping between strongly interacting bosons and weakly interacting fermions, we derive the phase diagram in the parameter space of lattice depth and chemical potential. This extends previous knowledge from tight-binding (Bose-Hubbard) studies in a new direction which is important because the lattice depth is a readily adjustable experimental parameter. Several other results (equations of state, energy gaps, profiles in harmonic trap) are presented as corollaries to the physics contained in this phase diagram. Generically, both incompressible (gapped) and compressible phases coexist in a trap; this has implications for experimental measurements.