1112.3657 (Achilleas Lazarides et al.)

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

Achilleas Lazarides, Masudul Haque

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.

View original: http://arxiv.org/abs/1112.3657