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

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.

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Dynamic properties of the one-dimensional Bose-Hubbard model
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• Do mixtures of bosonic and fermionic atoms adiabatically heat up in optical lattices?
• Adiabatic cooling of Fermions in an optical lattice
• Bosonic superfluid-insulator transition in continuous space
• Lieb-Liniger gas in a constant force potential
• Strongly interacting bosons in a 1D optical lattice at incommensurate densities
• Perturbative correction to the ground state properties of one-dimensional strongly interacting bosons in a harmonic trap
• Approximate expression for the dynamic structure factor in the Lieb-Liniger model

Cited by in corpus (7)

• The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo
• Correlation induced localization of lattice trapped bosons coupled to a Bose-Einstein condensate
• Static and dynamic phases of a Tonks-Girardeau gas in an optical lattice
• A continuous model for bosonic hard spheres in quasi one-dimensional optical lattices
• Zero-temperature phase diagram of hard sphere bosons in asymmetric three dimensional optical lattices
• Quasi-superfluid and Quasi-Mott phases of strongly interacting bosons in shallow optical lattice
• One-Dimensional Quench Dynamics in an Optical Lattice: sine-Gordon and Bose-Hubbard Descriptions