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arXiv:1402.6925 · Physical Review A

Continuous model for bosonic hard spheres in quasi-one-dimensional optical lattices

C. Carbonell-Coronado, Feliciano De Soto, M. C. Gordillo

Published Jun 24, 2013• 6 citations
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Abstract

By means of diffusion Monte Carlo calculations, we investigated the quantum phase transition between a superfluid and a Mott insulator for a system of hard-sphere bosons in a quasi-one-dimensional optical lattice. For this continuous Hamiltonian, we studied how the stability limits of the Mott phase changed with the optical lattice depth and the transverse confinement width. A comparison of these results to those of a one-dimensional homogeneous Bose-Hubbard model indicates that this last model describes accurately the phase diagram only in the limit of deep lattices. For shallow ones, our results are comparable to those of the sine-Gordon model in its limit of application. We provide an estimate of the critical parameters when none of those models are realistic descriptions of a quasi-one-dimensional optical lattice.

DOI
10.1103/physreva.87.063631

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By means of diffusion Monte Carlo calculations, we investigated the quantum phase transition between a superfluid and a Mott insulator for a system of hard-sphere bosons in a quasi-one-dimensional optical lattice. For this continuous Hamiltonian, we studied how the stability limits of the Mott phase changed with the optical lattice depth and the transverse confinement width. A comparison of these results to those of a one-dimensional homogeneous Bose-Hubbard model indicates that this last model describes accurately the phase diagram only in the limit of deep lattices. For shallow ones, our results are comparable to those of the sine-Gordon model in its limit of application. We provide an estimate of the critical parameters when none of those models are realistic descriptions of a quasi-one-dimensional optical lattice.
We studied the superfluid-to-Mott-insulator transition for bosonic hard spheres loaded in asymmetric three-dimensional optical lattices by means of diffusion Monte Carlo calculations. The onset of the transition was monitored through the change in the chemical potential around the density corresponding to one particle per potential well. With this method, we were able to reproduce the results given in the literature for three-dimensional symmetric lattices and for systems whose asymmetry makes them equivalent to a set of quasi-one-dimensional tubes. The location of the same transition for asymmetric systems akin to a stack of quasi-two-dimensional lattices will be also given. Our results were checked against those given by a Bose-Hubbard model for similar arrangements.
We studied the appearance of Mott insulator domains of hard sphere bosons on quasi-one-dimensional optical lattices when a harmonic trap was superimposed along the main axis of the system. Instead of the standard approximation represented by the Bose-Hubbard model, we described those arrangements by continuous Hamiltonians that depended on the same parameters as the experimental setups. We found that for a given trap the optical potential depth, V0{V}_{0}V0​, needed to create a single connected Mott domain decreased with the number of atoms loaded on the lattice. If the confinement was large enough, it reached a minimum when, in the absence of any optical lattice, the atom density at the center of the trap was the equivalent of one particle per optical well. For larger densities, the creation of that single domain proceeded via an intermediate shell structure in which Mott domains alternated with superfluid ones.
We investigate the superfluid-insulator transition of one-dimensional interacting bosons in both deep and shallow periodic potentials. We compare a theoretical analysis based on quantum Monte Carlo simulations in continuum space and Luttinger liquid approach with experiments on ultracold atoms with tunable interactions and optical lattice depth. Experiments and theory are in excellent agreement. Our study provides a quantitative determination of the critical parameters for the Mott transition and defines the regimes of validity of widely used approximate models, namely, the Bose-Hubbard and sine-Gordon models.
One-dimensional Bose gas with contact interaction in optical lattices at zero temperature is investigated by means of the exact diffusion Monte Carlo algorithm. The results obtained from the fundamental continuous model are compared with those obtained from the lattice (discrete) Bose-Hubbard model, using exact diagonalization, and from the quantum sine-Gordon model. We map out the complete phase diagram of the continuous model and determine the regions of applicability of the Bose-Hubbard model. Various physical quantities characterizing the systems are calculated, and it is demonstrated that the sine-Gordon model used for shallow lattices is inaccurate.
We calculated the phase diagram of a continuous system of hard spheres loaded in a quasi-one-dimensional bichromatic optical lattice. The wavelengths of both lattice-defining lasers were chosen to model an incommensurate arrangement. Densities of one particle and half a particle per potential well were considered. Our results can be compared directly to those of the experimental system [L. Fallani, J. E. Lye, V. Guarrera, C. Fort, and M. Inguscio, Phys. Rev. Lett. 98, 130404 (2007)] from which our initial parameters were taken. The phase diagrams for both densities are significatively different from those obtained by describing the same experimental setup with a Bose-Hubbard model.