Optical lattices as a tool to study defect-induced superfluidity

Abstract

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides a extremely well-controlled model for studying defect-induced superfluidity.

Mott transition for strongly interacting one-dimensional bosons in a shallow periodic potential

“…Recently, a preprint appeared reporting the numerical study of the Mott-U transition with results consistent with ours [49].…”

Static and dynamic phases of a Tonks–Girardeau gas in an optical lattice

“…The gas in this phase therefore represents a momentum delocalized superfluid that exhibits some of the distinct characteristics of both the superfluid and the pinned phase. The observed momentum distribution is similar to the momentum distributions found in supersolids [52] and it has recently been suggested that the incommensurate phase of the TG gas in deep lattices is similar to a defect-induced superfluid phase and can be utilized to investigate the Andreev-Lifschitz-Chester mechanism [12,53].…”

“…If the deviation from the commensurate phase at F=1 is microscopic, such that N=M±1, the phase becomes gapless with a quadratic dispersion relation. On the other hand, for a macroscopic number of defects, such as N=M±M/2, the phase is also gapless, but with a linear dispersion relation [12]. These regimes are, however, continuously connected which can be seen in figure 4(a), where the momentum distribution as a function of F is plotted for a constant depth = V E 20 r 0 .…”

“…In this case, a commensurate particle density leads to an integer filling of each lattice site and thus realizes an insulating pinned phase where dynamics is suppressed due to vanishing long range coherence. For incommensurate particle densities each lattice site has a non-integer filling which has the effect of creating delocalized modes which can be considered as defects [11,12]. These defects promote dynamics as they preserve a degree of coherence and allow the system to attain superfluid-like properties.…”

Quantum phase transition of a two-dimensional quadrupolar system

“…4 indicate the strong rotonization of the collective excitation branch near the phase transition. By introducing a small fraction of vacancies one can expect the formation of a quadrupolar supersolid in the strongly interacting regime [38], which is similar to the vacancy-induced Andreev-Lifshitz mechanism [70][71][72][73][74].…”