Critical parameters from trap-size scaling in systems of trapped particles

Abstract

We investigate the critical behavior of trapped particle systems at the low-temperature superfluid transition. In particular, we consider the three-dimensional Bose-Hubbard model in the presence of a trapping harmonic potential coupled with the particle density, which is a realistic model of cold bosonic atoms in optical lattices. We present a numerical study based on quantum Monte Carlo simulations, analyzed in the framework of the trap-size scaling (TSS). We show how the critical parameters can be derived from the trap-size dependencies of appropriate observables, matching them with TSS. This provides a systematic scheme which is supposed to exactly converge to the critical parameters of the transition in the large-trap-size limit. Our numerical analysis may provide a guide for experimental investigations of trapped systems at finite-temperature and quantum transitions, showing how critical parameters may be determined by looking at the scaling of the critical modes with respect to the trap size, i.e., by matching the trap-size dependence of the experimental data with the expected TSS ansat

Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

“…It is bounded by a BEC transition line Tc(µ), which satisfies Tc(µ) = Tc(−µ) due to a particle-hole symmetry. Its maximum occurs at µ = 0, where [27,29] Tc(µ = 0) = 2.01599(5); we also know that [26] Tc(µ ± 4) = 1.4820 (2). At T = 0 two further quantum phases exist: the vacuum phase (µ < −6) and the incompressible n = 1 Mott phase (µ > 6).…”

“…This has been accurately verified by numerical studies, see, e.g., Refs. [25][26][27]29]. The BEC phase extends below the BEC transition line.…”

Critical Temperature of Interacting Bose Gases in Periodic Potentials

“…We also find that, by tuning the filling factor above unity, one can reach a regime where the presence of the periodic potential becomes essentially irrelevant due to a screening effect caused by interactions. The recent realization of quasiuniform trapping potentials [15,49] for atomic clouds and the development of new theories to describe the critical behavior in the presence of confinement [16] give us strong hope that these findings can be observed in experiments in the near future.…”

“…This setup allows a more direct investigation of critical points where a correlation length diverges and the arguments based on the local density approximation become invalid. Alternatively, critical properties can be extracted directly from experiments with harmonic confinements by using trap-size scaling at fixed chemical potential [16].The superfluid transition in the presence of periodic potentials is even more complex than in homogeneous systems due to the intricate interplay between interparticle interactions and the external potential and to the role of commensurability. In this Letter, we employ unbiased quantum Monte Carlo methods to determine the critical temperature of a 3D repulsive Bose gas in the presence of a simple-cubic optical lattice with spacing d. We find that at the integer filling nd 3 ¼ 1 (an average density of one bosons per well of the external field) the critical temperature T c has an intriguing nonmonotonic dependence on the interaction strength (parametrized by the ratio a=d) with an initial sharp increase in the regime of small a=d followed by a rapid suppression terminating at the Mott insulator quantum phase transition.…”

“…This setup allows a more direct investigation of critical points where a correlation length diverges and the arguments based on the local density approximation become invalid. Alternatively, critical properties can be extracted directly from experiments with harmonic confinements by using trap-size scaling at fixed chemical potential [16].…”