We present diffusion Monte Carlo (DMC) and path-integral Monte Carlo (PIMC) calculations of a one-dimensional Bose system with realistic interparticle interactions in a periodic external potential. Our main aim is to test the predictions of the Luttinger liquid (LL) theory, in particular with respect to the superfluid-Mott insulator transition at both zero and finite temperatures, in the predicted robust and fragile superfluid regimes. For that purpose, we present our results of the superfluid fraction ${\ensuremath{\rho}}_{s}/{\ensuremath{\rho}}_{0}$, the one-body density matrix, the two-body correlation functions, and the static structure factor. The DMC and PIMC results in the limit of very low temperature for ${\ensuremath{\rho}}_{s}/{\ensuremath{\rho}}_{0}$ agree, but the LL model for scaling ${\ensuremath{\rho}}_{s}/{\ensuremath{\rho}}_{0}$ does not fit the data well. The critical depth of the periodic potential is close to the values obtained for ultracold gases with different models of interaction, but with the same value of the bare LL parameter, demonstrating the universality of LL description. Algebraic decay of correlation functions is observed in the superfluid regime and exponential decay in the Mott-insulator one, as well as in all regimes at finite temperature for distances larger than a characteristic length.
We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$, the one-body density matrix
n(x), the pair distribution function
g(x), and the static structure factor
S(q) are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter
K. The 1D Bose fluid examined is a single chain of
4He atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid
4He. In this range,
K varies from
K>2 at low density, where a robust superfluid is predicted, to
K<0.5, where fragile 1D superflow and solidlike peaks in
S(q) are predicted. For uniform pore walls, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ scales as predicted by LL theory. The
n(x) and
g(x) show long range oscillations and decay with
x as predicted by LL theory. The amplitude of the oscillations is large at high density (small
K) and small at low density (large
K). The
K values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ${\ensuremath{\rho}}_{S}/{\ensuremath{\rho}}_{0}$ does not scale as predicted by LL theory. A single
vJ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The ``dynamical'' superfluid fraction, ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$, is determined. The physics of the deviation from LL theory in disorder and the ``dynamical'' ${\ensuremath{\rho}}_{S}^{D}/{\ensuremath{\rho}}_{0}$ are discussed.
As helium-4 is cooled below 2.17 K it undergoes a phase transition to a fundamentally quantum mechanical state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent experiments have highlighted the feasibility of fabricating smooth pores with nanometer radii, that approach the truly one-dimensional limit where it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one-dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid (LL) theory, where no type of long range order can be sustained. In the limit where the pore radius is small, LL theory would predict that helium inside the channel behaves as a sort of quasi-supersolid with all correlations decaying as power-law functions of distance at zero temperature. We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperature with realistic helium–helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical shells surrounding a core that can be described via LL theory and provides insights into the exciting possibility of the experimental detection of this intriguing low-dimensional state of matter.
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.
Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.