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arXiv:2112.11748 · Condensed Matter

Mixtures of Dipolar Gases in Two Dimensions: A Quantum Monte Carlo Study

Sergi Pradas, Jordi Boronat

Published Apr 1, 2022• 4 citations
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Abstract

We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed of a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are all considered to be perpendicular to the plane, turning the dipolar potential in a purely repulsive and isotropic model. Our analysis is carried out by using the diffusion Monte Carlo method, which allows for an exact solution to the many-body problem within some statistical noise. Our results show that the miscibility between the two species is rather constrained as a function of the relative dipolar moments and masses of the two components. A narrow regime is predicted where both species mix and we introduce an adimensional parameter whose value quite accurately predicts the miscibility of the two dipolar gases.

DOI
10.3390/condmat7020032

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We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed of a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are all considered to be perpendicular to the plane, turning the dipolar potential in a purely repulsive and isotropic model. Our analysis is carried out by using the diffusion Monte Carlo method, which allows for an exact solution to the many-body problem within some statistical noise. Our results show that the miscibility between the two species is rather constrained as a function of the relative dipolar moments and masses of the two components. A narrow regime is predicted where both species mix and we introduce an adimensional parameter whose value quite accurately predicts the miscibility of the two dipolar gases.
In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.
Quantum Monte Carlo simulations of a two-component Bose mixture of trapped dipolar atoms of identical masses and dipole moments, provide numerical evidence of demixing at low finite temperatures. Demixing occurs as a consequence of quantum statistics, which results in an effective attraction between like bosons. Spatial separation of two components takes place at low temperature with the onset of long exchanges of identical particles, underlying Bose-Einstein condensation of both components. Conversely, at higher temperature the system is miscible due to the entropy of mixing. Exchanges are also found to enhance demixing in the case of mixtures of nonidentical and distinguishable species.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
We study a harmonically confined Bose–Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross–Pitaevskii (GP) equation in the same conditions. The phase space as a function of the interaction strengths and the relation between masses is quite rich. The miscibility criterion for the homogeneous system applies rather well to the system, with some discrepancies close to the critical line for separation. We observe significant differences between the mean-field results and the Monte Carlo ones, that magnify when the asymmetry between masses increases. In the analyzed interaction regime, we observe universality of our results which extend beyond the applicability regime for the GP equation.
We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive 1/r31/{r}^{3}1/r3 potential. This model can be realized with ultracold atoms or molecules when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely, whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully polarized ground state up to the freezing density.
We perform a full three-dimensional study on miscible-immiscible conditions for coupled dipolar and non-dipolar Bose–Einstein condensates (BEC), confined in anisotropic traps. In view of recent experimental studies, our focus was the atomic erbium–dysprosium ( 168 Er– 164 Dy) and dysprosium–dysprosium ( 164 Dy– 162 Dy) mixtures. The miscibility is quantified by the overlap of the two-component densities, using an appropriate defined parameter. By verifying that stable regimes for pure-dipolar coupled BECs are only possible in pancake-type traps, we obtain some non-trivial local minimum biconcave-shaped states with density oscillations in both components. For non-dipolar systems with repulsive interactions, we show that immiscible stable configurations are also possible in cigar-type geometries. The main role of the trap aspect ratio and inter-species contact interaction for the miscibility is verified for different configurations, from non-dipolar to pure dipolar systems.