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arXiv:1509.08506 · Journal of Physics B Atomic Molecular and Optical Physics

Thermodynamics of a two-dimensional dipolar Bose gas with correlated disorder in the roton regime

Abdelâali Boudjemâa

Published Apr 22, 2016• 16 citations
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Abstract

Abstract We study the impact of a weak random potential with a Gaussian correlation function on the thermodynamics of a two-dimensional dipolar bosonic gas. Analytical expressions for the quantum depletion, anomalous density, the ground state energy, the equation of state and the sound velocity are derived in the roton regime within the framework of the Bogoliubov theory. Surprisingly, we find that the condensate depletion and the anomalous density are comparable. The structure factor and the superfluid fraction are also obtained analytically and numerically. We show that these quantities acquire dramatically modified profiles when the roton is close to zero yielding the transition to an unusual quantum state.

DOI
10.1088/0953-4075/49/10/105301

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Abstract We study the impact of a weak random potential with a Gaussian correlation function on the thermodynamics of a two-dimensional dipolar bosonic gas. Analytical expressions for the quantum depletion, anomalous density, the ground state energy, the equation of state and the sound velocity are derived in the roton regime within the framework of the Bogoliubov theory. Surprisingly, we find that the condensate depletion and the anomalous density are comparable. The structure factor and the superfluid fraction are also obtained analytically and numerically. We show that these quantities acquire dramatically modified profiles when the roton is close to zero yielding the transition to an unusual quantum state.
We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0T=0T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to 0. At finite temperatures exceeding the roton energy, the effect of thermal fluctuations is stronger and it may lead to a large normal fraction of the gas and compressibility.
We investigate the behavior of the anomalous correlation function in two-dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify, in particular, the chemical potential, the ground-state energy, the depletion, and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the noncondensed one at zero temperature. The single-particle anomalous correlation function is expressed in two-dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature, while it does not exist at finite temperature.
Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second order in the random potential strength and obtain analytic results for the disorder ensemble averages of both the condensate and the superfluid depletion, the equation of state, and the sound velocity. For a pure contact interaction and a vanishing correlation length, we reproduce the seminal results of Huang and Meng, which were originally derived within a Bogoliubov theory around a disorder-averaged background field. For dipolar interaction and isotropic Lorentzian-correlated disorder, we obtain results which are qualitatively similar to the case of an isotropic Gaussian-correlated disorder. In the case of an anisotropic disorder, the physical observables show characteristic anisotropies which arise from the formation of fragmented dipolar condensates in the local minima of the disorder potential.
We investigate the properties of a homogeneous dipolar Bose gas in a weak three-dimensional isotropic speckle disorder at finite temperatures. By using the Bogoliubov theory (beyond the mean field), we calculate the condensate and the superfluid fractions as a function of density and strengths of disorder and interaction. The disorder impact on the anomalous density, the chemical potential, and the ground-state energy is also analyzed. We show that the peculiar interplay of the dipole-dipole interaction and weak disorder makes the superfluid fraction and sound velocity anisotropic.
Abstract Using the Green's function approach, the density–density correlation function and the dielectric function in the random‐phase approximation for a quasi‐two‐dimensional (quasi‐2D) dipolar Bose gas are derived. From the pole of the density correlation function, by considering thermally induced roton‐like excitations, the excitation spectrum of the system is calculated. It is shown that the position and depth of the roton minimum of the excitation spectrum are tunable by changing the temperature. To show how the position of the roton minimum influences the phenomenon of superfluidity, the superfluid density of the system is obtained and it is shown that the interplay of the thermal rotonization, contact and dipole–dipole interaction (DDI) can affect the superfluid fraction of a quasi‐2D Bose gas. It is found that contact, DDI interactions, and thermally induced rotons enhance the fluctuations and reduce the superfluid density. In the absence of DDI and thermally induced rotons, the usual T3 dependence of superfluid density in 2D is obtained and the correction T4 term arises from DDI. It is shown that if the roton minimum is close to zero, the thermally induced rotons change the linear temperature dependence of the superfluid fraction, leading to a transition to nontrivial supersolid phase.
We present a systematic study of dilute three-dimensional dipolar Bose gas employing a finite temperature perturbation theory (beyond the mean field). We analyze in particular the behavior of the anomalous density, we find that this quantity has a finite value in the limit of weak interactions at both zero and finite temperatures. We show that the presence of the dipole–dipole interaction enhances fluctuations, the second order correlation function and thermodynamic quantities such as the chemical potential, the ground state energy, the compressibility and the superfluid fraction. We identify the validity criterion of the small parameter of the theory for Bose-condensed dipolar gases.