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arXiv:1811.12743 · Journal of Physics A Mathematical and Theoretical

Superfluidity and coherence in uniform dipolar binary Bose mixtures

Abdelâali Boudjemâa

Published Sep 14, 2020• 2 citations
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Abstract

Abstract We investigate the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formulas for the excitation spectra, the first-order correlation function, the static structure factor, and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely low temperatures. The behavior of the first-order correlation function for both dipolar and nondipolar Bose mixtures is deeply analyzed. Then we face the two-dimensional case which encodes a non-trivial physics due to the roton modes.

DOI
10.1088/1751-8121/abb843

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Abstract We investigate the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formulas for the excitation spectra, the first-order correlation function, the static structure factor, and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely low temperatures. The behavior of the first-order correlation function for both dipolar and nondipolar Bose mixtures is deeply analyzed. Then we face the two-dimensional case which encodes a non-trivial physics due to the roton modes.
We study the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formula for the excitations spectrum, the correlation function and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely low temperatures. The behavior of the first-order correlation function for both dipolar and nondipolar Bose mixtures is deeply analyzed. Then we face the two-dimensional case which encodes a non-trivial physics due to the roton modes.
We rigorously analyze the low-temperature properties of homogeneous three-dimensional two-component Bose mixture with dipole-dipole interaction. For such a system the effective hydrodynamic action that governs the behavior of low-energy excitations is derived. The infrared structure of the exact single-particle Green's functions is obtained in terms of macroscopic parameters, namely the inverse compressibility and the superfluid density matrices. Within the one-loop approximation we calculate some of the most relevant observable quantities and give the beyond mean-field stability condition for the binary dipolar Bose gas in the dilute limit. A brief variational derivation of the coupled equations that describe macroscopic hydrodynamics of the system in the external nonuniform potential at zero temperature is presented.
Dipolar Bose-Einstein condensates are excellent platforms for studying supersolidity, characterized by coexisting density modulation and superfluidity. The realization of dipolar mixtures opens intriguing new scenarios, most remarkably the possibility of realizing a double supersolid, composed of two interacting superfluids. We analyze the complex excitation spectrum of a miscible trapped dipolar Bose mixture, showing that it provides key insights about the double-supersolid regime. We show that this regime may be readily probed experimentally by monitoring the appearance of a doublet of superfluid compressional modes, linked to the different superfluid character of each component. Additionally, the dipolar supersolid mixture exhibits a nontrivial spin nature of the dipolar rotons, the Higgs excitation, and the low-lying Goldstone modes. Interestingly, the analysis of the lowest-lying modes allows for monitoring the transition of just one of the components into the incoherent-droplet regime, whereas the other remains coherent, highlighting their disparate superfluid properties.
We systematically investigate the properties of three-dimensional dipolar binary Bose mixture at low temperatures. A set of coupled self-consistent equations of motion are derived for the two condensates. In the homogeneous case, useful analytical formulas for the condensate depletion, the anomalous density, the ground-state energy, and the equation of state are obtained. The theory is extended to the inhomogeneous case and the importance of the inhomogeneity is highlighted. Our results open up an avenue for studying dipolar mixture droplets. Impacts of the dipole-dipole interaction on the stability, density profiles, and the size of the self-bound droplet are deeply discussed. The finite-temperature behavior of such a state is also examined.
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.
Using the effective action formalism, we investigate collective excitations of a dilute mixture of a Bose gas and a two component Fermi gas when both bosons and fermions have undergone superfluid transitions. We show that there is a repulsion between Bogoliubov and Anderson modes, which has important implications including disappearance of boson superfluidity. We derive an analytic expression for the long-wavelength dispersion relation of the mixture at zero temperature and give a condition for the instability. We also numerically calculate the damping rate due to boson-fermion interaction at finite temperatures and show that the two modes are stable at sufficiently low temperatures.