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Effects of disorder on bosonic superfluids

Nicola Dragoni

Published Sep 1, 2018• 0 citations
OpenAlex

Abstract

In this work we showed and review a modern approach to treat disorder in bosonic superfluids, within the framework of path-integral approach to quantum field theory. The methods we present are focused on the evaluation of physical quantities of interest, like the condensate depletion and normal-fluid particle density, using correlators evaluated in harmonic approximation. We treated different kinds of disorder and presented an original extension of the theory to the case of particles interacting with a finite-range potential, instead of the contact interaction. We also showed how this formalism can be applied to the problem of flux lines in type-II sueprconductors.

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•Jan 1, 2019•0 citations
In this work we showed and review a modern approach to treat disorder in bosonic superfluids, within the framework of path-integral approach to quantum field theory.
The methods we present are focused on the evaluation of physical quantities of interest, like the condensate depletion and normal-fluid particle density, using correlators evaluated in harmonic approximation.
We treated different kinds of disorder and presented an original extension of the theory to the case of particles interacting with a finite-range potential, instead of the contact interaction.
We also showed how this formalism can be applied to the problem of flux lines in type-II sueprconductors.
Abstract At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined effects of which are rather intriguing, and difficult to describe quantitatively. By inhomogeneous Bogoliubov theory, applicable to weakly interacting condensed Bose gases in static external potentials with arbitrary spatial correlations, we calculate the normal fluid density via the transverse current–current correlation. We obtain finite-temperature disorder corrections to the normal fraction known since Laudau’s seminal two-fluid theory, using diagrammatic perturbation theory for systems of any dimensionality, with closed analytical expressions to leading, quadratic order in disorder strength.
We present a field-theory description of ultracold bosonic atoms in the presence of a disordered external potential. By means of functional integration techniques, we aim to investigate and review the interplay between disordered energy landscapes and fluctuations, both thermal and quantum ones. Within the broken-symmetry phase, up to the Gaussian level of approximation, the disorder contribution crucially modifies both the condensate depletion and the superfluid response. Remarkably, it is found that the ordered (i.e., superfluid) phase can be destroyed also in regimes where the random external potential is suitable for a perturbative analysis. We analyze the simplest case of quenched disorder and then we move to present the implementation of the replica trick for ultracold bosonic systems. In both cases, we discuss strengths and limitations of the reviewed approach, paying specific attention to possible extensions and the most recent experimental outputs.
We investigate the low-temperature properties of an ultracold gas made of bosonic alkali-metal atoms with finite-range interaction under the effect of a disordered environment. The statistical characterization of the disorder is investigated within an effective-field-theory formalism for a generic spatial dimension ddd. Moving to d=3d=3d=3, where all the arising divergences are properly regularized, we focus on the depletion of both the condensate and superfluid densities. At zero temperature we obtain meaningful analytical formulas for the condensate fraction and the superfluid fraction which take into account the interplay among scattering length, effective range, and disorder strength.
Abstract A finite-temperature current-density functional theory for bosonic superfluids (sf-CDFT) in the thermal equilibrium state is proposed herein. In the sf-CDFT, hydrodynamic physical quantities, such as particle number density, current density, and the order parameter of the Bose–Einstein condensation, are chosen as the basic variables. This theory enables the simultaneous reproduction of the particle number and current densities of both the superfluid and normal fluid components with incorporating effects of the interaction between these components. Specifically, these components are determined by solving two single-particle equations, i.e., the Gross–Pitaevskii–Kohn–Sham and Kohn–Sham equations. Furthermore, using the continuity equation of superfluids, we present the sum rule for the exchange-correlation energy functional of the sf-CDFT, which is useful for developing the approximate form.
We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a three-dimensional (3D) speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a T 2 dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree–Fock mean-field approach that holds if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature, we find that the energy and the particle distribution of the gas are very well described by the T =0 Gross–Pitaevskii theory, even in the regime of very strong disorder.