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arXiv:2304.09021 · New Journal of Physics

Collective excitations of a Bose–Einstein condensate of hard-core bosons and their mediated interactions: from two-body bound states to mediated superfluidity

Moroni Santiago-García, Arturo Camacho-Guardian

Published Sep 1, 2023• 12 citations
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Abstract

Abstract The exchange of collective modes has been demonstrated to be a powerful tool for inducing superconductivity and superfluidity in various condensed matter and atomic systems. In this article, we study the mediated interactions of collective excitations in an ultracold gas of hard-core bosons. We show that the induced interaction supports two-body states with energies, symmetries, and a number of bound states strongly dependent on the properties of the hard-core boson gas. The ability to control the nature of the two-body bound states motivates the study of superfluid phases, which we address within the BKT theory. We demonstrate how the superfluid parameters and critical temperatures can be tuned in our system. Our findings may pave the way for future theoretical and experimental studies with ultracold gases and solid-state systems.

DOI
10.1088/1367-2630/acf72d

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Abstract The exchange of collective modes has been demonstrated to be a powerful tool for inducing superconductivity and superfluidity in various condensed matter and atomic systems. In this article, we study the mediated interactions of collective excitations in an ultracold gas of hard-core bosons. We show that the induced interaction supports two-body states with energies, symmetries, and a number of bound states strongly dependent on the properties of the hard-core boson gas. The ability to control the nature of the two-body bound states motivates the study of superfluid phases, which we address within the BKT theory. We demonstrate how the superfluid parameters and critical temperatures can be tuned in our system. Our findings may pave the way for future theoretical and experimental studies with ultracold gases and solid-state systems.
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Achieving strong interactions in fermionic many-body systems is a major theme of research in condensed matter physics. It is well-known that interactions between fermions can be mediated through a bosonic medium, such as a phonon bath or Bose-Einstein condensate (BEC). Here we show that such induced attraction can be resonantly enhanced when the bosonic medium is a two-component spinor BEC. The strongest interaction is achieved by tuning the boson-boson scattering to the quantum critical spinodal point of the BEC where the sound velocity vanishes. The fermion pairing gap and the superconducting critical temperature can thus be dramatically enhanced. We propose two experimental realizations of this scenario, with exciton-polariton systems in two-dimensional semiconductors and ultracold atomic Bose-Fermi mixtures.
Bose–Einstein condensation represents a quintessential manifestation of quantum mechanics at macroscopic scales, where a dilute gas of bosonic atoms undergoes a phase transition to form a coherent matter wave. This study presents a comprehensive theoretical investigation of collective excitations and critical phenomena in interacting Bose–Einstein condensates (BECs). Beginning with the Gross–Pitaevskii equation , we develop the Bogoliubov theory of excitations yielding the spectrum , where is the free-particle energy and characterizes contact interactions. The spectrum reveals phonon behavior at low momenta with sound velocity , transitioning to free-particle dispersion at momenta exceeding the inverse healing length . Collective modes in harmonically trapped condensates are analyzed in the Thomas–Fermi regime, yielding breathing mode frequency and quadrupole frequency . Damping mechanisms including Landau damping ( ) and Beliaev damping ( ) are characterized. The Lee–Huang–Yang correction extends the equation of state beyond mean field. Critical phenomena near are analyzed within the 3D XY universality class, with critical exponents , , and the interaction-induced shift with . All predictions show excellent agreement with experimental measurements on ultracold atomic gases.
We investigate strong-coupling superfluidity in a uniform two-component gas of ultracold Fermi atoms attractively interacting via quasimolecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy $2\ensuremath{\nu}$ of the Feshbach resonance, becoming large as $2\ensuremath{\nu}$ is decreased (relative to $2{\ensuremath{\varepsilon}}_{\mathrm{F}},$ where ${\ensuremath{\varepsilon}}_{\mathrm{F}}$ is the Fermi energy of one component). In recent work, we showed that the enhancement of this tunable pairing interaction naturally leads to the BCS-BEC (Bose-Einstein condensation) crossover, where the character of the superfluid phase transition changes from the BCS type to a BEC of composite bosons consisting of preformed Cooper-pairs and Feshbach-induced molecules. In this paper, we extend our previous work and study both the quasiparticles and the collective dynamics of the superfluid phase below the phase-transition temperature Tc,{T}_{\mathrm{c}},Tc​, limiting ourselves to a uniform gas. We show how the superfluid order parameter changes from the Cooper-pair amplitude $\ensuremath{\Delta}$ to the square root of the number of condensed molecules $({\ensuremath{\varphi}}_{\mathrm{m}})$ associated with the Feshbach resonance, as the threshold energy $2\ensuremath{\nu}$ is lowered. In the intermediate coupling regime, the superfluidity is shown to be characterized by an order parameter consisting of a superposition of $\ensuremath{\Delta}$ and ${\ensuremath{\varphi}}_{\mathrm{m}}.$ We also discuss the Goldstone mode associated with superfluidity, and show how its character smoothly changes from the Anderson-Bogoliubov phonon in the BCS regime to the Bogoliubov phonon in the BEC regime in the BCS-BEC crossover. The velocity of this Goldstone phonon mode is shown to strongly depend on the value of $2\ensuremath{\nu}.$ We also show that this Goldstone mode appears as a resonance in the spectrum of the density-density correlation function, which is experimentally accessible.
We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective sss-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.
The properties of Bose-Einstein-condensed systems of hard spheres at high density are studied by taking into account higher-order corrections beyond the Hartree-Fock-Bogoliubov approximation. Based on a diagrammatic technique of the perturbation expansion starting from the Bogoliubov approximation, we show that the effective interactions separate into two distinct parts: the screened and condensate-mediated interactions. The latter is described by the exchange of virtual quasiparticles between noncondensate bosons via the Bose-Einstein condensate and is attractive for small energy transfer. We calculate the condensation temperature, excitation spectrum, and condensate density in the whole region of the gas parameter. It is shown that the condensate temperature decreases compared to that of an ideal Bose gas due to hard-sphere interactions. We find that the condensate-mediated attraction between noncondensate bosons leads to an enhancement of the anomalous self-energy and, as a consequence, to the emergence of a roton minimum in the excitation spectrum and to the strong suppression of the condensate fraction in the region of high density.