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arXiv:2206.12599 · Physical Review A

Role of the effective range in the density-induced BEC-BCS crossover

Hiroyuki Tajima, Haozhao Liang

Published Oct 12, 2022• 11 citations
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Abstract

We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length $a$ and effective range $r$, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum $k$ is much less than $1/r$. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.

DOI
10.1103/physreva.106.043308

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We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length aaa and effective range rrr, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum kkk is much less than 1/r1/r1/r. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.
We generalize the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover of two-component fermions, which is realized by tuning the sss-wave scattering length aaa between the fermions, to the case of an arbitrary effective range rer_{\rm e}re​. By using the Nozières-Schmitt-Rink (NSR) approach, we show another crossover by changing rer_{\rm e}re​ and present several similarities and differences between these two crossovers. Furthermore, the region (re>a/2r_{\rm e}>a/2re​>a/2) where the effective range expansion breaks down and the Hamiltonian becomes non-Hermitian is found, being consistent with the Wigner's causality bound. Our results are universal for low-density interacting fermions with low-energy constants aaa and rer_{\rm e}re​ and are directly relevant to ultracold Fermi atomic gases as well as dilute neutron matter.
This work studies zero-temperature Fermi gases with short-ranged and attractive interactions with focus on the dimensionality aspects by confining the system from three to two dimensions. Interacting Fermi gases are superfluids characterized as being strongly correlated if the scattering length is much larger than the other scales present. In the many-body context, this category of systems requires a careful treatment since mean-field approaches are not expected to hold under the conditions which define the strong pairing. For this reason, we employ quantum Monte Carlo methods to study the dimensionality effects in two-component Fermi gases in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover. To be able to investigate such aspects, we consider a three-dimensional gas with periodic boundary conditions in the xy plane and a confining potential in the z direction capable of reducing the dimensionality of the system, which defines a dimensional BCS-BEC crossover. We calculate the equation of state as the energy per particle as a function of the dimensionality and as a function of the interaction parameter, which are characterized by the oscillator length in the z direction and the scattering length respectively. The greater confinement in the system lowers the interparticle distances, which increases the effects of the attractive interactions between antiparallel-spin fermions.We also calculate the density profile in the z direction over the crossover for different confinements and different interaction parameters to quantify their influence on the spatial distribution of the particles. This study connects the perspectives between theoretical and experimental works in low-dimensional ultracold Fermi gases by utilizing an approach that is similar to what it is realized in modern experiments.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover.
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, aF,a_{F},aF​, and the effective range parameter, re.r_{\mathrm{e}}.re​. In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances. By matching two-body scattering properties near a Feshbach resonance to a simple renormalized model potential, a broad resonance is characterized by a small effective range and the gas displays a universal BCS-BEC crossover behavior. On the other hand, for a narrow resonance thermodynamic quantities depend the effective range which may be large and negative at resonance. For increasing values of −re-r_{\mathrm{e}}−re​ we find the transition temperature to be suppressed in the crossover region. We furthermore argue for existence of a lower bound of TcT_{c}Tc​ at fixed coupling for increasing −re-r_{\mathrm{e}}−re​ in the crossover region.
Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.
Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the 1S0{}^{1\phantom{\rule{-0.16em}{0ex}}}{S}_{0}1S0​ channel to Bose-Einstein condensation of dineutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than 1.101.101.10, a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than 0.850.850.85, the neutron Cooper pairs are found totally in the weak coupling Bardeen-Cooper-Schrieffer (BCS) region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained, respectively, from the dimensionless parameter 1/(kFna)1/({k}_{\mathrm{Fn}}a)1/(kFn​a) with aaa the scattering length and kFn{k}_{\mathrm{Fn}}kFn​ the neutron Fermi momentum, the zero-momentum transfer density correlation function D(0)D(0)D(0), and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.