Magnetic Properties and Strong-Coupling Corrections in an Ultracold Fermi Gas with Population Imbalance

Kashimura, Takashi; Watanabe, Ryota; Ōhashi, Y.

doi:10.1007/s10909-012-0724-2

Cited by 5 publications

(7 citation statements)

References 18 publications

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“…Unfortunately, as it was already observed by several authors [13][14][15], this scheme that works nicely in the balanced case fails in the imbalanced case. To be specific, the problem is that near the unitary limit (i.e., for large scattering length: |a| → ∞) one finds in some regions of the phase diagram ρ ↑ < ρ ↓ in spite of µ ↑ > µ ↓ .…”

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confidence: 68%

“…It is straight-forward to extend the NSR theory to the imbalanced case, by introducing two different chemical potentials µ σ (σ =↑, ↓). Unfortunately, as it was already observed by several authors [13][14][15], this scheme that works nicely in the balanced case fails in the imbalanced case. To be specific, the problem is that near the unitary limit (i.e., for large scattering length: |a| → ∞) one finds in some regions of the phase diagram…”

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confidence: 68%

“…The contributions of the delta functions in Im Γ, see Eq. (15), are of course included analytically, while the continuum contributions are computed numerically. The remaining integrals over k are done numerically, too.…”

Section: B Self-energy and Occupation Numbersmentioning

confidence: 99%

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Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

Urban

Schuck

2014

Phys. Rev. A

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We study a two-component Fermi gas that is so strongly polarized that it remains normal fluid at zero temperature. We calculate the occupation numbers within the particle-particle random-phase approximation, which is similar to the Nozières-Schmitt-Rink approach. We show that the Luttinger theorem is fulfilled in this approach. We also study the change of the chemical potentials which allows us to extract, in the limit of extreme polarization, the polaron energy. [3]. In this theory, only equal densities of the two species forming the pairs (which we will denote by spin indices σ =↑, ↓) were considered. Nowadays, the crossover can be realized in experiments with ultracold trapped atoms whose scattering length a can be tuned with the help of a Feshbach resonance [4]. In these experiments, it is also possible to study systems with different densities of the two species, n ↑ = n ↓ [5]. In this way, one tries to discover, e.g., phases with exotic pairing, like the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase [6,7]. Also the extremely polarized case, where only a single particle of spin ↓ is put into a Fermi sea of spin ↑, bears interesting physics: when passing though the Feshbach resonance from the attractive (a < 0) to the repulsive (a > 0) side, one expects that the ground state transforms from a Fermi sea plus a fermionic quasiparticle, the so-called polaron, into a Fermi sea plus a bosonic molecule [8]. To our knowledge, there is so far no unique many-body theory that can describe the imbalanced Fermi gas in the cross-over and that reproduces in the limit of extreme polarization the polaronic and the molecular ground state, depending on the value of the scattering length a.As mentioned before, the original NSR theory was formulated in order to describe the BEC-BCS crossover in a two-component (σ =↑, ↓) Fermi gas with equal populations. Within this approach, the critical temperature T c as a function of the chemical potential µ is obtained from the Thouless criterion, i.e., it is the temperature where the in-medium T matrix develops a pole,where ω and k are, respectively, the total energy (measured from 2µ) and momentum of the pair, and Γ is ob- tained by summing ladder diagrams, see Fig. 1. As a function of µ, the critical temperature obtained in this way is exactly the same as within BCS theory. The difference between BCS and NSR comes from the inclusion of pair correlations into the relationship n(µ) between the number density and the chemical potential. This is done by including diagrams of the type shown in Fig. 2(a) into the thermodynamic potential Ω(µ, T ) and then computing the density from n = −∂Ω/∂µ. This is equivalent to calculating the density from [9]where ω n = nπT is a fermionic (n odd) Matsubara frequency and G is the single-particle (s.p.) Green's function with at most one self-energy insertion,

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confidence: 68%

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Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

Urban

Schuck

2014

Phys. Rev. A

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“…This approach, however, breaks down near unitarity, because if one calculates the densities for µ ↑ > µ ↓ one finds n ↑ < n ↓ in some regions of the phase diagram [206,140]. A warning about this problem exists already in the unpolarized case, where the spin susceptibility becomes negative at temperatures slightly above T c in a region about unitarity [138,207] (see also Ref. [208]).…”

Section: Pairing Fluctuations In Polarized Fermi Gasesmentioning

confidence: 99%

The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems

et al. 2018

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This report adresses topics and questions of common interest in the fields of ultra-cold gases and nuclear physics in the context of the BCS-BEC crossover. By this crossover, the phenomena of Bardeen-Cooper-Schrieffer (BCS) superfluidity and Bose-Einstein condensation (BEC), which share the same kind of spontaneous symmetry breaking, are smoothly connected through the progressive reduction of the size of the fermion pairs involved as the fundamental entities in both phenomena. This size ranges, from large values when Cooper pairs are strongly overlapping in the BCS limit of a weak inter-particle attraction, to small values when composite bosons are non-overlapping in the BEC limit of a strong inter-particle attraction, across the intermediate unitarity limit where the size of the pairs is comparable with the average inter-particle distance.The BCS-BEC crossover has recently been realized experimentally, and essentially in all of its aspects, with ultracold Fermi gases. This realization, in turn, has raised the interest of the nuclear physics community in the crossover problem, since it represents an unprecedented tool to test fundamental and unanswered questions of nuclear manybody theory. Here, we focus on the several aspects of the BCS-BEC crossover, which are of broad joint interest to both ultra-cold Fermi gases and nuclear matter, and which will likely help to solve in the future some open problems in nuclear physics (concerning, for instance, neutron stars). Similarities and differences occurring in ultra-cold Fermi gases and nuclear matter will then be emphasized, not only about the relative phenomenologies but also about the theoretical approaches to be used in the two contexts. Common to both contexts is the fact that at zero temperature the BCS-BEC crossover can be described at the mean-field level with reasonable accuracy. At finite temperature, on the other hand, inclusion of pairing fluctuations beyond mean field represents an essential ingredient of the theory, especially in the normal phase where they account for precursor pairing effects.After an introduction to present the key concepts of the BCS-BEC crossover, this report discusses the mean-field treatment of the superfluid phase, both for homogeneous and inhomogeneous systems, as well as for symmetric (spinor isospin-balanced) and asymmetric (spin-or isospin-imbalanced) matter. Pairing fluctuations in the normal phase are then considered, with their manifestations in thermodynamic and dynamic quantities. The last two Sections provide a more specialized discussion of the BCS-BEC crossover in ultra-cold Fermi gases and nuclear matter, respectively. The separate discussion in the two contexts aims at cross communicating to both communities topics and aspects which, albeit arising in one of the two fields, share a strong common interest.

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“…Originally, this interest was stimulated by novel experimental studies of superfluid trapped Fermi atoms [11,12], for which imbalanced populations can be maintained independently of the orbital degrees of freedom. From a theoretical point of view, it turns out that the (non-selfconsistent) t-matrix approximation (sometimes referred to as the G 0 G 0 t-matrix [13]) or else its expanded NSR version [14], which has often been used with (at least qualitative) success to describe the BCS-BEC crossover for gases with balanced populations, fails instead in the imbalanced case when two different chemical potentials µ σ are introduced [15,16,17]. For instance, if one calculates the densities for µ ↑ > µ ↓ , one finds inconsistently that n ↑ < n ↓ in some regions of the phase diagram [15,16].…”

Section: Introductionmentioning

confidence: 99%

Luttinger theorem and imbalanced Fermi systems

Pieri

Strinati

2017

Eur. Phys. J. B

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Abstract. The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any "Φ-derivable" approximation, and illustrate it in particular for the self-consistent t-matrix approximation.PACS. 71.10.Ay Fermi-liquid theory and other phenomenological models

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Magnetic Properties and Strong-Coupling Corrections in an Ultracold Fermi Gas with Population Imbalance

Cited by 5 publications

References 18 publications

Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

Occupation numbers in strongly polarized Fermi gases and the Luttinger theorem

The BCS–BEC crossover: From ultra-cold Fermi gases to nuclear systems

Luttinger theorem and imbalanced Fermi systems

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