Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

Liu, Xia-Ji; Hu, Hui

doi:10.1103/physreva.82.043626

Cited by 26 publications

(32 citation statements)

References 51 publications

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“…where Q n,n ′ is the partition function of a cluster containing n − n ′ fermions of species ν and n ′ of species µ [60]. Thus the interacting components of the grand thermodynamic potential can be written…”

Section: Discussionmentioning

confidence: 99%

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

et al. 2016

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A universal k −4 decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable SU (κ) symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the κ components of the gas and the Young tableaux for the SN permutation symmetry group identifying the magnetic structure of the groundstate. This opens a route for the experimental determination of magnetic configurations in cold atomic gases, employing only standard (spin-resolved) time-of-flight techniques. Combining the exact result with matrix-product-states simulations, we obtain the Tan's contact at all values of repulsive interactions. We show that a local density approximation (LDA) on the Bethe-Ansatz equation of state for the homogeneous mixture is in excellent agreement with the results for the harmonically confined gas. At strong interactions, the LDA predicts a scaling behavior of the Tan's contact. This provides a useful analytical expression for the dependence on the number of fermions, number of components and on interaction strength. Moreover, using a virial approach, we study the Tan's contact behaviour at large temperatures and in the limit of infinite interactions and we show that it increases with the temperature and the number of components. At zero temperature, we predict that the weight of the momentum distribution tails increases with interaction strength and the number of components if the population per component is kept constant. This latter property was experimentally observed in Ref. [Nat. Phys. 10, 198 (2014)].

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Section: Discussionmentioning

confidence: 99%

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

et al. 2016

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“…Following the derivation of the imbalanced thermodynamic potential by Refs. [47,84], we write it in the following third order form,…”

Section: Appendix A: Virial Expansion Of An Imbalanced Fermi Gasmentioning

confidence: 99%

Breakdown of the Fermi polaron description near Fermi degeneracy at unitarity

Mulkerin

Liu

2019

Annals of Physics

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We theoretically investigate attractive and repulsive Fermi polarons in three dimensions at finite temperature and impurity concentration through the many-body T -matrix theory and hightemperature virial expansion. By using the analytically continued impurity Green's function, we calculate the direct rf spectroscopy of attractive polarons in the unitary regime. Taking the peak value of the rf spectroscopy as the polaron energy and the full width half maximum as the polaron lifetime, we determine the temperature range of validity for the quasi-particle description of Fermi polarons in the unitary limit. We also explore the temperature and impurity dependence of attractive and repulsive Fermi polarons using the direct and reverse rf spectroscopy. This methodology allows us to directly compare our results to the recent experimental data from the European Laboratory for Non-Linear Spectroscopy [F. Scazza et al., Phys. Rev. Lett. 118, 083602 (2017)].

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“…For a spin-polarized Fermi gas, it is necessary to introduce two fugacities z ↑ ≡ exp(βµ ↑ ) and z ↓ ≡ exp(βµ ↓ ) to distinguish different spin configurations, where β = 1/(k B T ), µ σ is the chemical potential for spin σ, T is the temperature, and k B is the Boltzmann constant. Generally, the thermodynamic potential can be written as [32,33] …”

Section: Virial Expansion For a Spin Polarized Fermi Gasmentioning

confidence: 99%

Universal relations and normal phase of an ultracold Fermi gas with coexistings- andp-wave interactions

Qin

Cui

2016

Phys. Rev. A

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We study the universal relations and normal-phase thermodynamics of a two-component ultracold Fermi gas with coexisting s-and p-wave interactions. Due to the orthogonality of two-body wave functions of different scattering channels, the universal thermodynamic relations of the system appear to be direct summations of contributions from each partial-wave scattering channels. These universal relations are dictated by a set of contacts, which can be associated with either s-or pwave interactions. Interestingly, due to the interplay of s-and p-wave interactions on the many-body level, the contacts, and hence all the relevant thermodynamic quantities, behave differently from those with only s-or p-wave interactions. These are manifest in our numerical calculations based on second-order virial expansions for 40 K atoms under typical experimental parameters. A particularly interesting finding is that, due to the coexistence of s-and p-wave scatterings, the interaction energy of the repulsive branch features abrupt changes across the p-wave resonances. Our results can be readily checked experimentally for 40 K atoms near the 198G p-wave Feshbach resonance, where multiple partial-wave scatterings naturally coexist.

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Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations

Cited by 26 publications

References 51 publications

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps

Breakdown of the Fermi polaron description near Fermi degeneracy at unitarity

Universal relations and normal phase of an ultracold Fermi gas with coexistings- andp-wave interactions

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