Superfluid Fermi atomic gas as a quantum simulator for the study of neutron-star equation of state

Abstract

We theoretically propose an idea to use an ultracold Fermi gas as a quantum simulator for the study of the neutron-star equation of state (EoS) in the low-density region. Our idea is different from the standard quantum simulator that heads for {\it perfect} replication of another system, such as a Hubbard model discussed in high-$T_{\mathrm{c}}$ cuprates. Instead, we use the {\it similarity} between two systems, and theoretically make up for the difference between them. That is, (1) we first show that the strong-coupling theory developed by Nozières-Schmitt Rink (NSR) can quantitatively explain the recent EoS experiment on a ${}^6$Li superfluid Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-unitary limit far below the superfluid phase transition temperature $T_{\mathrm{c}}$. This region is considered to be very similar to the low density region (crust regime) of a neutron star (where a nearly unitary $s$-wave neutron superfluid is expected). (2) We then theoretically compensate the difference that, while the effective range $r_{\mathrm{eff}}$ is negligibly small in a superfluid ${}^6$Li Fermi gas, it cannot be ignored ($r_{\mathrm{eff}}=2.7$ fm) in a neutron star, by extending the NSR theory to include effects of $r_{\mathrm{eff}}$. The calculated EoS when $r_{\mathrm{eff}}=2.7$ fm is shown to agree well with the previous neutron-star EoS in the low density region predicted in nuclear physics. Our idea indicates that an ultracold atomic gas may more flexibly be used as a quantum simulator for the study of other complicated quantum many-body systems, when we use, not only the experimental high tunability, but also the recent theoretical development in this field. Since it is difficult to directly observe a neutron-star interior, our idea would provide a useful approach to the exploration for this mysterious astronomical object.

29 pages, 7 figures

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• Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions
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• QCD-like phase diagram with Efimov trimers and Cooper pairs in resonantly interacting SU(3) Fermi gases
• Equation of state of neutron star matter and its warm extension with an interacting hadron resonance gas
• Role of the effective range in the density-induced BEC-BCS crossover
• Feasibility of a Fulde-Ferrell-Larkin-Ovchinnikov superfluid Fermi atomic gas
• Low-Dimensional Fluctuations and Pseudogap in Gaudin-Yang Fermi Gases
• Brueckner $G$-matrix approach to two-dimensional Fermi gases with the finite-range attractive interaction
• Nonequilibrium BCS-BEC crossover and unconventional FFLO superfluid in a strongly interacting driven-dissipative Fermi gas
• Stable non-equilibrium Fulde-Ferrell-Larkin-Ovchinnikov state in a spin-imbalanced driven-dissipative Fermi gas loaded on a three-dimensional cubic optical lattice
• Exploring ${}^3{P}_0$ Superfluid in Dilute Spin-Polarized Neutron Matter
• Effects of dilute neutron matter on the neutron star crust equation of state
• Polaronic neutron in dilute alpha matter: A $p$-wave Bose polaron
• Finite-range effect in the two-dimensional density-induced BCS-BEC crossover
• Faraday Waves in strongly interacting superfluids
• Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas
• Equivalence of dissipative and dissipationless dynamics of interacting quantum systems with its application to the unitary Fermi gas
• A model study on superfluidity of a unitary Fermi gas of atoms interacting with a finite-ranged potential