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

Abstract

We propose a theoretical idea to use an ultracold Fermi gas as a quantum simulator for the study of the low-density region of a neutron-star interior. Our idea is different from the standard quantum simulator that heads for perfect replication of another system, such as the Hubbard model discussed in high-Tc cuprates. Instead, we use the 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 and Schmitt–Rink (NSR) can quantitatively explain the recent experiment on the equation of state (EoS) in a ⁶Li superfluid Fermi gas in the BCS (Bardeen–Cooper–Schrieffer) unitary limit far below the superfluid phase-transition temperature Tc. 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 reff is negligibly small in a superfluid ⁶Li Fermi gas, it cannot be ignored (reff = 207 fm) in a neutron star, by extending the NSR theory to include effects of reff. The calculated EoS when reff = 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.