  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-$T_{\rm c}$ 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 Nozi\`eres-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 $T_{\rm c}$. 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 $r_{\rm
eff}$ is negligibly small in a superfluid $^6$Li Fermi gas, it cannot be
ignored ($r_{\rm eff}=2.7$ fm) in a neutron star, by extending the NSR theory
to include effects of $r_{\rm eff}$. The calculated EoS when $r_{\rm eff}=2.7$
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.
