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-T c 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 6 Li superfluid Fermi gas in the BCS (Bardeen-CooperSchrieffer) unitary limit far below the superfluid phase-transition temperature T 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 eff is negligibly small in a superfluid 6 Li Fermi gas, it cannot be ignored (r eff = 2.7 fm) in a neutron star, by extending the NSR theory to include effects of r eff . The calculated EoS when r 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.

We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential µ.Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated µ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of µ in a superfluid 6 Li Fermi gas, we show that an extended T -matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.

We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a Tmatrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature T c . Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength.However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the strong-coupling regime. This non-monotonic interaction dependence is quite different from the case of an s-wave interaction, where the pseudogap simply develops with increasing the interaction strength. The difference between the two cases is shown to originate from the momentum dependence of the p-wave interaction, which vanishes in the low momentum limit.We also identify the pseudogap regime in the phase diagram with respect to the temperature and the p-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of p-wave superfluid Fermi gases.

We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary T -matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature T c in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the T -matrix level. Using this extended T -matrix theory, we calculate single-particle excitations in the normal state above T c . The so-called pseudogap phenomena originating from pairing fluctuations are shown to be different between the light-mass component and heavy-mass component, which becomes more remarkable at higher temperatures. Since Fermi condensates with hetero-Cooper pairs have recently been discussed in various fields, such as exciton (polariton) condensates as well as color superconductivity, our results would be useful for the further development of Fermi superfluid physics, beyond the conventional superfluid state with homo-Cooper pairs.

An extension of the Ambegaokar-Baratoff relation to a superconductor-insulator-superconductor (SIS) Josephson junction with multiple tunneling channels is derived. Appling the resultant relation to a SIS Josephson junction formed by an iron-based (five-band) and a single-band Bardeen-Cooper-Schrieffer (BCS) type superconductors, a theoretical bound of the Josephson critical current (Ic) multiplied by the resistance of the junction (Rn) is given. We reveal that such a bound is useful for identifying the pairing symmetry of iron-pnictide superconductors. One finds that if a measured value of IcRn is smaller than the bound then the symmetry is ±s-wave, and otherwise s-wave without any sign changes. In addition, we stress that temperature dependence of IcRn is sensitive to the difference of the gap functions from the BCS type gap formula in the above heterojunction.