Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction (6Li), we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by BardeenCooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are quantitatively measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.
We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (BCS) regime of Cooper Fermi pairs) to a small and positive value (corresponding to the regime of the Bose-Einstein condensate (BEC) of molecular dimers), crossing the unitarity regime where the scattering length diverges. In the case of bulk neutron matter the s-wave scattering length of neutron-neutron potential is negative but fixed, and the condensate fraction of neutron-neutron pairs is studied as a function of the total neutron density. Our results clearly show a BCS-quasiunitary-BCS crossover by increasing the neutron density. Finally, in the case of neutron stars, where again the neutron-neutron scattering length is negative and fixed, we determine the condensate fraction as a function of the distance from the center of the neutron star, finding that the maximum condensate fraction appears in the crust of the neutron star.
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 Nozi\`eres 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=2.7 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.
Experiments with cold Fermi atoms can be tuned to probe strongly-interacting fluids that are very similar to the low-density neutron matter found in the crusts of neutron stars. In contrast to traditional superfluids and superconductors, matter in this regime is very strongly paired, with gaps of the order of the Fermi energy. We compute the
T=0 equation of state and pairing gap for cold atoms and low-density neutron matter as a function of the Fermi momentum times the scattering length. Results of quantum Monte Carlo calculations show that the equations of state are very similar. The neutron matter pairing gap at low densities is found to be very large but, except at the smallest densities, significantly suppressed relative to cold atoms because of the finite effective range in the neutron-neutron interaction.
Dilute Fermi gases with large scattering lengths are intriguing physical systems which are just now becoming accessible in laboratory experiments with cold trapped atoms. Their properties are closely related to those of the dilute neutron‐rich matter which may be present in the surface of neutron stars. Fermi systems with such strong short‐range attractive forces lie between traditional BCS theories with small gaps and those where the fermions are tightly bound into pairs, yielding composite bosons. We discuss the Quantum Monte Carlo methods used to study such systems, and report results for the ground‐state energy, the superfluid gap, and other properties. In particular, we compare results with those of neutron matter at subnuclear densities.
Dilute Fermi systems with large
s-wave scattering length
as exhibit universal properties if the interparticle spacing
r0 greatly exceeds the range of the underlying two-body interaction potential. In this regime,
r0 is the only relevant length scale and observables such as the energy per particle depend only on
r0 (or, equivalently, the energy
EFG of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum
l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an
l-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite
l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.