We study a single component Fermi gas near a p -wave resonance with the lowest order constrained variational (LOCV) method. We obtain the energy per particle for the ground state of the single component Fermi gas near a p -wave resonance with the LOCV method. We also calculate the compressibility of the single component Fermi gas near a p -wave resonance and it shows that in the strongly interacting BCS side, the system would lose its stability and collapse. The width of the unstable region is proportional to the Fermi energy which reflects the universality of the dilute Fermi gas. The two p -wave contacts are also obtained and their variation tendencies with the interaction strength are qualitatively in agreement with recent experimental results.
We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the
p-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is,
p-wave scattering length and effective range. At the unitarity limit where the
p-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact
s-wave interaction in three dimensions. It is in contrast to a Fermi gas with the
p-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary
p-wave Fermi gas within the many-body
T-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary
p-wave Fermi gas.
Abstract We revisit the properties of the two-component Fermi gas with short-range interactions in three dimensions, in the limit where the s -wave scattering length diverges. Such a unitary Fermi gas possesses universal thermodynamic and dynamical observables that are independent of any interaction length scale. Focusing on trapped systems of N fermions, where N ≤ 10 , we investigate how well we can determine the zero-temperature behavior of the many-body system from published few-body data on the ground-state energy and the contact. For the unpolarized case, we find that the Bertsch parameters extracted from trapped few-body systems all lie within 15% of the established value. Furthermore, the few-body values for the contact are well within the range of values determined in the literature for the many-body system. In the limit of large spin polarization, we obtain a similar accuracy for the polaron energy, and we estimate the polaron’s effective mass from the dependence of its energy on N . We also compute an upper bound for the squared wave-function overlap between the unitary Fermi system and the non-interacting ground state, both for the trapped and uniform cases. This allows us to prove that the trapped unpolarized ground state at unitarity has zero overlap with its non-interacting counterpart in the many-body limit N → ∞ .
We study the Fermi liquid properties of a single component Fermi gas with p-wave interactions. In the weak repulsive limit, we obtain exact perturbative expansions for the ground state energy, the chemical potential, and the effective mass of the Landau quasiparticle up to second order in scattering volume a. We also calculated the corresponding Landau functions and Landau parameters and show that they satisfy the general Fermi liquid identities. Using the Landau transport equation, we show that undamped zero sound only appears in the second order in scattering volume, in contrast to the s-wave case.
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.
Dilute Fermi systems with large s-wave scattering length a_s exhibit universal properties if the interparticle spacing r_o greatly exceeds the range of the underlying two-body interaction potential. In this regime, r_o is the only relevant length scale and observables such as the energy per particle depend only on r_o (or, equivalently, the energy E_{FG} of the free Fermi gas). This paper investigates Bose and Fermi systems with non-vanishing 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 a l-dependent length scale ξ_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.