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Register a new userPairing in low-density Fermi gases
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We consider pairing in a dilute system of Fermions with a short-range interaction. While the theory is ill-defined for a contact interaction, the BCS equations can be solved in the leading order of low-energy effective field theory. The integrals are evaluated with the dimensional regularization technique, giving analytic formulas relating the pairing gap, the density, and the energy density to the two-particle scattering length.
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Some thoughts regarding pairing in atomic Fermi gases were considered, meant for starting discussion on the topic.
We study the properties of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons. In particular, we analyze its energy ($E_downarrow$), effective mass ($m^*_downarrow$) and quasiparticle residue ($Z_downarrow$). Results are compared with those of state-of-the-art quantum Monte Carlo calculations of the attractive Fermi polaron realized in ultracold atomic gases experiments, and with those of previous studies of the neutron polaron. Calculations are performed within the Brueckner--Hartree--Fock approach using the chiral two-body nucleon-nucleon interaction of Entem and Machleidt at N$^3$LO with a 500 MeV cut-off and the Argonne V18 phenomenological potential. Only contributions from the $^1S_0$ partial wave, which is the dominant one in the low-density region considered, are included. Contributions from three-nucleon forces are expected to be irrelevant at these densities and, therefore, are neglected in the calculation. Our results show that for Fermi momenta between $sim 0.25$ and $sim 0.45$ fm$^{-1}$ the energy, effective mass and quasiparticle residue of the impurity vary only slightly, respectively, in the ranges $-0.604,E_F < E_downarrow < -0.635,E_F $, $1.300,m < m^*_downarrow < 1.085, m$ and $0.741 <Z_downarrow< 0.836$ in the case of the chiral interaction, and $-0.621,E_F < E_downarrow < -0.643,E_F $, $1.310,m < m^*_downarrow < 1.089, m$ and $0.739 <Z_downarrow< 0.832$ when using the Argonne V18 potential. These results are compatible with those derived from ultracold atoms and show that a spin-down neutron impurity in a free Fermi gas of spin-up neutrons with a Fermi momentum in the range $0.25lesssim k_F lesssim 0.45$ fm$^{-1}$ exhibits properties very similar to those of an attractive Fermi polaron in the unitary limit.
We propose a pairing-based method for cooling an atomic Fermi gas. A three component (labels 1, 2, 3) mixture of Fermions is considered where the components 1 and 2 interact and, for instance, form pairs whereas the component 3 is in the normal state. For cooling, the components 2 and 3 are coupled by an electromagnetic field. Since the quasiparticle distributions in the paired and in the normal states are different, the coupling leads to cooling of the normal state even when initially $T_{paired}geq T_{normal}$ (notation $T_Sgeq T_N$). The cooling efficiency is given by the pairing energy and by the linewidth of the coupling field. No superfluidity is required: any type of pairing, or other phenomenon that produces a suitable spectral density, is sufficient. In principle, the paired state could be cooled as well but this requires $T_N<T_S$. The method has a conceptual analogy to cooling based on superconductor -- normal metal (SN) tunneling junctions. Main differences arise from the exact momentum conservation in the case of the field-matter coupling vs. non-conservation of momentum in the solid state tunneling process. Moreover, the role of processes that relax the energy conservation requirement in the tunneling, e.g. thermal fluctuations of an external reservoir, is now played by the linewidth of the field. The proposed method should be experimentally feasible due to its close connection to RF-spectroscopy of ultracold gases which is already in use.
We present ground state calculations for low-density Fermi gases described by two model interactions, an attractive square-well potential and a Lennard-Jones potential, of varying strength. We use the optimized Fermi-Hypernetted Chain integral equation method which has been proved to provide, in the density regimes of interest here, an accuracy better than one percent. We first examine the low-density expansion of the energy and compare with the exact answer by Huang and Yang (H. Huang and C. N. Yang, {em Phys. Rev./} {bf 105}, 767 (1957)). It is shown that a locally correlated wave function of the Jastrow-Feenberg type does not recover the quadratic term in the expansion of the energy in powers of $a0KF$, where $a0$ is the vacuum $s$-wave scattering length and $KF$ the Fermi wave number. The problem is cured by adding second-order perturbation corrections in a correlated basis. Going to higher densities and/or more strongly coupled systems, we encounter an instability of the normal state of the system which is characterized by a divergence of the {em in-medium/} scattering length. We interpret this divergence as a phonon-exchange driven dimerization of the system, similar to what one has at zero density when the vacuum scattering length $a0$ diverges. We then study, in the stable regime, the superfluid gap and its dependence on the density and the interaction strength. We identify two different corrections to low-density expansions: One is medium corrections to the pairing interaction, and the other one finite-range corrections. We show that the most important finite-range corrections are a direct manifestation of the many-body nature of the system.
We study a three-component superfluid Fermi gas in a spherically symmetric harmonic trap using the Bogoliubov-deGennes method. We predict a coexistence phase in which two pairing field order parameters are simultaneously nonzero, in stark contrast to studies performed for trapped gases using local density approximation. We also discuss the role of atom number conservation in the context of a homogeneous system.
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