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Register a new userA phenomenological approach to the equation of state of a unitary Fermi gas
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We propose a phenomenological approach for the equation of state of a unitary Fermi gas. The universal equation of state is parametrised in terms of Fermi-Dirac integrals. This reproduces the experimental data over the accessible range of fugacity and normalised temperature, but cannot describe the superfluid phase transition found in the MIT experiment cite{ku}. The most sensitive data for compressibility and specific heat at phase transition can, however, befitted by introducing into the grand partition function a pair of complex conjugate zeros lying in the complex fugacity plane slightly off the real axis.
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Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to BEC crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy S(E) as a function of the total energy E. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at T=0 and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.
We study the evolution of the energy gap in a unitary Fermi gas as a function of temperature. To this end we approximate the Fermi gas by the Hubbard lattice Hamiltonian and solve using the dynamical mean-field approximation. We have found that below the critical temperature, Tc, the system is a superfluid and the energy gap is decreasing monotonously. For temperatures above Tc the system is an insulator and the corresponding energy gap is monotonously increasing.
A unitary Fermi gas has a surprisingly rich spectrum of large amplitude modes of the pairing field alone, which defies a description within a formalism involving only a reduced set of degrees of freedom, such as quantum hydrodynamics or a Landau-Ginzburg-like description. These modes are very slow, with oscillation frequencies well below the pairing gap, which makes their damping through quasiparticle excitations quite ineffective. In atomic traps these modes couple naturally with the density oscillations, and the corresponding oscillations of the atomic cloud are an example of a new type of collective mode in superfluid Fermi systems. They have lower frequencies than the compressional collective hydrodynamic oscillations, have a non-spherical momentum distribution, and could be excited by a quick time variation of the scattering length.
We calculate the one-body temperature Greens (Matsubara) function of the unitary Fermi gas via Quantum Monte Carlo, and extract the spectral weight function $A(p,omega)$ using the methods of maximum entropy and singular value decomposition. From $A(p,omega)$ we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass $m^*$, a mean-field potential $U$, and a gap $Delta$. Below the critical temperature $T_c=0.15varepsilon_F$ the results for $m^*$, $U$ and $Delta$ can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to {$T^*approx 0.20varepsilon_{F} > T_c$}.
A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HR) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Non-analytical contributions to the one--body density matrix are also discussed and found to be less relevant with increasing density.
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