Fermi gas of atoms

A rapidly developing field, experimental physics of ultracold gases of Fermi atoms, is briefly reviewed. The contribution of this field to fundamental physics is shown along with connection to other fields which explore systems of Fermi particles. The basic parameters of atomic Fermi gas are described together with its unique properties and advantages and disadvantages in comparison to other Fermi systems. The prospects of this field and its short history are considered. Research groups working in this field are listed.     

Classical simulation of the Fermi gas

We demonstrate that it is possible to approximate the one-particle phase-space distribution of the excited Fermi gas within the framework of classical mechanics by employing a momentum-dependent two-body repulsion, to simulate the Pauli exculsion principle. For a suitable choice of the parameters in this potential, it is possible to achieve a quite good approximation to the momentum distribution over a broad range of temperatures and densities.     

Barnett slip of the Fermi gas

A half-space problem of the Barnett slip of the quantum Fermi gas is solved analytically. A formula for calculating the velocity of the Barnett slip of the Fermi gas along a plane surface and a distribution function of particles moving toward a wall are derived in an explicit form. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 44–49, October, 2007.     

Universal relations for the strongly-interacting Fermi gas

Shina Tan has derived some universal relations that hold for any state of a system consisting of fermions with two spin states that have a large scattering length. These relations involve an intensive quantity called the contact that measures the number of pairs of atoms that are very close together. We show how these relations can be derived in the framework of quantum field theory using standard renormalization methods and the operator product expansion. They allow the contact density to be identified as the expectation value of a local operator constructed out of quantum fields.     

Composite-fermionization of the mixture composed of Tonks gas and Fermi gas

This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks-Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose-Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson-fermion interaction, the system exhibits composite-fermionization crossover.     

Magnetism of a relativistic Fermi gas

The parametric dependence of the magnetic susceptibility of an extremely degenerate relativistic gas of charged fermions on the induction of the quantizing magnetic field and particle density is obtained taking into account the anomalous static magnetic moments of the particles. The case of the quantum limit of ultrastrong magnetic fields is examined.A. S. Pushkin Brest State Pedagogical Institute. Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 1, pp. 37–38, January, 1994.     

Damping of a unitary Fermi gas

We measure the temperature dependence of the radial breathing mode in an optically trapped, unitary Fermi gas of 6Li, just above the center of a broad Feshbach resonance. The damping rate reveals a clear change in behavior which we interpret as arising from a superfluid transition. We suggest pair breaking as a mechanism for an increase in the damping rate which occurs at temperatures well above the transition. In contrast to the damping, the frequency varies smoothly and remains close to the unitary hydrodynamic value. At low temperature T, the damping depends on the atom number only through the reduced temperature, and extrapolates to 0 at T = 0.     

Thermodynamic coefficients of ideal Fermi gas

We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low-temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg .     

Renormalization group theory for the imbalanced Fermi gas

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)10.1038/nature06473].     

Level-density parameters in the back-shifted Fermi gas model

The parameters a and δ_eff appearing in the back-shifted Fermi gas model are determined for about 3000 nuclei on the basis of modern estimated experimental data and the proposed systematics. For 272 of these nuclei, the parameters are deduced from experimental data on the cumulative numbers of low-lying levels and on mean spacings between S-wave neutron resonances at the neutron binding energy in the nuclei. For 952 nuclei, the parameter δ_eff is calculated by using the cumulative numbers of low-lying levels and values of the parameter a that were obtained via an interpolation from the points corresponding to the aforementioned 272 nuclei. For the remaining nuclei, the parameters a and δ_eff are obtained on the basis of the proposed systematics. An expression is constructed for taking into account the damping of shell effects with increasing excitation energy of nuclei. The results are compared with those from other studies.     

Theory of fluctuations in non-equilibrium Fermi gas

We present the equations for the equal-time two-particle correlation functions in degenerate electron gas. In association with the Onsager-type equation for the time-displaced correlation function, the equations constitute the basis of the theory of fluctuations in non-equilibrium degenerate electron gas. Thanks to the prevalence of the small-angle inter-electron scattering, the theory takes a rather simple form.     

Momentum distribution and contact of the unitary Fermi gas

We calculate the momentum distribution n(k) of the unitary Fermi gas by using quantum Monte Carlo calculations at finite temperature T/?(F) as well as in the ground state. At large momenta k/k(F), we find that n(k) falls off as C/k?, in agreement with the Tan relations. From the asymptotics of n(k), we determine the contact C as a function of T/?(F) and present a comparison with theory. At low T/?(F), we find that C increases with temperature, and we tentatively identify a maximum around T/?(F) ? 0.4. Our calculations are performed on lattices of spatial extent up to N(x) = 14 with a particle number per unit volume of ? 0.03-0.07.     

All-optical production of a degenerate Fermi gas

We achieve degeneracy in a mixture of the two lowest hyperfine states of 6Li by direct evaporation in a CO2 laser trap, yielding the first all optically produced degenerate Fermi gas. More than 10(5) atoms are confined at temperatures below 4 microK at full trap depth, where the Fermi temperature for each state is 8 microK. This degenerate two-component mixture is ideal for exploring mechanisms of superconductivity ranging from Cooper pairing to Bose-Einstein condensation of strongly bound pairs.     

Thermodynamics of a trapped unitary Fermi gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.     

Condensate fraction of asymmetric three-component Fermi gas

In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.     

Derivation of the Boltzmann equation for a Fermi gas

Point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables (stationary renewal process). For a fixed configuration of scatterers a particle performs the following random walk: The particle starts at the pointx with velocityυ, ¦υ¦=1. In between scatterers the particle moves freely. At a scatterer the particle is either transmitted or reflected, both with probability 1/2. For given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations. If this variable is averaged over the distribution of scatterers, it decays not faster thant ^?3/2.