Universal properties of a trapped two-component fermi gas at unitarity

We treat the trapped two-component Fermi system, in which unlike fermions interact through a two-body short-range potential having no bound state but an infinite scattering length. By accurately solving the Schr?dinger equation for up to N=6 fermions, we show that no many-body bound states exist other than those bound by the trapping potential, and we demonstrate unique universal properties of the system: Certain excitation frequencies are separated by 2variant Planck's over 2piomega, the wave functions agree with analytical predictions and a virial theorem is fulfilled. Further calculations up to N=30 determine the excitation gap, an experimentally accessible universal quantity, and it agrees with recent predictions based on a density functional approach.     

Visualization of vortex bound states in polarized fermi gases at unitarity

We theoretically analyze a single vortex in a spin polarized 3D trapped atomic Fermi gas near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied by the majority spin component. As a result, the local density difference at the core center suddenly rises at low temperatures. This provides a way to visualize the lowest bound state using phase-contrast imaging. As the polarization increases, the core expands gradually and the energy of the lowest bound state decreases.     

Normal state of highly polarized fermi gases: simple many-body approaches

We consider the problem of a single downward arrow atom in the presence of a Fermi sea of upward arrow atoms, in the vicinity of a Feshbach resonance. We calculate the chemical potential and the effective mass of the downward arrow atom using two simple approaches: a many-body variational wave function and a T-matrix approximation. These two methods lead to the same results and are in good agreement with existing quantum Monte Carlo calculations performed at unitarity and, in one dimension, with the known exact solution. Surprisingly, our results suggest that, even at unitarity, the effect of interactions is fairly weak and can be accurately described using single particle-hole excitations. We also consider the case of unequal masses.     

Finite-temperature phase diagram of a polarized fermi gas in an optical lattice

We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair, and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.     

强相互作用极化费米气体中涡旋束缚态的研究

涡旋态的研究对理解冷原子体系超流特性有很重要的价值.文章在简要回顾涡旋态研究历史的基础上,介绍了文章作者近期在超冷极化费米气体中涡旋态的工作.通过应用平均场的方法,从理论上研究了强相互作用极化费米气中单个涡旋态的结构.发现在涡旋态核中,Andreev束缚态的填充可引起一种量子相变.这就提供了一种新颖的探测Andreev束缚态的方法,在冷原子物理中,可通过吸收成像方法来完成.进一步文章作者对涡旋态的核尺寸进行了研究,发现涡旋态的核尺寸随着体系极化程度的增加而变大.     

Quasi-one-dimensional polarized fermi superfluids

We calculate the zero-temperature (T=0) phase diagram of a polarized two-component Fermi gas in an array of weakly coupled parallel one-dimensional (1D) "tubes" produced by a two-dimensional optical lattice. Increasing the lattice strength drives a crossover from three-dimensional (3D) to 1D behavior, stabilizing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid phase. We argue that the most promising regime for observing the FFLO phase is in the quasi-1D regime, where the atomic motion is largely 1D but there is weak tunneling in the other directions that stabilizes long-range order. In the FFLO phase, we describe a phase transition where the quasiparticle spectrum changes from gapless near the 3D regime to gapped in quasi-1D.     

强相互作用极化费米气体中涡旋束缚态的研究

涡旋态的研究对理解冷原子体系超流特性有很重要的价值. 文章在简要回顾涡旋态研究历史的基础上,介绍了文章作者近期在超冷极化费米气体中涡旋态的工作.通过应用平均场的方法,从理论上研究了强相互作用极化费米气中单个涡旋态的结构.发现在涡旋态核中,Andreev 束缚态的填充可引起一种量子相变.这就提供了一种新颖的探测Andreev 束缚态的方法,在冷原子物理中,可通过吸收成像方法来完成.进一步文章作者对涡旋态的核尺寸进行了研究,发现涡旋态的核尺寸随着体系极化程度的增加而变大.     

Destroying superfluidity by rotating a Fermi gas at unitarity

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.     

Tomographic rf spectroscopy of a trapped Fermi gas at unitarity

We present spatially resolved radio-frequency spectroscopy of a trapped Fermi gas with resonant interactions and observe a spectral gap at low temperatures. The spatial distribution of the spectral response of the trapped gas is obtained using in situ phase-contrast imaging and 3D image reconstruction. At the lowest temperature, the homogeneous rf spectrum shows an asymmetric excitation line shape with a peak at 0.48(4)epsilonF with respect to the free atomic line, where epsilonF is the local Fermi energy.     

On the ground state of an impurity in a dilute fermi gas

The system under consideration is a large collection of identical fermions (B), forming a background, into which is inserted a relatively small number of distinct impurity (I) particles. The background is considered to be dilute in the sense that R ? a, where R is the average separation of the B particles, and a is the range of their interaction potential; and the I particles are so dilute with respect to the B particles that I-I interactions can be ignored. The I particles are then all essentially at rest in their ground state. The BB and BI interaction potentials are chosen to be hard cores of the same range a. A series expansion is developed for the ground-state energy of the I particles, and the first four terms are calculated explicitly using two distinct methods, employing Feynman and Goldstone diagrams respectively. It is shown that each method has distinct advantages over the other, and that a judicious combination of both can be used to considerable benefit.     

Normal state of highly polarized Fermi gases: The bound state

We consider a highly polarized Fermi gas with a single ↓ atom within a Fermi sea of ↑ atoms. We extend a preceding many-body analysis to the case where a bound state is formed between the ↓ atom and an ↑ atom.     

Absence of fermionic quasiparticles in the superfluid state of the attractive fermi gas

We calculate the effect of order parameter fluctuations on the fermionic single-particle excitations in the superfluid state of neutral fermions interacting with short-range attractive forces. We show that in dimensions D< or =3 the singular effective interaction between the fermions mediated by the gapless Bogoliubov-Anderson mode prohibits the existence of well-defined quasiparticles. We explicitly calculate the single-particle spectral function in the BEC regime in D=3 and show that in this case the quasiparticle residue and the density of states are logarithmically suppressed.     

Current correlation functions of ideal fermi gas at finite temperature

Expressions for transverse and longitudinal current-current correlation functions of an ideal Fermi gas describing the current fluctuations induced in the electron system by external probe perpendicular and parallel to the propagation of electron wave, have been obtained at finite temperature. The results obtained for transverse and longitudinal functions are presented for different values of wavelength and frequency at different temperatures. The diamagnetic susceptibility as a function of temperature has also been obtained from transverse current correlation function as its long wavelength and static limit, which smoothly cross over from known quantum values to the classical limit with increase in temperature.     

The hot fermi gas model

Ample production of fast particles has been observed in intermediate heavy ion reactions [1]. These particles have often been related to sources having velocities close to half that of the beam and temperatures ranging between a few and several tens MeV. For such temperatures neither the low temperature Fermi gas model nor the Boltzmann gas model are valid. A more correct treatment is necessary in order to understand the relationship between the incident energy per nucleon, the excitation energy of the source and its temperature. In this short paper we give simple closed expressions allowing to interpolate between the Fermi and the Boltzmann regimes. In the following we consider a gas of fermions (Nucleons) at a temperatureT trapped in a square potential well of depthU. We shall not deal with the dynamics of the expansion of the gas except through the calculation of the particle evaporation rate. Likewise we do not consider the implications of a possible liquid gas transition [2]. We first approximate the variation of the chemical potential as a function of the temperature. Using that, we are able to compute and find approximations to the variations of the excitation energy with temperature and vice-versa. Finally we give expressions for the particle evaporation rate of a hot Fermi gas and compare them to the Weisskopf formula.     

Ground state correlation in the two-dimensional polarized electron gas

The ground state energy and radial distribution functions of the polarized two-dimensional electron gas with valley degeneracyn _v =1 and 2 are calculated using the hypernetted-chain approximation with the effective correlation factor method for Fermions. The paramagnetic susceptibility is calculated and compared with experiment in silicon inversion layers.     

Normal state of highly polarized Fermi gases: full many-body treatment

We consider a single atom within a Fermi sea of atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wave vectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.     

Normal state of highly polarized Fermi gases: Full many-body treatment

We present a full many-body analysis of the problem of a single ↓ atom resonantly interacting with a Fermi sea of ↑ atoms. A series of successive approximations permits us to clarify the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. We show that it results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. Our treatment provides, at the same time, an essentially exact solution to this problem.     

Phase separation in a polarized Fermi gas at zero temperature

We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.     

Fluctuations in the level density of a fermi gas

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many-body density of states, related to shell effects, are obtained. The fluctuations depend nontrivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single-particle motion.     

Anomalous specific-heat jump in a two-component ultracold fermi gas

The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.