Superfluid transition in a rotating fermi gas with resonant interactions

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial trap with frequencies Omega perpendicular, Omega z. We predict the upper-critical angular velocity, omega c2(delta,T), as a function of temperature T and detuning delta across the BEC-BCS crossover. The suppression of superfluidity at omega c2 is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low T and Omega z < Omega perpendicular, in the BCS and crossover regimes of 0 less similar delta less similar delta c, omega c2 is implicitly given by [formula: see text], vanishing as omega c2 approximately Omega perpendicular(1 - delta/delta c)(1/2) near [formula: see text] (with Delta the BCS gap and gamma the resonance width), and extending the bulk result variant Planck's over 2pi omega c2 approximately 2Delta2/epsilonF to a trap. In the BEC regime of delta < 0 we find omega c2-->Omega perpendicular-, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.     

Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.     

Superfluid-insulator transition of strongly interacting fermi gases in optical lattices

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in lattice height Vo/ER between 2.23 and 4.14. The latter is the prediction of mean-field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF-Mott-insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-insulator transition for the BCS-BEC family.     

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.     

Virial theorem and universality in a unitary fermi gas

Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of 6Li, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.     

The relativistic fermi gas in a nonuniform velocity field

We review the relativistic Fermi gas in an inhomogeneous velocity field and calculate components of the current vector and the energy-momentum tensor in a comoving frame. We derive quantum corrections to the classical distribution function in the framework of the grand canonical ensemble.     

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.     

Induced scalar interaction in the analysis of superallowed fermi β transitions

Nuclear Structure superallowed Fermiβ transitions; derivation of the coupling constant for the induced scalar interactionf _s from experimental data. Very recent works reported a significant improvement in the consistency of ?t values for superallowed Fermiβ-decays. This fact led us to investigate some aspects which are not usually tackled in a study of this kind of transition. In a recent paper we suggested that an upper limit for the coupling constantf _s for the induced scalar interaction can be derived analyzing superallowed Fermiβ-transitions. In the present work we revise and improve the method for the determination off _s . The result obtained,f _s /f _v =(? 0.4±1.4) × 10^?3, agrees with the prediction of the CVC theory.     

Superfluid fermi gas in a 1D optical lattice

We calculate the superfluid transition temperature for a two-component 3D Fermi gas in a 1D tight optical lattice and discuss a dimensional crossover from the 3D to quasi-2D regime. For the geometry of finite size discs in the 1D lattice, we find that even for a large number of atoms per disc the critical effective tunneling rate for a quantum transition to the Mott insulator state can be large compared to the loss rate caused by three-body recombination. This allows the observation of the Mott transition, in contrast to the case of Bose-condensed gases in the same geometry.     

Universal fermi gas with two- and three-body resonances

We consider a Fermi gas with two components of different masses, with the s-wave two-body interaction tuned to unitarity. In the range of mass ratio 8.62相似文献   

Optical transitions and cyclotron resonance at Landau levels split by a periodic potential

The structure of the electron spectrum is investigated and selection rules are found for transitions between magnetic subbands in a surface 2D superlattice of quantum dots in a perpendicular magnetic field. The photon absorption probabilities are calculated, and the profiles of the absorption lines are determined for allowed and forbidden direct dipole transitions between subbands split off from different Landau levels. Zh. éksp. Teor. Fiz. 114, 1795–1803 (November 1998)     

Minigap plasmons in a two-dimensional electron gas subjected to a one-dimensional periodic potential

We investigate the plasmon excitations in a two-dimensional electron gas subjected to a one-dimensional weak periodic potential. We derive and discuss the dispersion relations for both intrasubband and intersubband excitations within the framework of Bohm-Pines' random-phase approximation. For such an anisotropic system with spatially modulated charge density, we observe a splitting of the 2D plasmon dispersion. The splitting is caused by the superlattice effect of the charge-density modulation on the collective excitation spectrum. We also discuss how the tunneling and the potential amplitude affect the plasmon excitations.     

Normal state of a polarized fermi gas at unitarity

We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n downward arrow/n upward arrow of minority atoms. We predict a first order phase transition from normal to superfluid at x(c)=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P(c)=(N upward arrow - N downward arrow/(N upward arrow + N downward arrow)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.     

Dynamics of dark solitons in a trapped superfluid fermi gas

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation for the oscillation period in terms of observable quantities, which we confirm by solving the time-dependent Bogoliubov-de Gennes equations. Hence we reveal the appearance and dynamics of solitons across the crossover, and show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.     

Hatano-Nelson model with a periodic potential

We study a generalisation of the Hatano-Nelson Hamiltonian in which a periodic modulation of the site energies is present in addition to the usual random distribution. The system can then become localized by disorder or develop a band gap, and the eigenspectrum shows a wide variety of topologies. We determine the phase diagram, and perform a finite size scaling analysis of the localization transition.     

Size-dependent energy scales in the ideal fermi gas

Abstract

The simplest model for the electronic properties of small metal particles is an ideal Fermi gas confined to a finite volume. When the confining region of size L has a regular shape such as a sphere or a cube, there are two distinct scales of energy which characterize the spectrum of eigenvalues near the Fermi energy E_F ≡ ?² k ² _f/2m. The inner scale δ ～ E_F /(k_FL)² is the mean spacing between successive energy levels, while the outer energy scale Δ ～ E_F /(k_FL) describes clustering of several levels, or shell structure. Consequences for the behaviour of thermodynamic properties are investigated. There are three regimes of temperature T: normal metallic (T > Δ), shell-metallic (δ < T < Δ) and semiconductor-like (T < δ). Finally, if the shape of a hard-walled container is allowed to vary so as to minimize the energy, it is argued that the optimal shape fluctuates between spherical and distorted as L is changed.     

Intermediate-temperature superfluidity in an atomic fermi gas with population imbalance

We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature, superfluid transition temperature Tc, and superfluid density in a manner consistent with the standard ground state equations and, thereby, present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for Tc or by low T instabilities. At unitarity, the polarized state is an "intermediate-temperature superfluid."     

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.