arXiv subjects

Xia-Ji Liu

Publications and source records attributed to Xia-Ji Liu.

At least 163 records · Page 9Linked to original sources

arXiv2008

Multi-component strongly attractive Fermi gas: a color superconductor in a one-dimensional harmonic trap

Recent advances in ultra-cold atomic Fermi gases make it possible to achieve a fermionic superfluid with multiple spin components. In this context, any mean-field description is expected to fail, owing to the presence of tightly bound clusters or molecules that consist of more than two particles. Here we present a detailed study of a strongly interacting multi-component Fermi gas in a highly elongated or quasi-one-dimensional harmonic trap, which could be readily obtained in experiment. By using the exact Bethe ansatz solution and a local density approximation treatment of the harmonic trap, we investigate the equation of state of the multi-component Fermi gas in both a homogeneous and trapped environment, as well as the density profiles and low-energy collective modes. The binding energy of multi-component bound clusters is also given. We show that there is a peak in the collective mode frequency at the critical density for a deconfining transition to a many-body state that is analogous to the quark color superconductor state expected in neutron stars.

cond-mat.supr-con↗

arXiv2007

Probing two-fluid hydrodynamics in a trapped Fermi superfluid at unitarity

We develop a variational approach to calculate the density response function at finite temperatures of the lowest-lying two-fluid modes in a trapped two-component Fermi superfluid close to a Feshbach resonance. The out-of-phase oscillations, which are the analogue in trapped gases of second sound in uniform superfluids, have so far not been observed in cold-atom experiments. At unitarity, we show that these modes are observable at finite temperatures via two-photon Bragg scattering, whose spectrum is related to the imaginary part of density response function. This provides direct evidence for superfluidity and a promising way to test microscopic results for thermodynamics at unitarity.

cond-mat.other↗

arXiv2007

Variational theory of two-fluid hydrodynamic modes at unitarity

We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau's two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence, can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these new modes as function of temperature in an isotropic trap at unitarity.

cond-mat.other↗

arXiv2007

Fulde-Ferrell-Larkin-Ovchinnikov states in one-dimensional spin-polarized ultracold atomic Fermi gases

We present a systematic study of quantum phases in a one-dimensional spin-polarized Fermi gas. Three comparative theoretical methods are used to explore the phase diagram at zero temperature: the mean-field theory with either an order parameter in a single-plane-wave form or a self-consistently determined order parameter using the Bogoliubov-de Gennes equations, as well as the exact soluble Bethe ansatz method. We find that a spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov phase, which lies between the fully paired BCS state and the fully polarized normal state, dominates most of the phase diagram of a uniform gas. The phase transition from the BCS state to the Fulde-Ferrell-Larkin-Ovchinnikov phase is of second order, and therefore there are no phase separation states in one-dimensional homogeneous polarized gases. This is in sharp contrast to the three-dimensional situation, where a phase separation regime is predicted to occupy a very large space in the phase diagram. We conjecture that the prediction of the dominance of the phase separation phases in three dimension could be an artifact of the non-self-consistent mean-field approximation, which is heavily used in the study of three-dimensional polarized Fermi gases. We consider also the effect of a harmonic trapping potential on the phase diagram, and find that in this case the trap generally leads to phase separation, in accord with the experimental observations for a trapped gas in three dimension. We finally investigate the local fermionic density of states of the Fulde-Ferrell-Larkin-Ovchinnikov ansatz. A two-energy-gap structure is shown up, which could be used as an experimental probe of the Fulde-Ferrell-Larkin-Ovchinnikov states.

cond-mat.stat-mech↗

arXiv2007

Universal thermodynamics of strongly interacting Fermi gases

Strongly interacting Fermi gases are of great current interest. Not only are fermions the most common particles in the universe, but they are also thought to have a universal thermodynamic behavior for strong interactions \cite{heiselberg,carlson,ho}. Recent experiments on ultra-cold Fermi gases provide an unprecedented opportunity to test universality in the laboratory \cite{hara,thomas,partridge,stewart,luo}. In principle this allows - for example - the interior properties of hot, dense neutron stars to be investigated on earth. Here we carry out a detailed test of this prediction. We analyze results from three ultra-cold fermion experiments involving two completely distinct atomic species in different kinds of atomic trap environments \cite{partridge,stewart,luo}. The data is compared with the predictions of a recent strong interaction theory \cite{hldepl,hldpra}. Excellent agreement is obtained, with no adjustable parameters. By extrapolating to zero temperature, we show that the experimental measurements yield a many-body parameter} $\mathbf{β\simeq-0.59\pm.07}$, \textbf{describing the universal energy of strongly interacting Fermi gases.

cond-mat.str-el↗

arXiv2007

Density fingerprint of giant vortices in Fermi gases near a Feshbach resonance

The structure of multiply quantized or giant vortex states in atomic Fermi gases across a Feshbach resonance is studied within the context of self-consistent Bogoliubov-de Gennes theory. The particle density profile of vortices with $κ>1$ flux quanta is calculated. Owing to $κ$ discrete branches of vortex core bound states, inside the core the density oscillates as a function of the distance from the vortex line and displays a non-monotoic dependence on the interaction strengths, in marked contrast to the singly quantized case, in which the density depletes monotonically. This feature, never reported so far, can make a direct visualization of the giant vortices in atomic Fermi gases.

cond-mat.supr-con↗

arXiv2007

Mean field thermodynamics of a spin-polarized spherically trapped Fermi gas at unitarity

We calculate the mean-field thermodynamics of a spherically trapped Fermi gas with unequal spin populations in the unitarity limit, comparing results from the Bogoliubov-de Gennes equations and the local density approximation. We follow the usual mean-field decoupling in deriving the Bogoliubov-de Gennes equations and set up an efficient and accurate method for solving these equations. In the local density approximation we consider locally homogeneous solutions, with a slowly varying order parameter. With a large particle number these two approximation schemes give rise to essentially the same results for various thermodynamic quantities, including the density profiles. This excellent agreement strongly indicates that the small oscillation of order parameters near the edge of trap, sometimes interpreted as spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states in previous studies of Bogoliubov-de Gennes equations, is a finite size effect. We find that a bimodal structure emerges in the density profile of the minority spin state at finite temperature, as observed in experiments. The superfluid transition temperature as a function of the population imbalance is determined, and is shown to be consistent with recent experimental measurements. The temperature dependence of the equation of state is discussed.

cond-mat.str-el↗

arXiv2007

Visualization of vortex bound states in polarized Fermi gases at unitarity

We analyse theoretically a single vortex in 3D trapped atomic Fermi gases with population polarization near a broad Feshbach resonance. Above a critical polarization the Andreev-like bound states inside the core become occupied for the majority component. As a result, the local density difference at the core center acquires a sudden rise at low temperautres. This provides a visualization of the lowest bound state within the absorption imaging technique. As the polarization increases, the core expands gradually, and correspondingly, the energy of the lowest bound state decreases.

cond-mat.supr-con↗

arXiv2007

Phase diagram of a strongly interacting polarized Fermi gas in one dimension

Based on the integrable Gaudin model and local density approximation, we discuss the phase structure of one-dimensional trapped Fermi gases with imbalanced spin populations for arbitrary attractive interactions. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, a coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an FFLO structure, and predict the resulting mode frequency as a function of the spin polarization.

cond-mat.supr-con↗

arXiv2006

BCS-BEC crossover in an asymmetric two-component Fermi gas

We discuss the superfluid phase transition of a strongly interacting Fermi gas with unequal (asymmetric) chemical potentials in two pairing hyperfine states, and map out its phase diagram near the BCS-BEC crossover. Our approach includes the fluctuation contributions of {}``preformed Cooper pairs'' to the thermodynamic potential at finite temperature. We show that, below a critical difference in chemical potentials between species, a normal gas is unstable towards the formation of either a finite-momentum paired Fulde-Ferrell-Larkin-Ovchinnikov superconducting phase or a uniform superfluid, depending on the asymmetry and interaction strengths. We determine the value of critical chemical potential mismatch, and find good qualitative agreement with a recent measurement by Zwierlein \textit{et al.} {[}Science \textbf{311}, 492 (2006){]}.

cond-mat.stat-mech↗

arXiv2006

Mean field phase diagrams of imbalanced Fermi gases near a Feshbach resonance

We propose phase diagrams for an imbalanced (unequal number of atoms or Fermi surface in two pairing hyperfine states) gas of atomic fermions near a broad Feshbach resonance using mean field theory. Particularly, in the plane of interaction and polarization we determine the region for a phase separation phase composed of normal and superfluid components. We compare our prediction of phase boundaries with the recent measurment, and find a good qualitative agreement.

cond-mat.str-el↗

arXiv2006

Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozieres and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available.

cond-mat.supr-con↗

arXiv2006

Temperature of a trapped unitary Fermi gas at finite entropy

We present theoretical predictions for the equation of state of a harmonically-trapped Fermi gas in the unitary limit. Our calculations rest on a study of the equation of state of a uniform gas using three distinct perturbation schemes, compared to Monte-Carlo results. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly-interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.

cond-mat.supr-con↗

arXiv2005

A self-consistent theory of atomic Fermi gases with a Feshbach resonance at the superfluid transition

A self-consistent theory is derived to describe the BCS-BEC crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper-pairs and ``bare'' Feshbach molecules, has been included within a self-consistent $T$-matrix approximation, beyond the Nozières and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature $T_c$ increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor $Z_m$ of the molecule's Green function and a complex effective mass have been determined, to characterize the fraction and lifetime of Feshbach molecules at $T_c$. Our many-body calculations of $Z_m$ agree qualitatively well with the recent measurments on the gas of $^6$Li atoms near the broad resonance at 834 Gauss. The crossover from narrow to broad resonances has also been studied.

cond-mat.str-el↗

arXiv2005

Signature of Mott-insulator transition with ultra-cold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultra-cold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.

cond-mat.stat-mech↗

arXiv2004

Collective modes and ballistic expansion of a Fermi gas in the BCS-BEC crossover

We evaluate the frequencies of collective modes and the anisotropic expansion rate of a harmonically trapped Fermi superfluid at varying coupling strengths across a Feshbach resonance driving a BCS-BEC crossover. The equations of motion for the superfluid are obtained from a microscopic mean-field expression for the compressibility and are solved within a scaling ansatz. Our results confirm non-monotonic behavior in the crossover region and are in quantitative agreement with current measurements of the transverse breathing mode by Kinast {\it et al.} [Phys. Rev. Lett. {\bf 92}, 150402 (2004)] and of the axial breathing mode by Bartenstein {\it et al.} [Phys. Rev. Lett. {\bf 92}, 203201 (2004)].

cond-mat.stat-mech↗

arXiv2003

Collective oscillations of a confined Bose gas at finite temperature in the random-phase approximation

We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the non-condensate on an equal footing within a generalized random-phase approximation, which ({\it i}) extends the second-order Beliaev-Popov approach by allowing for the dynamical coupling between fluctuations in the thermal cloud, and ({\it ii}) reduces to an earlier random-phase scheme when the anomalous density fluctuations are omitted. Numerical calculations of the low-lying spectra in the case of isotropic confinement show that the present theory obeys with high accuracy the generalized Kohn theorem for the dipolar excitations and demonstrate that combined normal and anomalous density fluctuations play an important role in the monopolar excitations of the condensate. Mean-field theory is instead found to yield accurate results for the quadrupolar modes of the condensate. Although the restriction to spherical confinement prevents quantitative comparisons with measured spectra, it appears that the non-mean field effects that we examine may be relevant to explain the features exhibited by the breathing mode as a function of temperature in the experiments carried out at JILA on a gas of $^{87}$Rb atoms.

cond-mat.stat-mech↗

arXiv2003

Finite temperature effects on the collapse of trapped Bose-Fermi mixtures

By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture.

cond-mat.stat-mech↗