Spin Susceptibility and Strong Coupling Effects in an Ultracold Fermi Gas

We investigate magnetic properties and strong coupling corrections in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Within the framework of an extended T-matrix theory, we calculate the spin susceptibility χ above the superfluid phase transition temperature $T_{\rm c}$ . In the crossover region, the formation of preformed Cooper pairs is shown to cause a non-monotonic temperature dependence of χ, which is similar to the so-called spin-gap phenomenon observed in the under-doped regime of high-T _c cuprates. From this behavior of χ, we determine the spin-gap temperature as the temperature at which χ takes a maximum value, in the BCS-BEC crossover region. Since the spin susceptibility is sensitive to the formation of singlet Cooper pairs, our results would be useful in considering the temperature region where pairing fluctuations are important in the BCS-BEC crossover regime of an ultracold Fermi gas.     

Dispersive Effects in the Unitary Fermi Gas

We investigate within density functional theory various physical properties of the zero-temperature unitary Fermi gas which critically depend on the presence of a dispersive gradient term in the equation of state. First, we consider the unitary Fermi superfluid gas confined to a semi-infinite domain and calculate analytically its density profile and surface tension. Then we study the quadrupole modes of the superfluid system under harmonic confinement finding a reliable analytical formula for the oscillation frequency, which reduces to the familiar Thomas-Fermi one in the limit of a large number of atoms. Finally, we discuss the formation and propagation of dispersive shock waves in the collision between two resonant fermionic clouds, and compare our findings with recent experimental results.     

Thermodynamic Quantities of Imbalanced 2D Fermi Gases Near the Berezinskii-Kosterlitz-Thouless Transition

We investigate the effects of imbalance on the two-dimensional Berezinskii-Kosterlitz-Thouless superfluid transition for a Fermi gas in a parabolic trap. Thermodynamic parameters of the Fermi gas are determined using the functional integral formalism in combination with a hydrodynamic action functional for the phase fluctuations.     

线性化AlGaN/GaN HEMT费米能级与二维电子气密度关系的解析模型

通过化简复杂非线性的费米能级EF与二维电子气密度ns关系,并利用化简后函数的一阶泰勒多项式建立了线性化AlGaN/GaN HEMT中EF与ns关系的解析模型。该模型可以根据二维电子气密度ns的范围及温度计算EF与ns非线性关系之线性近似的参数斜率a和截距EF0。计算结果表明,所述模型的线性EF-ns计算结果对非线性精确解近似效果较好,且基于该模型计算的ns-VG曲线与实验数据符合良好。     

Free Energy of a d-Wave Superconductor in the Nearly Antiferromagnetic Fermi Liquid Model

A very general Hamiltonian which describes the coupling of charge carriers via a spin susceptibility is used to derive a formula for the free energy difference between the superconducting and the normal state of a d-wave superconductor. The formula is then specialized to the nearly antiferromagnetic Fermi liquid (NAFL) model and evaluated numerically. The comparison with specific heat data measured for optimally doped YBa₂Cu₃O_6.95 reveals the necessity to include even contributions far away from the Fermi surface to the free energy. The usual restriction to a narrow shell around the Fermi surface in deriving the free energy formula is proved to be inadequate.     

Shell Effects in the First Sound Velocity of an Ultracold Fermi Gas

We investigate the first sound of a normal dilute and ultracold two-component Fermi gas in a cylindrical trap with harmonic radial confinement. We show that the velocity of the sound that propagates along the axial direction strongly varies in the dimensional crossover of the system. In particular, we predict that the first-sound velocity exhibits shell effects: by increasing the density, that is by inducing the crossover from one to three-dimensions, the first-sound velocity shows jumps in correspondence with the filling of harmonic modes. The experimental achievability of these effects is discussed by considering ⁴⁰K atoms.      

Collisional Damping of the Collective Oscillations of a Trapped Fermi Gas

We consider a Fermi gas confined by a harmonic trapping potential and we highlight the role of the Fermi–Dirac statistics by studying frequency and damping of collective oscillations of quadrupole type in the framework of the quantum Boltzmann equation, in which statistical corrections are taken into account in the collisional integral. We are able to describe the crossover from the collisionless regime to the hydrodynamic one by introducing a temperature-dependent relaxation time _Q . We show that, in the degenerate regime, the relaxation rate ^–1 _Q exhibits a temperature dependence different from the collision rate . We finally compare the collisional properties of the Fermi gas with the ones of the Bose gas for temperatures above the Bose–Einstein condensation.     

Viscosity-Entropy Ratio of the Unitary Fermi Gas from Zero-Temperature Elementary Excitations

We investigate the low-temperature behavior of the ratio between the shear viscosity ?? and the entropy density s in the unitary Fermi gas by using a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. Our theoretical curve of ??/s as a function of the temperature T is in qualitative agreement with the experimental data of trapped ultracold ⁶Li atomic gases. We find the minimum value ??/s?0.44 (in units of ?/k _B ) at the temperature T/T _F ?0.27, with T _F the Fermi temperature.     

2D liquid3He near solidification: a highly correlated Fermi liquid

The magnetic susceptibility of two-dimensional liquid³He adsorbed on graphite has been measured by NMR techniques for submonolayer and second layer coverages in a large temperature range around the Fermi temperature. The susceptibility enhancement factor determined in the vicinity of second layer solidification is larger than that found in the bulk liquid at high pressures. The results are discussed in the framework of the quasi-localized and the paramagnon models of liquid³He.     

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behaviour between the high field spin-rotation dominated regime in which D H^–2 , D T^–2 , and the low-field isotropic, collision dominated regime with D = D T^–2 . In this intermediate regime, D_, T^–2 but D D. We emphasize that the low-field crossover cannot be described within the relaxation time approximation. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized ³ He and ³ He– ⁴ He mixtures.     

Two-Dimensional Pseudogap Effects of an Ultracold Fermi Gas in the BCS-BEC Crossover Region

We investigate pseudogap phenomena originating from pairing fluctuations in the BCS-BEC crossover regime of a two-dimensional Fermi gas in a harmonic trap. Including pairing fluctuations within a T-matrix theory and effects of a trap within the local density approximation, we calculate the local density of states (LDOS) at the superfluid phase transition temperature T _c. In the weak-coupling regime, we show that the pseudogap already appears in LDOS around the trap center. The spatial region where the pseudogap can be seen in LDOS becomes wider for a strong pairing interaction. We also discuss how the pseudogap affects the spectrum of the photoemission-type experiment developed by JILA group.     

Temperature Dependence of Renormalized Spin Susceptibility for Interacting 2D Electrons in Silicon

By using Shubnikov-de Haas oscillations in crossed magnetic fields, we measured the temperature dependence of the renormalized spin susceptibility \(\chi _{i}^{*}(T)\) for strongly interacting itinerant 2D electrons in silicon. The weak \(\delta \chi _{i}^{*}(T)\) dependence, only a few percent over the range T = (0.1 ? 1) K, agrees qualitatively with the predicted interaction corrections. However, in strong in-plane magnetic fields, the χ ^?(T) dependence does not vanish or weaken as expected for the interaction corrections. We found that the susceptibility variations are correlated with the T-dependence of the density of itinerant electrons extracted from the magnetooscillation period. We conclude therefore that the \(\chi _{i}^{*}(T)\) dependence is affected by a T-dependent exchange of electrons between the subsystems of itinerant and localized electrons which are in thermodynamic equilibrium.     

Relation of Spin Susceptibility and a.c. Conductivity in Nearly Antiferromagnetic Fermi Liquid

Coupling of the charge carriers through the magnetic spin susceptibility which is strongly peaked at (, ) in the two dimensional CuO ₂ Brillouin zone leads to strong momentum anisotropies and energy dependencies in the inelastic optical scattering rates. The a.c. conductivity is isotropic and can be used to extract an effective, isotropic spin-charge carrier spectral density which reproduces almost exactly the optical scattering rates. The technique is then applied to data in superconducting, optimally doped YBCO and used to measure the charge carrier coupling to the 41 meV peak observed in spin polarized neutron scattering.     

Dynamics of a Highly-Degenerate, Strongly-Interacting Fermi Gas of Atoms

We use all-optical methods to produce a highly-degenerate, Fermi gas of ⁶Li atoms near a Feshbach resonance, where strong interactions are predicted. In this regime, the zero-energy scattering length is larger than the interparticle spacing, and both the mean field energy and the collision rate take on universal forms as a consequence of unitarity and many-body interactions. Our experiments study universal hydrodynamic expansion of the gas and universal mean field interactions. By measuring the cloud radii of the trapped gas, we determine a universal parameter for strongly interacting two-component Fermi systems, the ratio of the mean field energy to the kinetic energy.     

Collective Modes in a Bilayer Dipolar Fermi Gas and the Dissipationless Drag Effect

We consider the collective modes of a bilayer dipolar Fermi system in which the particles interact via long range (～1/r ³) interaction. Assuming that each layer has a background flow which varies little and that the dynamics of the superfluid near T=0 is the same as that of a normal fluid, we obtain the dispersion relations for the collective modes in the presence of background flow. Decomposing the background flow into two parts, the center-of-mass flow and counterflow, we focus on the properties of the counterflow. We first find an estimate of the change in the zero-point energy ΔE _ZP due to counterflow for a unit area of bilayer. Combining this with the free energy F of the system and taking the partial derivatives with respect to background velocities in the layers, we determine the current densities which reveal the fact that current in one layer does not only depend on the velocity in the same layer but also on the velocity of the other layer. This is the drag effect and we calculate the drag coefficient.     

Collective Excitations of a One-Dimensional Fermi Gas Under Harmonic Confinement

We study the spectrum of collective excitations of a spin-polarized Fermi gas confined in a one-dimensional harmonic trap at zero temperature. In the collisionless regime we evaluate exactly the dynamic structure factor, while in the collisional regime we solve analytically the linearized equations of hydrodynamics in the Thomas-Fermi approximation. We also verify the validity of the Thomas-Fermi theory by solving numerically a time-dependent nonlinear Schroedinger equation with a fifth-order interaction term. We find that in both the collisionless and the collisional regime the excitation frequencies of the Fermi gas are multiples of the trap frequency, analogously to the case of the one-dimensional homogeneous Fermi fluid where the velocities of zero and first sound coincide. Due to boson-fermion dynamical mapping our results for the spectrum apply as well to a one-dimensional Bose gas with hard-core point-like interactions (Tonks gas).     

Influence of Spin Fluctuations Upon Heat Capacity of 2D Fermi Liquid Formed on Hectorite

We measured low-temperature heat capacities of two-dimensional Fermi liquid (2D FL) formed on Hectorite down to 15mK. At a coverage where mean atomic distance is comparable to that of bulk ³ He liquid, we found that the temperature dependence deviates considerably from the expected linearity. To account for the deviation we carried through integrals including RPA spin susceptibility for the Stoner-Hubbard(SH) or the Landau's Fermi liquid (LFL) models over the effectively entire, energy-momentum space without imposing the paramagnon approximation or the like. We found numerically that the spin fluctuation develops a T ² correction at T<T* which, at T>T*, is taken over by a Tlog T term where T* is some hundredths of T _F . With these corrections we are able to interprete the data and have determined the parameters for each model consistently at the densities observed.     

Thermodynamic Measurements in a Strongly Interacting Fermi Gas

Strongly interacting Fermi gases provide a clean and controllable laboratory system for modeling strong interparticle interactions between fermions in nature, from high temperature superconductors to neutron matter and quark-gluon plasmas. Model-independent thermodynamic measurements, which do not require theoretical models for calibrations, are very important for exploring this important system experimentally, as they enable direct tests of predictions based on the best current non-perturbative many-body theories. At Duke University, we use all-optical methods to produce a strongly interacting Fermi gas of spin-1/2-up and spin-1/2-down ⁶Li atoms that is magnetically tuned near a collisional (Feshbach) resonance. We conduct a series of measurements on the thermodynamic properties of this unique quantum gas, including the energy E, entropy S, and sound velocity  c. Our model-independent measurements of E and S enable a precision study of the finite temperature thermodynamics. The E(S) data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation T=? E/? S by parameterizing the E(S) data using two different power laws that are joined with continuous E and T at a certain entropy S _c, where the fit is optimized. We observe a significant change in the scaling of E with S above and below S _c. Taking the fitted value of S _c as an estimate of the critical entropy for a superfluid-normal fluid phase transition in the strongly interacting Fermi gas, we estimate the critical parameters. Our E(S) data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes. This enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation, where the ideal Fermi gas temperature is measured before sweeping the magnetic field to the strongly interacting regime. Our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature T _c estimated in the strongly interacting regime from the fits to our E(S) data. We also calibrate the empirical temperature employed in studies of the heat capacity and obtain nearly the same T _c. We determine the ground state energy by three different methods, using sound velocity measurements, by extrapolating E(S) to S=0 and by measuring the ratio of the cloud sizes in the strongly and weakly interacting regimes. The results are in very good agreement with recent predictions. Finally, using universal thermodynamic relations, we estimate the chemical potential and heat capacity of the trapped gas from the E(S) data.     

Trapping Effect of Periodic Structures on the Thermodynamic Properties of a Fermi Gas

We report the thermodynamic properties of an ideal Fermi gas immersed in periodic structures such as penetrable multilayers or multitubes simulated by one (planes) or two perpendicular (tubes) external Dirac comb potentials, while the particles are allowed to move freely in the remaining directions. In contrast to what happens to the bosonic chemical potential, which is a constant for T<T _c , a non decreasing with temperature anomalous behavior of the fermionic chemical potential is confirmed and monitored as the tube bundle goes from 3D to 1D when the wall impenetrability overcomes a threshold value. In the specific heat curves dimensional crossovers are very noticeable at high temperatures, where the system behavior goes from 3D to 2D for multilayers or from 3D to 1D for multitubes, as the wall impenetrability is increased.