Quantum limited sound attenuation in a dilute atomic Fermi gas

Discontinuities in the First and Second Sound Velocities at the Berezinskii-Kosterlitz-Thouless Transition

We calculate the temperature dependence of the first and second sound velocities in the superfluid phase of a 2D dilute Bose gas by solving Landau's two fluid hydrodynamic equations. We predict the occurrence of a significant discontinuity in both velocities at the critical temperature, as a consequence of the jump of the superfluid density characterizing the Berezinskii-Kosterlitz-Thouless transition. The key role of the thermal expansion coefficient is discussed. We find that second sound in this dilute Bose gas can be easily excited through a density perturbation, thereby, making the perspe…

Scale breaking and fluid dynamics in a dilute two-dimensional Fermi gas

We study two observables related to the anomalous breaking of scale invariance in a dilute two dimensional Fermi gas, the frequency shift and damping rate of the monopole mode in a harmonic confinement potential. For this purpose we compute the speed of sound and the bulk viscosity of the two dimensional gas in the high temperature limit. We show that the anomaly in the speed of sound scales as $(2P-ρc_s^2)/P\sim z/[\log(T/E_B)]^2$, and that the bulk viscosity $ζ$ scales as $ζ/η\sim z^2/[\log(T/E_B)]^6$. Here, $P$ is the pressure, $c_s^2$ is the speed of sound, $η$ is the shear viscosity, $z$ …

Scalar quanta in Fermi liquids: zero sounds, instabilities, Bose condensation, and a metastable state in dilute nuclear matter

Spectrum of bosonic scalar-mode excitations in a normal Fermi liquid with a local scalar interaction is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations. An effective Lagrangian for the scalar excitation modes is derived after performing a boson…

一维超固态中的声波与涨落

Sounds waves and fluctuations in one-dimensional supersolids

本文研究一维晶体结构稀薄超固态的低能激发，基于拉格朗日量建立广义弹性参数的流体力学描述，并通过Bogoliubov-de Gennes方程验证声速与涨落预测，揭示偶极BEC与软芯相互作用模型分别近似实现体不可压缩与刚性晶格超固态极限。

二维简并费米气体中的声耗散机制

Mechanism for sound dissipation in a two-dimensional degenerate Fermi gas

该研究通过数值模拟结合相位印记技术与Metropolis算法，探究二维简并费米气体在超流相变附近不同相互作用区域的声输运特性，明确了声速、扩散系数的温度及相互作用强度依赖关系，揭示了虚涡旋-反涡旋对在声耗散中的关键作用。

Comparison of three approaches to light scattering by dilute cold atomic ensembles

Collective effects in atom-light interaction is of great importance for cold-atom-based quantum devices or fundamental studies on light transport in complex media. Here we discuss and compare three different approaches to light scattering by dilute cold atomic ensembles. The first approach is a coupled-dipole model, valid at low intensity, which includes cooperative effects, like superradiance, and other coherent properties. The second one is a random-walk model, which includes classical multiple scattering and neglects coherence effects. The third approach is a crude approximation only based …

关于稀均匀玻色气体的反常密度

On the anomalous density of a dilute homogeneous Bose gas

本文发展了考虑任意相位的Hartree-Fock-Bogoliubov理论，证明反常密度σ的符号与相位相关而不可观测，但其绝对值可通过声速和凝聚分数测量提取，并给出了均匀盒中BEC的理论预测。

Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound

We investigate the low-temperature thermodynamics of the unitary Fermi gas by introducing a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. We calculate the Helmholtz free energy and from it we obtain the entropy, the internal energy and the chemical potential as a function of the temperature. By using these quantities and the Landau's expression for the superfluid density we determine analytically the superfluid fraction, the critical temperature, the first sound velocity and the second sound velocity. We compare our analy…

Viscosity spectral functions of the dilute Fermi gas in kinetic theory

We compute the viscosity spectral function of the dilute Fermi gas for different values of the s-wave scattering length $a$, including the unitarity limit $a\to\infty$. We perform the calculation in kinetic theory by studying the response to a non-trivial background metric. We find the expected structure consisting of a diffusive peak in the transverse shear channel and a sound peak in the longitudinal channel. At zero momentum the width of the diffusive peak is $ω_0\simeq (2ε)/(3η)$ where $ε$ is the energy density and $η$ is the shear viscosity. At finite momentum the spectral function approa…

Second sound with ultracold atoms: A brief historical account

We briefly review the research on second sound in ultracold atomic physics, with emphasis on strongly interacting unitary Fermi gases with infinitely large $s$-wave scattering length. Second sound is a smoking-gun feature of superfluidity in any quantum superfluids. The observation and characterization of second sound in ultracold quantum gases has been a long-standing challenge, and in recent years there are rapid developments due to the experimental realization of a uniform box-trap potential. The purpose of this review is to present a brief historical account of the key research activities …

Effective-range signatures in quasi-1D matter waves: sound velocity and solitons

We investigate ultracold and dilute bosonic atoms under strong transverse harmonic confinement by using a 1D modified Gross-Pitaevskii equation (1D MGPE), which accounts for the energy dependence of the two-body scattering amplitude within an effective-range expansion. We study sound waves and solitons of the quasi-1D system comparing 1D MGPE results with the 1D GPE ones. We point out that, when the finite-size nature of the interaction is taken into account, the speed of sound and the density profiles of both dark and bright solitons show relevant quantitative changes with respect to what pre…

Information scrambling of the dilute Bose gas at low temperature

We calculate the quantum Lyapunov exponent $λ_L$ and butterfly velocity $v_B$ in the dilute Bose gas at temperature $T$ deep in the Bose-Einstein condensation phase. The generalized Boltzmann equation approach is used for calculating out-of-time ordered correlators, from which $λ_L$ and $v_B$ are extracted. At very low temperature where elementary excitations are phonon-like, we find $λ_L\propto T^5$ and $v_B\sim c$, the sound velocity. At relatively high temperature, we have $λ_L\propto T$ and $v_B\sim c(T/T_*)^{0.23}$. We find $λ_L$ is always comparable to the damping rate of a quasiparticle…

Second Sound in Ultracold Atomic Gases

We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagatio…

Collective excitations of a dilute Bose gas at finite temperature: TDHFB Theory

Using the time-dependent Hartree-Fock-Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings c…

Universal Sound Diffusion in a Strongly Interacting Fermi Gas

Transport of strongly interacting fermions governs modern materials -- from the high-$T_c$ cuprates to bilayer graphene --, but also nuclear fission, the merging of neutron stars and the expansion of the early universe. Here we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting Fermi gas of atoms by studying sound propagation and its attenuation via the coupled transport of momentum and heat. In the normal state, the sound diffusivity ${D}$ monotonically decreases upon lowering the temperature $T$, in contrast to the diverging behavior of weakly interacting…

Ab initio quantum-statistical approach to kinetic theory of low-temperature dilute gases of hydrogen-like atoms

We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound states of particles and the method of reduced description of relaxation processes. Within the approach we developed the first-order perturbation theory over the weak interaction for a system of kinetic equations for the Wigner distribution functions of free fermions of both kinds and their bound states, the hydrogen-like atoms. It is shown that the condition…