Two-Fluid Hydrodynamics in Trapped Bose Gases and in Superfluid Helium

A review is given of recent theoretical work on the superfluid dynamics of trapped Bose gases at finite temperatures, where there is a significant fraction of non-condensate atoms. One can now reach large enough densities and collision cross-sections needed to probe the collective modes in the collision-dominated hydrodynamic region where the gas exhibits characteristic superfluid behavior involving the relative motions of the condensate and non-condensate components. The precise analogue of the Landau-Khalatnikov two-fluid hydrodynamic equations was recently derived from trapped Bose gases, starting from a generalized Gross-Pitaevskii equation for the condensate macroscopic wavefunction and a kinetic equation for the non-condensate atoms.     

Recent Progress and New Challenges in Quantum Fluids and Solids

The exact expression for the average kinetic energy of an inhomogeneous Bose gas in the ground state is obtained as a functional of the inhomogeneous density of the Bose–Einstein condensate. The result is based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose–Einstein condensate. This makes it possible to avoid the use of anomalous averages. On this basis, the explicit expressions for the ground-state energy and the local pressure of an inhomogeneous Bose gas are derived within the self-consistent Hartree–Fock approximation.     

Quasiparticle Kinetic Equation in a Trapped Bose Gas at Low Temperatures

Recently the authors used the Kadanoff–Baym non-equilibrium Green's function formalism to derive kinetic equation for the non-condensate atoms, in conjunction with a consistent generalization of the Gross–Pitaevskii equation for the Bose condensate wavefunction. This work was limited to high temperatures, where the excited atoms could be described by a Hartree–Fock particle-like spectrum. Following the approach of Kane and Kadanoff in 1965, we present the generalization of our recent work which is valid at low temperatures, where the input single-particle spectrum is now described by the Bogoliubov–Popov approximation. We derive a kinetic equation for the quasiparticle distribution function with collision integrals describing scattering between quasiparticles and the condensate atoms. From the general expression for the collision integral for the scattering between quasiparticle excitations, we find the quasiparticle distribution function corresponding to local equilibrium. This expression includes a quasiparticle chemical potential that controls the non-diffusive equilibrium between condensate atoms and the quasiparticle excitations. We derive a generalized Gross–Pitaevskii equation for the condensate wavefunction that also includes the damping effects due to collisions between atoms in the condensate and the thermally excited quasiparticles. For a uniform Bose gas, our kinetic equation for the thermally excited quasiparticles reduces to that found by Eckern, as well as by Kirkpatrick and Dorfman.     

Spin Dynamics of a Trapped Spin-1 Bose Gas above the Bose-Einstein Transition Temperature

We study collective spin oscillations in a trapped spin-1 Bose gas above the Bose-Einstein transition temperature. Starting from the Heisenberg equation of motion, we derive a kinetic equation describing the dynamics of a thermal gas with the spin-1 internal degree of freedom. Applying the moment method to the kinetic equation, we study spin-wave collective modes with dipole symmetry. The dipole modes in the spin-1 system are classified into the three types of modes. These frequencies and damping rates are obtained as functions of the peak density. Moreover we find that the damping rate is characterized by three relaxation times associated with collisions.      

Kinetics of phase transition in ideal and weakly interacting bose gas

The time evolution of a Bose system passing through the critical point is considered. The solution of the nonlinear integrodifferential equation that governs the kinetics demonstrates that the new phase formation proceeds by the set of essentially nonequilibrium states. The phase transition in an ideal Bose gas is of first order and can be completed att= only if there are no nuclei of the new phase at the beginning of the cooling process. With nuclei the Bose condensate formation takes a finite time. A Bose gas with interaction between Bose particles exhibits a second-order phase transition with a finite time of new phase formation even without nuclei. The time evolution of an energy spectrum of a Bose system following the variation of its distribution function is considered and it is shown that the appearance of superfluidity coincides with the instant of Bose condensate formation.     

Population Dynamics of a Spin-1 Bose Gas at Finite Temperatures

We study population dynamics of a trapped spin-1 Bose gas above the Bose-Einstein transition temperature. Starting from the semiclassical kinetic equation for a spin-1 gas, we derive coupled rate equations for the populations of internal states. Solving the rate equations, we study the dynamical evolution of spin populations. We also estimate the characteristic timescale in which the system reaches equilibrium. Finally, we briefly discuss the extension of the theory to Bose-condensed phase below the Bose-Einstein transition temperature, and discuss the static equilibrium condition for the spin-1 system.     

Kinetic Theory of a Spin-1 Bose Condensed Gas at?Finite Temperatures

We derive a kinetic theory of a spin-1 Bose condensed gas at finite temperatures. The theory consists of coupled equations for the condensate and noncondensate. The condensate dynamics is described by a generalized Gross?CPitaevskii (GP) equation including the spin degree of freedom. The condensate and noncondensate atoms interact with each other through the mean field and collisions. From the coupled equations, we determine the condition for static equilibrium of the spin-1 system. We also use the static thermal cloud approximation to derive a generalized GP equation including a dissipative term due to the coupling to a thermal cloud.     

Anisotropic Spin Diffusion in Trapped Boltzmann Gases

No Heading Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.PACS numbers: 03.75.Mn,05.30Jp,05.60.Gg,51.10.+y.67.20.+k.     

Relaxation processes in a condensed Bose gas

We develop, on the basis of the self-consistent mean-field approximation, the kinetic theory for a dilute Bose gas below the Bose-Einstein transition temperature. The collision operator in the Boltzmann equation is calculated by golden rule arguments, and the momentum and temperature dependences of the scattering rates are determined. As an application, we consider the relaxation of a nonequilibrium distribution of the quasiparticles. We discuss the relevance of our calculation for the (hypothetical) condensed state of spinpolarized hydrogen.Zur Erlangung der Lehrbefähigung für das Lehrgebiet Physik der Fakultät für Physik der Universität Karlsruhe vorgelegte Habilitationsschrift.     

Padé approximants applied to the equation of state and heat capacity of quantum ideal gases

Padé approximants have been applied to the equation of state and heat capacity of the quantum ideal gases. For the Bose gas the agreement is almost perfect. For the Fermi gas, the maximum relative error is 0.03% for the former and 0.4% for the latter.     

Kinetic theory and dynamic structure factor of a condensate in the random phase approximation

No Heading We present the microscopic kinetic theory of a homogeneous dilute Bose condensed gas in the generalized random phase approximation (GRPA), which satisfies the following requirements: 1) the mass, momentum and energy conservation laws; 2) the H-theorem; 3) the superfluidity property and 4) the recovery of the Bogoliubov theory at zero temperature ¹. In this approach, the condensate influences the binary collisional process between two normal atoms, in the sense that their interaction force results from the mediation of a Bogoliubov collective excitation traveling throughout the condensate. Furthermore, as long as the Bose gas is stable, no collision happens between condensed and normal atoms. In this paper, we show how the kinetic theory in the GRPA allows to calculate the dynamic structure factor at finite temperature and when the normal and superfluid are in a relative motion. The obtained spectrum for this factor provides a prediction which, compared to the experimental results, allows to validate the GRPA.PACS numbers:03.75.Hh, 03.75.Kk, 05.30.–d     

Dynamics of Fluctuating Bose–Einstein Condensates

We present a generalized Gross–Pitaevskii equation that describes the dissipative dynamics of a trapped partially Bose-condensed gas. It takes the form of a complex nonlinear Schrödinger equation with noise. We consider an approximation to this Langevin field equation that preserves the correct equilibrium for both the condensed and the noncondensed parts of the gas. We then use this formalism to describe the reversible formation of a one-dimensional Bose condensate, and compare with recent experiments. In addition, we determine the frequencies and the damping of collective modes in this case.     

Superfluid-Insulator Transition of a Bose–Einstein Condensation in a Periodic Potential and Its Interference Pattern

Recent experiments have succeeded in observing the superfluid-Mott insulator quantum phase transition of an alkali atomic Bose–Einstein condensate in an optical lattice potential. Motivated by this work, we studied the two-dimensional Bose gas in a periodic potential by analyzing the Gross–Pitaevskii equation. We found evidence of a superfluid-insulator transition that occurs as the potential depth of the lattice is increased. For the periodic potential, the phase of the macroscopic wave function in the ground state is localized in each potential minimum. Also, according to the resugts using the Hartree–Fock–Bogoliubov equation, an energy gap appears in the lowest excitation state. We then added a parabolic trapping potential to the periodic potential and studied how the dynamics of the wave function and its interference pattern depend on the initial ground state. For the initial ground state localized by the deep periodic potential, the wave function oscillates in the central potential minimum after removing only the trapping potential. After turning off both the trapping and periodic potentials, the wave packets with periodicity escape from the condensate.     

不可逆回热式玻色布雷顿制冷循环性能分析

基于玻色气体的热力学性质和回热式布雷顿制冷循环的不可逆模型,导出循环的一些重要性能参数,如循环的制冷量、回热量、输入功和性能系数的一般表达式。通过数值计算获得了循环的一些重要的性能特性曲线,分析了循环的不可逆性和回热特性对玻色布雷顿制冷机性能的影响。     

Coherent states and the suppression of Bose-Einstein condensation in restricted geometries

A coherent state formalism involving density-phase variables is used to show that for the ideal Bose gas the suppression of Bose condensation in restricted geometries is due to thermal fluctuations of the superfluid velocity potential. The phase factor correlation function has the same form in one, two, and three dimensions as that obtained by Rice for superconductors, with the thermal wavelength setting the scale in this case.     

Quasiparticle scattering in Fermi fluids

The scattering of quasiparticles in a normal Fermi fluid is analyzed within the framework of Landau's kinetic theory, and a generalized Bethe-Salpeter equation for the scattering amplitude is derived. This integral equation accounts for both large and small momentum and energy transfers ; in the forward-scattering limit it reduces to Landau's well-known equation. An explicit expression for the scattering probability is also derived. An off-diagonal generalization of the quasiparticle interaction function f is introduced and its calculation from microscopic theory is discussed. The results are applied to an explicit calculation of the scattering amplitude in a dilute hard-sphere Fermi gas, to second order in the scattering-length parameter k _F a _s, and the calculation is shown to be consistent with symmetry requirements for the scattering of fermions. Based in part on a Ph.D. thesis submitted to the University of Colorado.     

The Schrödinger Cat Family in Attractive Bose Gases

We show that the ground state of an attractive Bose gas in a double well evolves from a coherent state to a Schrödinger Cat like state as the tunneling barrier is decreased. The latter exhibits super-fragmentation similar to the ground state of a spin-1 Bose gas with antiferromagnetic interactions. We also show that the fragmented condensates of attractive and repulsive Bose gases in double wells lead to very different interference patterns.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.