This article is devoted to the study of two-dimensional Bose gases harmonically confined. We first summarize their equilibrium properties. For such a gas above the critical temperature, we also derive the frequencies and the damping of the collective oscillations and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. We establish the link between the relaxation times relevant for the damping of the collective oscillations and for the time-of-flight expansion. We also evaluate the collision rate and its relationship with the relaxation time.This article is devoted to the study of two-dimensional Bose gases harmonically confined. We first summarize their equilibrium properties. For such a gas above the critical temperature, we also derive the frequencies and the damping of the collective oscillations and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. We establish the link between the relaxation times relevant for the damping of the collective oscillations and for the time-of-flight expansion. We also evaluate the collision rate and its relationship with the relaxation time.

Jan 1, 20040 citations

Collective oscillations of a trapped atomic gas in low dimensions and thermodynamics of one-dimensional Bose gas

Giulia De Rosi

Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit.

Jan 1, 20170 citations

Dynamics of a classical gas including dissipative and mean-field effects

P. Pedri, David Guéry-Odelin, S. Stringari

By means of a scaling ansatz, we investigate an approximated solution of the Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive the frequencies and the damping of the collective oscillations of a harmonically trapped gas and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. An explicit link between the relaxation times relevant for the damping of the collective oscillations and for the expansion is established.By means of a scaling ansatz, we investigate an approximated solution of the Boltzmann-Vlasov equation for a classical gas. Within this framework, we derive the frequencies and the damping of the collective oscillations of a harmonically trapped gas and we investigate its expansion after releasing of the trap. The method is well suited to study the collisional effects taking place in the system and in particular to discuss the crossover between the hydrodynamic and the collisionless regimes. An explicit link between the relaxation times relevant for the damping of the collective oscillations and for the expansion is established.

arXiv:cond-mat/0305624Physical Review AOct 9, 200371 citations

Temperature-dependent relaxation times in a trapped Bose-condensed gas

Tetsuro Nikuni, Adam Griffin

Explicit expressions for all the transport coefficients have recently been found for a trapped Bose-condensed gas at finite temperatures. These transport coefficients are used to define the characteristic relaxation times, which determine the crossover between the mean-field collisionless and the two-fluid hydrodynamic regime. These relaxation times are evaluated as a function of the position in the trap potential. We show that all the relaxation times are dominated by the collisions between the condensate and the noncondensate atoms, and are much smaller than the standard classical collision time used in most of the current literature. The study [Stamper-Kurn et al., Phys. Rev. Lett. 81, 500 (1998)] of the collective modes at finite temperature is shown to have been well within the two-fluid hydrodynamic regime.Explicit expressions for all the transport coefficients have recently been found for a trapped Bose-condensed gas at finite temperatures. These transport coefficients are used to define the characteristic relaxation times, which determine the crossover between the mean-field collisionless and the two-fluid hydrodynamic regime. These relaxation times are evaluated as a function of the position in the trap potential. We show that all the relaxation times are dominated by the collisions between the condensate and the noncondensate atoms, and are much smaller than the standard classical collision time used in most of the current literature. The study [Stamper-Kurn et al., Phys. Rev. Lett. 81, 500 (1998)] of the collective modes at finite temperature is shown to have been well within the two-fluid hydrodynamic regime.

arXiv:cond-mat/0107444Physical Review ADec 14, 200118 citations

Collective excitation frequencies and damping rates of a two-dimensional deformed trapped Bose gas above the critical temperature

Tarun Kanti Ghosh

We derive an equation of motion for the velocity fluctuations of a two-dimensional deformed trapped Bose gas just above the critical temperature in the hydrodynamical regime. From this equation, we calculate the eigenfrequencies and the corresponding density fluctuations for a few low-lying excitation modes. Using the method of averages, we derive a dispersion relation in a deformed trap at very high temperature that interpolates between the collisionless and hydrodynamic regimes. We make use of this dispersion relation to calculate the frequencies and the damping rates for monopole and quadrupole mode in both the regimes. We also discuss the time evolution of the wave-packet width of a Bose gas in a time-independent trap as well as a time-dependent trap.We derive an equation of motion for the velocity fluctuations of a two-dimensional deformed trapped Bose gas just above the critical temperature in the hydrodynamical regime. From this equation, we calculate the eigenfrequencies and the corresponding density fluctuations for a few low-lying excitation modes. Using the method of averages, we derive a dispersion relation in a deformed trap at very high temperature that interpolates between the collisionless and hydrodynamic regimes. We make use of this dispersion relation to calculate the frequencies and the damping rates for monopole and quadrupole mode in both the regimes. We also discuss the time evolution of the wave-packet width of a Bose gas in a time-independent trap as well as a time-dependent trap.

arXiv:cond-mat/0007210Physical Review ADec 7, 20009 citations

Frequency and damping of hydrodynamic modes in a trapped Bose-condensed gas

Tetsuro Nikuni, Allan Griffin

Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable ${}^{4}\mathrm{He}$ is discussed. We also present calculations for the damping of the analogous $m=0$ monopole-quadrupole condensate mode in the superfluid phase.Recently it was shown that the Landau-Khalatnikov two-fluid hydrodynamics describes the collision-dominated region of a trapped Bose condensate interacting with a thermal cloud. We use these equations to discuss the low frequency hydrodynamic collective modes in a trapped Bose gas at finite temperatures. We derive variational expressions based on these equations for both the frequency and damping of collective modes. A new feature is our use of frequency-dependent transport coefficients, which produce a natural cutoff by eliminating the collisionless low-density tail of the thermal cloud. Above the superfluid transition, our expression for the damping in trapped inhomogeneous gases is analogous to the result first obtained by Landau and Lifshitz for uniform classical fluids. We also use the moment method to discuss the crossover from the collisionless to the hydrodynamic region. Recent data for the monopole-quadrupole mode in the hydrodynamic region of a trapped gas of metastable ${}^{4}\mathrm{He}$ is discussed. We also present calculations for the damping of the analogous $m=0$ monopole-quadrupole condensate mode in the superfluid phase.

arXiv:cond-mat/0309269Physical Review AFeb 4, 200423 citations

{}^{4}\mathrm{He}

is discussed. We also present calculations for the damping of the analogous

m=0

monopole-quadrupole condensate mode in the superfluid phase.