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Journal of Physics B Atomic Molecular and Optical Physics

Transition to hydrodynamics in colliding fermion clouds : Theory of quantum gases and quantum coherence

Francesco Toschi, P. Capuzzi, Sauro Succi A, Patrizia Vignolo, M. P. Tosi

Published Jan 1, 2004• 0 citations
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Abstract

We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40 K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov-Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.

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Transition to hydrodynamics in colliding fermion clouds

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We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40 K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov–Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.

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Transition to hydrodynamics in colliding fermion clouds

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We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov–Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.

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We develop a numerical method to study the dynamics of a two-component atomic Fermi gas trapped inside a harmonic potential at temperature T well below the Fermi temperature ${T}_{F}.$ We examine the transition from the collisionless to the collisional regime down to $T=0.2{T}_{F}$ and find a good qualitative agreement with the experiments of B. DeMarco and D.S. Jin [Phys. Rev. Lett. 88, 040405 (2002)]. We demonstrate a twofold role of temperature on the collision rate and on the efficiency of collisions. In particular, we observe a hitherto unreported effect, namely, the transition to hydrodynamic behavior is shifted towards lower collision rates as temperature decreases.

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Collective Modes in Bose-Fermi Mixture Gases

Asano Yoji, Yoji Asano

This thesis theoretically deals with collective modes in the normal phase of a Bose-Fermi mixture composed of single-species bosons and single-species fermions.The mixture is experimentally established as an ultracold atomic gas.While the community studies the mixture including a superfluid phase, relevant to Bose-Einstein condensation of bosons and Cooper paring of fermions, dynamical behaviors in the normal phase have been not fully understood so that we are interested in.We consider the mixture in both spatially uniform and harmonically trapped systems with the Boltzmann equation at finite temperatures.We perform the analysis under the assumption that the physical quantities are near to equilibrium.After the linerization, we apply the moment method to the equation, obtaining a closed set of coupled equations to describe sound or oscillation.The collisional property of the system characterizes the collective modes in the sense of the hydrodynamic regime, collisionless regime, and transition between these regimes.In the uniform system, we investigate sound mode and the dynamic density structure factor.With decreasing temperature, we find that the sound velocity deviates from that of the hydrodynamic mode.Even at a temperature much lower than the Fermi temperature, the sound velocity does not reach the collisionless limit analogous to the zero sound in a Fermi system.However, we show the existence of a long-lived sound at a low temperature as distinct from the first and zero sounds.Nature of the long-lived sound seems to be originated by Pauli blocking of fermions; this statistical effect makes the interspecies collision suppress in the Bose-Fermi mixture.In the trapped system, we mainly study dipole oscillation.We consistently define the relaxation time originated by the interspecies scattering.We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime; one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely-damped modes.We show the time evolution of the three types of hydrodynamic modes with suitable initial conditions.We discuss temperature dependence of the dipole modes.We observe that the relaxation time dominates the dependence compared to the mean-field contribution.We also observe the nonmonotonic behavior of the relaxation time when Pauli blocking of fermions is not negligible.i List of Figures 1.1 Two schematic images of collisions with a period of oscillation . . . . . . . . . . . . . . . . 1 1.2 Measurement of the zero sound in pure liquid 3 He . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Transition between the first sound and the zero sound in a two-component Fermi gas . . . 3 1.4 Dipole oscillations of the two-component gas of 40 K . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Frequencies of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . . . 4 1.6 Damping times of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . 5 1.7 Dipole oscillations of the mixture of 87 Rb and 40 K in the hydrodynamic regime . . . . . . .6 1.8 Dipole oscillations of the mixture of 87 Rb and 40 K in the deeper hydrodynamic regime . . .6 1.9 Dipole oscillations of the mixture of 87 Rb and 40 K in the collisionless regime . . . . . . . .7 2.1 Results obtained by solving the coupled moment equations for sound mode . . . . . . . . .26 3.1 Time evolution of the center-of-mass positions and velocity fields . . . . . . . . . . . . . .39 3.2 Dipole modes as a function of the relaxation time with N B = N F . . . . . . . . . . . . . . .40 3.3 Dipole modes as a function of the relaxation time with N B /N F = 0.2 . . . . . . . . . . . . .41 3.4 Ratio of the displacement of the center of mass to the velocity field as a function of the relaxation time . . . . . . . . . . . . . . . . . . .

•Mar 17, 2020•0 citations
We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40 K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov-Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.
We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40 K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov–Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.
We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov–Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as the temperature decreases.
Experiments at JILA on the collisions between two oscillating spin-polarized components of a Fermi gas of 40K atoms have shown that this setup is an important tool for studying the dynamics of quantum gases. We have developed advanced numerical methods to solve the Vlasov–Landau equations for a binary mixture of atomic Fermi gases inside a harmonic trap at very low temperatures. In particular, a locally adaptive importance-sampling technique allows us to handle collisional interactions several orders of magnitude more efficiently than in standard Monte Carlo calculations. These methods have been applied to study the dynamical and transport properties of a fermion mixture in the presence of mean-field interactions and of collisions between its components for system parameters ranging from the collisionless to the hydrodynamic regime.
We study the collective excitations of polarized single-component quasi-two-dimensional dipolar fermions in an isotropic harmonic trap by solving the collisional Boltzmann-Vlasov (CBV) equation via the method of moments. We study the response to monopole and quadrupole perturbations of the trap potential and investigate the dynamical character of excitations in each case. Simple analytic formulas are found using the linearized scaling ansatz approximation and accurate numerical results are obtained by satisfying the first eight moments of the CBV equation. Except for the lowest-lying monopole mode that is weakly affected by collisions, the quadrupole and the higher-order monopole modes undergo a transition from the collisionless regime to a dissipative crossover regime and finally approach the hydrodynamic regime upon increasing the dipolar interaction strength. For strong transverse confinement (2D limit), we predict the existence of a temperature window within which the characteristics of the collective modes become temperature independent. This plateau, which is a direct consequence of dipole-dipole scatterings, persists as long as the scattering energies remain in the near-threshold regime. The predictions of this work are expected to be observable in the current experiments.
We develop a numerical method to study the dynamics of a two-component atomic Fermi gas trapped inside a harmonic potential at temperature T well below the Fermi temperature TF.{T}_{F}.TF​. We examine the transition from the collisionless to the collisional regime down to T=0.2TFT=0.2{T}_{F}T=0.2TF​ and find a good qualitative agreement with the experiments of B. DeMarco and D.S. Jin [Phys. Rev. Lett. 88, 040405 (2002)]. We demonstrate a twofold role of temperature on the collision rate and on the efficiency of collisions. In particular, we observe a hitherto unreported effect, namely, the transition to hydrodynamic behavior is shifted towards lower collision rates as temperature decreases.
This thesis theoretically deals with collective modes in the normal phase of a Bose-Fermi mixture composed of single-species bosons and single-species fermions.The mixture is experimentally established as an ultracold atomic gas.While the community studies the mixture including a superfluid phase, relevant to Bose-Einstein condensation of bosons and Cooper paring of fermions, dynamical behaviors in the normal phase have been not fully understood so that we are interested in.We consider the mixture in both spatially uniform and harmonically trapped systems with the Boltzmann equation at finite temperatures.We perform the analysis under the assumption that the physical quantities are near to equilibrium.After the linerization, we apply the moment method to the equation, obtaining a closed set of coupled equations to describe sound or oscillation.The collisional property of the system characterizes the collective modes in the sense of the hydrodynamic regime, collisionless regime, and transition between these regimes.In the uniform system, we investigate sound mode and the dynamic density structure factor.With decreasing temperature, we find that the sound velocity deviates from that of the hydrodynamic mode.Even at a temperature much lower than the Fermi temperature, the sound velocity does not reach the collisionless limit analogous to the zero sound in a Fermi system.However, we show the existence of a long-lived sound at a low temperature as distinct from the first and zero sounds.Nature of the long-lived sound seems to be originated by Pauli blocking of fermions; this statistical effect makes the interspecies collision suppress in the Bose-Fermi mixture.In the trapped system, we mainly study dipole oscillation.We consistently define the relaxation time originated by the interspecies scattering.We find that two oscillating modes in the collisionless regime have distinct fates in the hydrodynamic regime; one collisionless mode shows a crossover to a hydrodynamic in-phase mode, and the other collisionless mode shows a transition to two purely-damped modes.We show the time evolution of the three types of hydrodynamic modes with suitable initial conditions.We discuss temperature dependence of the dipole modes.We observe that the relaxation time dominates the dependence compared to the mean-field contribution.We also observe the nonmonotonic behavior of the relaxation time when Pauli blocking of fermions is not negligible.i List of Figures 1.1 Two schematic images of collisions with a period of oscillation . . . . . . . . . . . . . . . . 1 1.2 Measurement of the zero sound in pure liquid 3 He . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Transition between the first sound and the zero sound in a two-component Fermi gas . . . 3 1.4 Dipole oscillations of the two-component gas of 40 K . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Frequencies of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . . . 4 1.6 Damping times of dipole mode in the two-component gas of 40 K . . . . . . . . . . . . . . . 5 1.7 Dipole oscillations of the mixture of 87 Rb and 40 K in the hydrodynamic regime . . . . . . .6 1.8 Dipole oscillations of the mixture of 87 Rb and 40 K in the deeper hydrodynamic regime . . .6 1.9 Dipole oscillations of the mixture of 87 Rb and 40 K in the collisionless regime . . . . . . . .7 2.1 Results obtained by solving the coupled moment equations for sound mode . . . . . . . . .26 3.1 Time evolution of the center-of-mass positions and velocity fields . . . . . . . . . . . . . .39 3.2 Dipole modes as a function of the relaxation time with N B = N F . . . . . . . . . . . . . . .40 3.3 Dipole modes as a function of the relaxation time with N B /N F = 0.2 . . . . . . . . . . . . .41 3.4 Ratio of the displacement of the center of mass to the velocity field as a function of the relaxation time . . . . . . . . . . . . . . . . . . .