Collective oscillations of a trapped quantum gas in low dimensions

Abstract

We present a comprehensive study of the discretized modes of an atomic gas in different conditions of confinement. Starting from the equations of hydrodynamics we derive a closed equation for the velocity field, depending on the adiabatic and isothermal compressibilities and applicable to different dimensions and quantum statistics. At zero temperature the equation reproduces the irrotational behavior of superfluid hydrodynamics. It is also applicable above the critical temperature in the collisional regime, where the appearence of rotational components in the velocity field is caused by the external potential. In the presence of harmonic trapping, a general class of analytic solutions is obtained for systems exhibiting a polytropic equation of state, characterized by a power law isoentropic dependence of the pressure on the density. Explicit results for the compressional modes are derived for both Bose and Fermi gases in the pancake, cigar as well as in the deep 2D and 1D regimes. Our results agree with the analytical predictions available in the literature in some limiting cases. They are particularly relevant in 1D configurations, where the study of the collective frequencies could provide a unique test of the achievement of the collisional regime at finite temperature.

11 pages

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• Superfluid behaviour of a two-dimensional Bose gas
• The critical velocity in the BEC-BCS crossover
• Finite-Temperature Collective Dynamics of a Fermi Gas in the BEC-BCS Crossover
• Apparent low-energy scale invariance in two-dimensional Fermi gases
• Collective Modes in a Unitary Fermi Gas across the Superfluid Phase Transition
• Sound propagation in elongated superfluid fermion clouds
• Scaling solutions of the two fluid hydrodynamic equations in a harmonically trapped gas at unitarity

Cited by in corpus (29)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Anomalous breaking of scale invariance in a two-dimensional Fermi gas
• Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases
• Thermal instability, evaporation and thermodynamics of one-dimensional liquids in weakly-interacting Bose-Bose mixtures
• Reduced quantum anomaly in a quasi-2D Fermi superfluid: The significance of the confinement-induced effective range of interactions
• Low-energy collective oscillations and Bogoliubov sound in an exciton-polariton condensate
• Collective many-body bounce in the breathing-mode oscillations of a Tonks-Girardeau gas
• Hydrodynamic VS collisionless dynamics of a 1D harmonically trapped Bose gas
• Probing superfluidity in a quasi two-dimensional Bose gas through its local dynamics
• Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas
• Dynamics of a Fermi gas quenched to unitarity
• Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics
• Collective modes of a two-dimensional Fermi gas at finite temperature
• Analytic thermodynamic properties of the Lieb-Liniger gas
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Geometric squeezing of rotating quantum gases into the lowest Landau level
• Breathing mode frequency of a strongly interacting Fermi gas across the 2D-3D dimensional crossover
• Collective oscillations of a Bose-Einstein condensate induced by a vortex ring
• Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• Thermodynamic contacts and breathing mode physics of 1D p-wave Fermi gases in the high temperature limit
• Higher-Harmonic Collective Modes in a Trapped Gas from Second-Order Hydrodynamics
• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Classical Dynamics of Harmonically Trapped Interacting Particles
• Dark solitons in a trapped gas of long-range interacting bosons
• Strongly Interacting Fermi Gases: Hydrodynamics and Beyond
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
• Particle-hole origin of thermal beating in dipole-compression modes of a 1D Bose gas
• Anomalous isothermal compressibility in spin-orbit coupled degenerate Fermi gases