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Physical Review A

Parametric generation of density and spin modes with formation of stationary condensed states in ultracold two-component quasi-one-dimensional Fermi gases

Yu. Kagan, L. A. Manakova

Published Aug 28, 2009• 8 citations
Publisher

Abstract

The temporal evolution of parametrically created collective excitations is studied in an ultracold two-component atomic Fermi gas. We consider quasi-one-dimensional geometry with a permanent modulation of the transverse trap frequency leading to the generation of longitudinal modes for both density and spin branches. After involvement of the interaction between excitations, the evolution comes to the formation of the stationary state with macroscopic filling of a single density or spin mode and zero occupancy for other modes located within the parametric energy interval. In the presence of this state correlation properties of fermions change essentially. Analysis of one-particle density matrix and density-density correlators reveals possibilities for experimental study of density and spin branches.

DOI
10.1103/physreva.80.023625

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A mechanism for the formation of a different type of stationary state with macroscopical number of phonons in condensed atomic gases is proposed. This mechanism is based on generating longitudinal phonons as a result of parametric resonance caused by a permanent modulation of the transverse trap frequency in an elongated trap. The phonon-phonon interaction predetermines the self-consistent evolution which is completed with macroscopic population of one from all levels within the energy interval of parametric amplification. This level proves to be shifted to the edge of this interval. All other levels end the evolution with zero population.
We report on the experimental measurement of the dispersion relation of the density and spin collective excitation modes in an elongated two-component superfluid of ultracold bosonic atoms. Our parametric spectroscopic technique is based on the external modulation of the transverse confinement frequency, leading to the formation of density and spin Faraday waves. We show that the application of a coherent coupling between the two components reduces the phase symmetry and gives a finite mass to the spin modes.
We theoretically analyze interference patterns of parametrically driven one-dimensional ultracold atomic gases. By modulating the interaction strength periodically in time, we propose to excite collective modes in a pair of independent one-dimensional gases at energies corresponding to the drive frequency. The excited collective modes lead to spatial oscillations in the correlations of the interference pattern, which can be analyzed to obtain the sound velocity of the collective modes. We discuss both bosonic and fermionic systems and how such experiments could be used to probe spin-charge separation.
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We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, triggered by the dynamical evolution of the condensate density. We first make use of a Thomas-Fermi approximation to develop a tractable theoretical model of the quantum dynamics of the Bogoliubov excitations in a harmonically trapped condensate with a time-dependent trapping frequency. The predictions of this model are then compared to an ab initio numerical study of the correlation functions of density and spin fluctuations for general spatially inhomogeneous configurations. Results are shown for the two cases of expanding and oscillating condensates: while the quantum excitation of spin modes remains weak and relatively featureless in the case of an expanding condensate, clear and experimentally promising signatures of particle creation are anticipated for the oscillating case under suitable resonance conditions between the density and the spin modes.