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Bulletin of the American Physical Society

Dynamics of particle density and noise correlators of a cold Fermi system expanding from a harmonic trap

Pavel Nagornykh, Victor Galitski

Published Mar 6, 2007• 0 citations
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•May 19, 2021•0 citations
We study the dynamics of time-of-flight expansion of an atomic Fermi system with a finite number of particles NNN after it is released from a harmonic trapping potential. We consider two different initial states: the Fermi sea state and the paired state. In the former case, we derive exact and simple analytic expressions for the dynamics of the particle density and density-density correlation functions, taking into account the level quantization and possible anisotropy of the trap. To describe the paired state, we use the projection of the grand-canonical BCS wave function onto the subspace with a fixed number of particles, and obtain analytic expressions for the density and its correlators in the leading order with respect to the ratio of the trap frequency and the superconducting gap (the ratio is assumed small). We discuss several dynamic features, such as the time evolution of the peak due to pair correlations, which may be used to distinguish between the Fermi sea and the paired state.
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.
We investigate the parametric amplification of the zero-point fluctuations in the spin modes of a two-component Bose-Einstein condensate, that is triggered by the dynamical evolution of the background density. By working in the Thomas-Fermi limit, we first develop a theoretical model for the free dynamics of the Bogoliubov excitations, in a system that is trapped by a time-dependent harmonic potential. Furthermore, we perform an ab-initio numerical study of the two-body (density-density) correlations in the more general inhomogeneous configuration. We consider both the cases of the expanding and oscillating systems. In the former case, we find that the signal due to the particle creation in the spin modes, driven by the dynamical evolution of the overall density of the system, is weak and does not show any particular feature. In the oscillating case instead, because of the onset of resonance between the density oscillations and certain spin modes, the density correlations show a strong signature of the parametric amplification, displaying a clear imprint of the structure of the resonant mode.