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arXiv:nucl-th/0407092 · Nuclear Physics A

Damped collective motion of many body systems: A variational approach to the quantal decay rate

Christian Rummel, Helmut Hofmann

Published Apr 18, 2005• 2 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysa.2005.04.001

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We investigate the dynamics of two trapped ions interacting with a common thermal reservoir, focusing on how cross-correlated dissipation influences heating, steady-state behavior, and parameter sensitivity. Starting from a microscopic system--reservoir model, we derive the corresponding Heisenberg--Langevin equations and show that reservoir-induced correlations generate collective decay channels and, when the cross-damping rate matches the local damping, a decoherence-free normal mode that preserves memory of the initial excitations. Using the Fisher information associated with motional population measurements, we identify the parameter regimes in which cross-damping enhances the estimability of both system and reservoir properties. For nonclassical initial states, we also show that reservoir-mediated correlations can generate or maintain entanglement, with the strongest effects occurring near the decoherence-free condition.
We present a variational solution of the Langevin field equation describing the nonequilibrium dynamics of a harmonically trapped Bose-Einstein condensate. If the thermal cloud remains in equilibrium at all times, we find that the equations of motion for the parameters in our variational ansatz are equivalent to the Langevin equations describing the motion of a massive Brownian particle in an external potential. Moreover, these equations are coupled to a stochastic rate equation for the number of atoms in the condensate. As applications of our approach, we have calculated the collisional damping rates and frequencies of the low-lying collective excitations of a condensate with repulsive interactions, and have obtained a description of the growth and subsequent collapse of a condensate with attractive interactions. We have found good agreement with the available experimental results in both cases.