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Computers & Mathematics with Applications

Nonstationary dressed states and effects of decay in nonadiabatic crossing of decaying levels

Vitaly V. Kocharovsky, Vl. V. Kocharovsky, E. A. Derishev, S. A. Litvak, I. A. Shereshevsky, S. Tasaki

Published Oct 1, 1997• 3 citations
Publisher
DOI
10.1016/s0898-1221(97)00172-7

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In this Letter we extend current perspectives in engineering reservoirs by producing a time-dependent master equation leading to a nonstationary superposition equilibrium state that can be nonadiabatically controlled by the system-reservoir parameters. Working with an ion trapped inside a nonideal cavity, we first engineer effective interactions, which allow us to achieve two classes of decoherence-free evolution of superpositions of the ground and excited ionic levels: those with a time-dependent azimuthal or polar angle. As an application, we generalize the purpose of an earlier study [Phys. Rev. Lett. 96, 150403 (2006)10.1103/PhysRevLett.96.150403], showing how to observe the geometric phases acquired by the protected nonstationary states even under nonadiabatic evolution.
We derive a dressed-state master equation in Lindblad form for two strongly coupled two-level atoms. The resulting decay dynamics are governed by Lindblad operators that couple different dressed states. We show that the eigenvalues and eigenvectors of the Liouvillian can be obtained in a compact form, since each off-diagonal element in the dressed-state basis constitutes an eigenvector. Depending on the interatomic distance and the atomic transition frequency, the decay exhibits two well-separated time scales. On short times, the system relaxes into a pair of states, one of which is a transient, maximally entangled state. On longer times, this intermediate entanglement irreversibly decays into a separable steady state. Our results demonstrate that the intrinsic decay mechanism can transiently generate maximal entanglement, an effect that is not captured without the dressed-state master-equation formalism.