Relaxation of a two-level system (TLS) into a resonant infinite-temperature reservoir with a Lorentzian spectrum is studied. The reservoir is described by a complex Gaussian-Markovian field coupled to the nondiagonal elements of the TLS Hamiltonian. The theory can be relevant for electromagnetic interactions in microwave high-Q cavities and muon spin depolarization. Analytical results are obtained for the strong-coupling regime, ${\Omega }_0\gg \nu ,$ where ${\Omega }_0$ is the rms coupling amplitude (Rabi frequency) and $\nu$ is the width of the reservoir spectrum. In this regime, the population difference and half of the initial coherence decay with two characteristic rates: most of the decay occurs at $t\sim {\Omega }_0^{-1},$ the relaxation being reversible for $t\ll ({\Omega }_0^2\nu {)}^{-1/3},$ whereas for $t\gg ({\Omega }_0^2\nu {)}^{-1/3}$ the relaxation becomes irreversible and is practically over. The other half of the coherence decays with a rate on the order of $\nu ,$ which may be slower by orders of magnitude than the time scale of the population relaxation. The above features are explained by the fact that at $t\ll {\nu }^{-1},$ the reservoir temporal fluctuations are effectively one-dimensional (adiabatic). Moreover, we identify the pointer basis, in which the reduction of the state vector occurs. The pointer states depend on the initial phase of the reservoir.

• Received 3 April 2001

DOI:https://doi.org/10.1103/PhysRevA.64.033809