On Decaying Rate of Quantum States

A.P. Grécos

M. S. Kim, Vladimír Bužek

Using the Wigner function formalism in phase space, we analyze the decay of quantum coherences in phase-sensitive reservoirs. We show that the decay rate of quantum coherences in phase-sensitive reservoirs can be significantly modified compared to the decay rate in ordinary (phase-insensitive) thermal reservoirs. Depending on the phases of the quantum system (field mode) and the squeezed reservoir, the decay rate of the quantum coherence can be either enhanced or significantly suppressed, which is in agreement with the results obtained recently by other methods [T. A. B. Kennedy and D. F. Walls, Phys. Rev. A 37, 152 (1988)]. We show that in an ideally squeezed reservoir with a high degree of squeezing, the decay rate of the quantum coherence (i.e., the decay rate of off-diagonal terms of the density matrix in the coherent-state basis) can be equal to the decay rate of the energy of the system (i.e., the decay rate of diagonal terms of the density matrix). Suppression of the decay rate of the quantum coherence leads to preservation of nonclassical effects such as the oscillations in the photon number distribution. Moreover, we find that some initial superposition states of light exhibiting super-Poissonian photon statistics can be transformed into intermediate sub-Poissonian states under the influence of phase-sensitive reservoirs.

V. G. Emel'Yanov, Dimitri P. Kostomarov, V. I. Kukulin

Fardin Kheirandish

Decaying rate of a quantum system investigated using the Fubini-Study definition of distance between states.

H. C. Fan, Liyun Hu

Ulrich D. Jentschura

We investigate the two-photon decay rate of a highly excited atomic state which can decay to bound states of lower energy via cascade processes. We show that a na\"{\i}ve treatment of the process, based on the introduction of phenomenological decay rates for the intermediate, resonant states, leads to lower-order terms which need to be subtracted in order to obtain the coherent two-photon correction to the decay rate. The sum of the lower-order terms is exactly equal to the one-photon decay rate of the initial state, provided the na\"{\i}ve two-photon decay rates are summed over all available two-photon channels. A quantum electrodynamics treatment of the problem leads to an ``automatic'' subtraction of the lower-order terms.