Wigner-Weisskopf atom and quantum Stochastic dilations

Hans Maassen

L. Davidovich

Y.K. Wang, I. C. Khoo

David Applebaum

Using techniques of quantum stochastic calculus, a dilation scheme is developed to describe the evolution of a two-level atom, which is initially in a (nontracial) Gibbs state, through a radiation field. The Wigner–Weisskopf approximation is assumed but not the rotating wave approximation, the latter being shown to be equivalent to the requirement that the dilation satisfies the quantum detailed balance condition with respect to the initial state.

Stephen L. Adler

We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schr\"odinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schr\"odinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects. In addition, elegant stochastic-theoretic methods suggested by Di\'osi are used to rederive the principal results, without the assumptions needed to linearize the stochastic equation, and to give analogous results for the Rabi oscillations of a two-level system.

Piotr Garbaczewski