Schrödinger-cat states at finite temperature: Influence of a finite-temperature heat bath on quantum interferences.

Abstract

Recently several methods have been proposed for generation of superposition (Schr\"odinger-cat) states in microwave cavities. At microwave frequencies, thermal photons can significantly affect statistical properties of superposition states. In the present paper we study the influence of a thermal heat bath on nonclassical properties of quantum superposition states. We show that at nonzero temperature the loss of coherences is much faster than at zero temperature. Using the formalism of quasiprobability distributions and solving the corresponding Fokker-Planck equations, we describe the time evolution of the super-position states in phase space and derive the rate of the decay of quantum coherence. This decay rate depends on the separation between the component states and on the temperature of the heat bath. Moreover, we discuss in detail how the interaction with a nonzero-temperature heat bath leads to a transformation of a nonclassical state to a classical state. We show that the sensitivity of the quantum coherence to the presence of thermal photons can lead to some difficulties in the preparation of Schr\"odinger-cat states in microwave cavities unless the temperature of the microwave cavity is sufficiently low.