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Physica Scripta

Phase properties of Schrödinger cat states of light decaying in phase-sensitive reservoirs

Vladimír Bužek, Ts. Gantsog, M S Kim

Published Jan 1, 1993• 23 citations
Publisher

Abstract

We study phase properties of quantum mechanical superposition states decaying into phase-sensitive reservoirs. We show that the Wigner phase quasiprobability distribution reflects the quantum interference effects very well while the Pegg–Barnett and the Husimi phase probability distributions are quite insensitive with respect to the character of the quantum interference between component states. We study in detail phase properties of the even coherent state which decays into the thermal and the squeezed reservoirs. In thermal reservoirs the phase of the superposition state becomes randomized under the influence of thermal fluctuations. The higher the number of thermal photons the faster the randomization process is. On the other hand we show that depending on the relative phase between the superposition state and the phase-sensitive reservoir the process of phase randomization can be either enhanced or completely suppressed.

DOI
10.1088/0031-8949/1993/t48/021

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We study phase properties of quantum mechanical superposition states decaying into phase-sensitive reservoirs. We show that the Wigner phase quasiprobability distribution reflects the quantum interference effects very well while the Pegg–Barnett and the Husimi phase probability distributions are quite insensitive with respect to the character of the quantum interference between component states. We study in detail phase properties of the even coherent state which decays into the thermal and the squeezed reservoirs. In thermal reservoirs the phase of the superposition state becomes randomized under the influence of thermal fluctuations. The higher the number of thermal photons the faster the randomization process is. On the other hand we show that depending on the relative phase between the superposition state and the phase-sensitive reservoir the process of phase randomization can be either enhanced or completely suppressed.
Any quantum-mechanical system is not isolated. It interacts with its environment (for instance, it interacts with reservoirs). It is known that the decay rate of quantum coherences in phase-sensitive (squeezed) reservoirs can be significantly modified compared to the decay rate in ordinary (phase- insensitive) thermal reservoirs. Depending on 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. In this paper we study in which way the phase properties of an even coherent state 1 (CS) are changed under the influence of reservoirs.
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.
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.
Phase properties of squeezed number states and squeezed thermal states are studied. Exact analytical formulae for phase distributions based on different phase approaches are derived and illustrated graphically. It is shown that the phase quasiprobability distribution P (W) ( theta ) associated with the Wigner function does not depend on the photon number of the initial number state and has the same form for both kinds of squeezed states under consideration while the Pegg-Barnett phase distribution and the phase quasiprobability distributions associated with the Q function and the Glauber-Sudarshan P function, approach P (W) ( theta ) in the limit of highly excited states.
In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.