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Journal of Physics B Atomic Molecular and Optical Physics

Preparing superposition of squeezed coherent states under thermal reservoir

José S. Sales, L. F. da Silva, N. G. de Almeida

Published Dec 1, 2010• 4 citations
Publisher

Abstract

We propose a scheme for engineering a superposition of squeezed coherent states into a lossy cavity and study its evolution under the influence of a thermal reservoir, providing analytical results for the Wigner function as well as for the Glauber–Sudarshan P function. To characterize this state, we study both the fidelity and the atomic inversion for several parameters, including some parameters taken out from recent experiments in cavity QED.

DOI
10.1088/0953-4075/43/24/245504

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We propose a scheme for engineering a superposition of squeezed coherent states into a lossy cavity and study its evolution under the influence of a thermal reservoir, providing analytical results for the Wigner function as well as for the Glauber–Sudarshan P function. To characterize this state, we study both the fidelity and the atomic inversion for several parameters, including some parameters taken out from recent experiments in cavity QED.
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In this paper, we alternatively study the evolution of squeezed vacuum state (SVS) in lossy channel by virtue of the phase space method. By using the formula of Wigner function (WF) in coherent representation and [Formula: see text] representation of quantum density operator, the WF formula in lossy channel is derived. After obtaining the analytical expressions of the WFs of the lossy SVS and the squeezed thermal state (STS), we further prove the fact that the lossy SVS is equivalent to a kind of STS. Our result is useful in dealing with the light field transmission problems in the presence of losses.
Squeezed thermal reservoirs, characterized by thermal noise with anisotropic fluctuations, have profound implications in quantum thermodynamics and serve as powerful resources for quantum information. However, their experimental realizations remain challenging. Existing schemes typically rely on injected squeezed light, time-dependent modulation, or driven nonlinear interactions, which introduce complexity and limit experimental feasibility. Using only time-independent linear coupling to a lossy mode within a normal thermal environment, we identify a general and experimentally accessible framework for squeezed-reservoir engineering, applicable across platforms such as circuit and cavity quantum electrodynamics as well as coupled cavity systems. We illustrate the framework through two experimentally relevant cases: directional phase coherence extension in two-level systems like qubits or atoms, and dissipative quadrature squeezing in bosonic modes like photons or phonons. By eliminating the need for active control or squeezed input, our passive linear-coupling approach provides a resource-efficient and practical pathway to dissipative squeezing, decoherence suppression, entanglement stabilization, quantum simulation, and the exploration of unconventional quantum thermodynamics and phase transitions.
We suggest a quantum state reconstruction scheme. Our proposal is applicable to the field inside a microwave cavity as well as to the harmonic motion of a trapped atom. It will be shown that the inversion of two-level atoms after a resonant interaction with a coherently displaced quantum state is directly related to the Wigner characteristic function of the initial state. This method neither requires the preparation of atoms in a quantum superposition of the upper and lower energy levels nor heavy numerical processing of the measured data. We demonstrate the reconstruction scheme for the example of a Schr\"odinger-cat superposition state.
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.