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Frontiers of Physics

Evolution of decoherence in a degenerate parametric-amplifier system with thermal noise

Xiang-Guo Meng, Jianming Liu, Lian-Zhen Cao, Xu-Cong Zhou, Zhen-Shan Yang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum decoherence is considered a core obstacle in quantum computing; therefore, suppressing decoherence is a primary task. Based on the integral representation of the solution to the thermal master equation, we focus on the evolution of decoherence in a degenerate parametric amplifier system described by a known Hamiltonian in a thermal environment. We also investigate the evolution of the photon number distribution, Wigner distribution, and von Neumann entropy in a thermal environment. This work can provide a theoretical reference for experimental studies of degenerate parametric amplifier systems.

DOI
10.15302/frontphys.2026.093201

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Quantum decoherence is considered a core obstacle in quantum computing; therefore, suppressing decoherence is a primary task. Based on the integral representation of the solution to the thermal master equation, we focus on the evolution of decoherence in a degenerate parametric amplifier system described by a known Hamiltonian in a thermal environment. We also investigate the evolution of the photon number distribution, Wigner distribution, and von Neumann entropy in a thermal environment. This work can provide a theoretical reference for experimental studies of degenerate parametric amplifier systems.
In this paper we investigate the single-mode properties (Wigner function, photon-number distribution and quadrature squeezing) of a dissipative parametric amplifier when the signal and idler modes are initially prepared in the Schrödinger-cat states. We show that there are two sources producing decoherence in the system, which are spontaneous pump photon decay and interaction with the environment. For the latter case, the system collapses to both statistical mixture states as well as thermal states governed by the interaction parameters.
Control of open quantum dynamics is of great interest for realizing quantum technologies. Therefore, it is an important task to quantify and characterize the entropy for open quantum systems under decoherence. In this paper, we study the time evolution of the von Neumann entropy for open quantum systems described by the Lindblad master equation. Note that, in particular, when the decoherence corresponds to the measurement for the observable in the system, the von Neumann entropy tends to monotonically increases as the variance becomes larger. Furthermore, we present a lower bound of the von Neumann entropy in the long-time limit. This lower bound has advantages of being straightforwardly calculated and applicable to a general Markovian open quantum system.
We study the decoherence of a renormalized quantum field theoretical system. We consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. Using out-of-equilibrium field theory techniques at finite temperatures, we show that the Gaussian von Neumann entropy for a pure quantum state asymptotes to the interacting thermal entropy. The decoherence rate can be well described by the single particle decay rate in our model. Connecting to electroweak baryogenesis scenarios, we moreover study the effects on the entropy of a changing mass of the system field. Finally, we compare our correlator approach to existing approaches to decoherence in the simple quantum mechanical analogue of our field theoretical model. The entropy following from the perturbative master equation suffers from physically unacceptable secular growth.
We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.
We study open quantum systems where the coupling between the system and its environment is of a quantum nondmolition (QND) type. Such a system undergoes decoherence without dissipation of energy. We obtain the master equation for the evolution of such a system under the influence of a squeezed thermal bath. From the master equation it can be seen explicitly that the process involves decoherence without any dissipation. We work out the decoherence causing term in the high and zero temperature limits and show that they match with known results in the different temperature regimes for the case of a thermal bath. We also make a comparison between the quantum statistical properties of QND and non-QND (i.e., involving decoherence as well as dissipation) types of evolution.
The analysis of the quantum-mechanical parametric amplifier begun in the preceding paper is extended to describe the joint quantum state of the two interacting modes of oscillation of the system. Equations are derived for the time evolution of the Schr\"odinger density operator. Comparison with classical theory is made by describing the state of the quantum-mechanical system by means of the PPP representation. The time evolution of the weight function $P(\ensuremath{\alpha}, \ensuremath{\beta}, t)$ for this representation, and of the corresponding Wigner distribution function $W(\ensuremath{\alpha}, \ensuremath{\beta}, t)$, is found. A decoupled form for the equations of motion for the field variables is exhibited which simplifies the solutions for these functions. It is shown that the amplification process gives rise to a correlation between the two mode amplitudes which becomes exceedingly strong with increasing time. The relation of this correlation to the time development of the functions $P(\ensuremath{\alpha}, \ensuremath{\beta}, t)$ and $W(\ensuremath{\alpha}, \ensuremath{\beta}, t)$ is discussed.