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Journal of Modern Optics

Noisy parametric amplifiers in non-equilibrium thermo field dynamics

Masashi Ban

Published Jun 26, 2014• 1 citation
Publisher

Abstract

Single-mode and two-mode parametric amplifiers under the influence of Markovian environments are studied by means of non-equilibrium thermo field dynamics. In the presence of both parametric coupling and system–environment interaction, the dissipative Heisenberg equations of motion are solved for the optical modes of interest. By making use of the solutions, it is examined whether the noisy parametric amplifiers can exhibit the non-classical properties. Furthermore, it is shown that the two-mode parametric amplifier is equivalent to the two single-mode parametric amplifiers with subsequent beam splitting, even if they are influenced by the environments.

DOI
10.1080/09500340.2014.932453

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Single-mode and two-mode parametric amplifiers under the influence of Markovian environments are studied by means of non-equilibrium thermo field dynamics. In the presence of both parametric coupling and system–environment interaction, the dissipative Heisenberg equations of motion are solved for the optical modes of interest. By making use of the solutions, it is examined whether the noisy parametric amplifiers can exhibit the non-classical properties. Furthermore, it is shown that the two-mode parametric amplifier is equivalent to the two single-mode parametric amplifiers with subsequent beam splitting, even if they are influenced by the environments.
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This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.
Abstract In the presented paper, we introduce an analytical description for a dissipative two-mode parametric amplifier coherent cavity containing a three-level system (qutrit). Based on normalized correlation function, Q-function and its associated Wehrl entropy, the dynamics of the quantum phenomena: two-mode cavity non-classically, qutrit phase space information, and quantum coherence are investigated under the physical parameters: qutrit-cavity interactions, initial coherent intensity, and the dissipation. It is found that the generated quantum phenomena, due to the qutrit-cavity interaction, depend on the physical parameters of the initial states and the dissipation. The robustness of the quantum phenomena against the dissipation can be enhanced by decreasing the initial coherent intensity cavity. The stability and strength of the generated bunching/anti-bunching behaviour can be controlled by the cavity dissipation.
The amplification of electromagnetic fields is analyzed in a quantum-mechanical context by discussing the behavior of a simple theoretical model of the parametric amplifier. The statistical properties of the amplifier fields are described by means of the time-dependent density operator for the system. In doing this, extensive use is made of the coherent states and the PPP representation of the density operator, which provide a quantum-mechanical description of the fields closely resembling their classical description. Explicit solutions are obtained for the density operator for either of the two field modes for a variety of initial states of the modes. Initial states considered include combinations of coherent states, chaotic mixtures, and nnn-quantum states. Particular attention is given the behavior of the amplifier fields in the limit of large amplification. The conditions are established under which the amplification process leads in this limit to the existence of a non-negative PPP representation for the density operator for a single mode of oscillation.
We describe the realization of multimode phononic correlations that arise from nonlinear interactions in a mechanical nondegenerate parametric amplifier. The nature of these correlations differs qualitatively depending on the strength of the driving field in relation to the threshold for parametric instability. Below this threshold, the correlations are manifest in a combined quadrature of the coupled mechanical modes. In this regime, the system is amenable to back-action evading measurement schemes for the detection of weak forces. Above threshold, the correlations are manifest in the amplitude difference between the two mechanical modes, akin to intensity difference squeezing observed in optical parametric oscillators. We discuss the crossover of correlations between these two regimes and applications of this quantum-compatible mechanical system to nonlinear metrology and out-of-equilibrium dynamics.