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Physical Review A

Cavity quantum electrodynamics in the presence of energy relaxation and pure dephasing: A unified quantum master-equation approach

Rui‐Xue Xu, YiJing Yan, Xin-Qi Li

Published Jan 10, 2002• 20 citations
Publisher

Abstract

This paper renders two main results. One is a unified quantum master equation, which satisfies the detailed-balance relation and can serve as a convenient starting formulation to study the dissipative dynamics in a variety of systems in quantum optics and solid-state physics. Another is based on the proposed quantum master equation to study cavity quantum electrodynamics in the presence of ${T}_{1}$ energy relaxation and pure ${T}_{2}$ dephasing. Demonstrated in detail is also the effect of cavity field--absorber interaction on dissipation, which is neglected in the conventional theory.

DOI
10.1103/physreva.65.023807

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This paper renders two main results. One is a unified quantum master equation, which satisfies the detailed-balance relation and can serve as a convenient starting formulation to study the dissipative dynamics in a variety of systems in quantum optics and solid-state physics. Another is based on the proposed quantum master equation to study cavity quantum electrodynamics in the presence of T1{T}_{1}T1​ energy relaxation and pure T2{T}_{2}T2​ dephasing. Demonstrated in detail is also the effect of cavity field--absorber interaction on dissipation, which is neglected in the conventional theory.
Quantum measurement of a solid-state qubit by a mesoscopic detector is of fundamental interest in quantum physics and an essential issue in quantum computing. In this work, by employing a unified quantum master equation approach constructed in our recent publications, we study the measurement-induced relaxation and dephasing of the coupled-quantum-dot states measured by a quantum-point contact. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. As a result, our theory is applicable to measurement at arbitrary voltage and temperature. Both numerical and analytical results for the qubit relaxation and dephasing are carried out, and important features are highlighted in concern with their possible relevance to future experiments.
We theoretically analyze the resonance fluorescence of a solid-state cavity quantum electrodynamics (QED) system that consists of a quantum dot and a cavity. We clarify the effects of pure dephasing by investigating the elastic and inelastic scattering probabilities, the fluorescence power spectrum, and the energy exchange with the environment. Pure dephasing interactions with the environment both enhance nonresonant coupling between the dot and the cavity and enable the pump light to continuously absorb energy from the environment under appropriate conditions.
Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.
We investigate a quantum-dot-based cavity system via the master-equation approach. The dynamics of the system is greatly affected by dissipation and dephasing processes. We include these phenomena to the theory through the master equation. The dissipation effects such as cavity loss, spontaneous recombination of excitons, and incoherent pumping are considered. The dephasing process is included as an electron--acoustic-phonon interaction. An intrinsic feature of solid-state cavity systems is the presence of electron-phonon interaction, which distinguishes this system from atomic cavity quantum electrodynamics. Due to the temperature dependence of phonons we use the complete form of the master equation (temperature dependence of dissipation rates) in this paper. We study the emission spectrum and photon statistics of the system. We show that cavity mode emission depends on temperature, and temperature strongly affects the photon statistics.
By using a rather simple algebraic approach, we revisit and further bridge between two most commonly used quantum dissipation theories, the Bloch–Redfield theory and a class of Fokker–Planck equations. The nature of the common approximation scheme involving in these two theories is analyzed in detail. While the Bloch–Redfield theory satisfies the detailed-balance relation, we also construct a class of Fokker–Planck equations that satisfy the detailed-balance relation up to the second moments in phase-space. Developed is also a generalized Fokker–Planck equation that preserves the general positivity of the reduced density operator. Both T1-relaxation and pure-T2 dephasing are considered, and their temperature dependence is shown to be very different. Provided is also an analogy between the quantum pure-T2 dephasing and the classical heat transport.
We propose a Markovian quantum master equation that can describe the Fano effect directly, by assuming a standard cavity quantum electrodynamics system.The framework allows us to generalize the Fano formula, applicable over the weak-and strong-coupling regimes with pure dephasing.A formulation of its emission spectrum is also given in a consistent manner.We then find that the interference responsible for the Fano effect is robust against pure dephasing.This is counterintuitive because the impact of interference is, in general, severely reduced by decoherence processes.Our approach thus provides a basis for theoretical treatments of the Fano effect and insights into the quantum interference in open quantum systems.