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arXiv:2203.07477 · Physical Review A

Interactions of quantum systems with pulses of quantized radiation: From a cascaded master equation to a traveling mode perspective

Victor Rueskov Christiansen, Alexander Holm Kiilerich, Klaus Mølmer

Published Jan 5, 2023• 8 citations

Abstract

The interaction of a propagating pulse of quantum radiation with a localized quantum system can be described by a cascaded master equation with a distinct initially populated input and a finally populated output field mode [Kiilerich and M\o{}lmer, Phys. Rev. Lett. 123, 123604 (2019)]. By transformation to an appropriate interaction picture, we break the cascaded nature of the master equation and recover an effective time-dependent interaction with a lossless single mode and a supplementary lossy mode. The former closely represents the traveling pulse, while the latter constitutes a non-Markovian component in the exchange of quanta between the scatterer and the quantized field. The transformed master equation offers important insights into the system dynamics, and it permits numerically efficient solutions.

DOI: 10.1103/physreva.107.013706

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This paper presents a general master equation formalism for the interaction between traveling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free-space radiation modes and the Jaynes-Cummings model, valid for a discrete eigenmode of a cavity, does not apply. We develop a complete input-output theory to describe the driving of quantum systems by arbitrary incident pulses of radiation and the quantum state of the field emitted into any desired outgoing temporal mode. Our theory is applicable to the transformation and interaction of pulses of radiation by their coupling to a wide class of material quantum systems. We discuss the most essential differences between quantum interactions with pulses and with discrete radiative eigenmodes and present examples relevant to quantum information protocols with optical, microwave, and acoustic waves.

We analyze the Markovian dynamics of a quantum system involving the interaction of two quantized fields at finite temperature decay. Utilizing superoperator techniques and applying two non-unitary transformations, we reformulate the Lindblad master equation into a von Neumann-like equation with an effective non-Hermitian Hamiltonian. Furthermore, an additional non-unitary transformation is employed to diagonalize this Hamiltonian, enabling us to derive an exact solution to the Lindblad master equation. This method provides a framework to calculate the evolution of any initial state in a fully quantum regime. As a specific example, we present the photon coincidence rates for two indistinguishable photons initially interacting within a cavity.