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Physical Review A

Interaction of photons with a coupled atom-cavity system through a bidirectional time-delayed feedback

Hamidreza Chalabi, Edo Waks A

Published Dec 21, 2018• 15 citations
Publisher

Abstract

In this paper, we have developed a method for describing the dynamics of an arbitrary quantum system under a bidirectional time-delayed feedback loop. For this purpose, we have described the evolution in terms of the time propagation of the quantum system of interest without feedback together with several identical systems, which represent the history of the quantum system under study. This technique provides a numerically efficient solution for describing a system's dynamics in the case of significant time delays in which direct investigation of the state of the reservoirs becomes numerically intractable. Using this method, we have studied two scenarios of multiple scatterings of photons incident on a cavity with a two-level atom positioned inside it, coupled to two waveguides that are connected at their ends. In the first scenario, two photons impinge on the cavity through separate waveguides with a delay between them. We have demonstrated that the maximum difference between the two output photon numbers occurs when the delay between the incident photons becomes close to the inverse of their linewidth. In the second scenario, multiple photons impinge on the cavity through the same waveguide and go through multiple interactions. We have shown that, for a fixed atom-cavity coupling rate, the transmission rate enhances as the number of photons increases and have quantified this enhancement. The developed method enables us to study a broad range of nonlinear dynamics in complex quantum networks.

DOI
10.1103/physreva.98.063832

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We study the quantum dynamics of multiple two-level atoms (qubits) in a waveguide quantum electrodynamics system, with a focus on modified superradiance effects between two or four atoms with finite delay times. Using a numerically exact matrix product approach, we explore both Markovian and non-Markovian regimes, and highlight the significant influence of time-delayed feedback effects and the clear breakdown of assuming instantaneous coupling dynamics. We first show a system composed of two spatially separated qubits, prepared in a doubly excited state (both fully excited), and provide a comprehensive study of how delayed feedback influences the collective system decay rates, as well as the quantum correlations between waveguide photons, atoms, and between atom and photons. The system is then extended to include two additional qubits located next to the initial ones (four qubits in total), and we demonstrate, by manipulating the initial excitations and the time-delay effects, how long-term quantum correlations and light-matter entangled states can be established.
A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a fictitious series of cascaded quantum systems, where the system is driven by past versions of itself. The derivation of this model relies on a tensor network representation of the system-reservoir time propagator. For concreteness, this general theory is applied to a driven two-level atom scattering into a coherent feedback loop. We demonstrate how delay effects can qualitatively change the dynamics of the atom and how quantum control can be implemented in the presence of time delays.