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Optics Communications

A large time delay of light via two dimensional atom localization in a coupled cavity waveguide

Ronggang Liu, Tong Liu, Yujie Li

Published May 15, 2019• 1 citation
Publisher
DOI
10.1016/j.optcom.2019.05.024

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In this paper, we present an H∞filter for a giant cavity system which couples to a single-mode waveguide at two spatially separated points. The dynamics of the cavity is described by a time-delay Langevin equation in the Heisenberg picture whose time-delay term results from the non-local interactions to a waveguide. The input-output relation with a time-delay feature is also derived. In addition, we design an H∞filter for estimating the evolution of the mode in the cavity using a quadrature representation state-space representation and Linear Matrix Inequality (LMI) approach. Finally, the efficacy of our method is numerically demonstrated in an example.
We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the delay due to the finite travel time of light between the two cavity mirrors is neglected. We show that Rabi oscillation analogous to that obtained with high-finesse classical cavities is achieved only when this travel time is much larger than the time scale that characterizes the collective response of the atomic chain. Therefore, the delay must be taken into account and the dynamics of the problem is inherently non-Markovian. Parameters of interest such as the Rabi frequency and the cavity loss rate due to photon leakage through the mirrors are obtained.
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.