Exact Markovian and non-Markovian time dynamics in waveguide QED: collective interactions, bound states in continuum, superradiance and subradiance

Fatih Dinc1,2, İlke Ercan3, and Agata M. Brańczyk1

1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada
2Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
3Electrical & Electronics Engineering Department, Boğaziçi University, Istanbul, 34342, Turkey

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Abstract

We develop a formalism for modelling $exact$ time dynamics in waveguide quantum electrodynamics (QED) using the real-space approach. The formalism does not assume any specific configuration of emitters and allows the study of Markovian dynamics $\textit{fully analytically}$ and non-Markovian dynamics semi-analytically with a simple numerical integration step. We use the formalism to study subradiance, superradiance and bound states in continuum. We discuss new phenomena such as subdivision of collective decay rates into symmetric and anti-symmetric subsets and non-Markovian superradiance effects that can lead to collective decay stronger than Dicke superradiance. We also discuss possible applications such as pulse-shaping and coherent absorption. We thus broaden the range of applicability of real-space approaches beyond steady-state photon transport.

The quantum internet has the potential to revolutionize how computers talk to each other. Such systems could give people access to cloud-based quantum computers, and provide a level of privacy, security and computational power not possible with today’s internet. The ultimate vision of the quantum internet is a connection of potentially billions of quantum devices within the same network. A key challenge in designing such networks involves theoretical modelling. Existing models could only cope with very simple networks. We develop an approach for modelling complex networks of many devices, and use that method to make predictions in regimes not previously accessible.
Quantum networks will most likely be realized by sending quantum light through waveguides, such as optical fibres, that are connected to quantum devices—the most simple of which is a quantum bit (qubit). Various approaches have been explored for modelling interactions between quantum light and qubits in waveguides. Each method offers unique intuition and can be preferable over another depending on the problem of interest.
The virtue of our approach lies in providing analytical or semi-analytical (with a simple numerical integration step) results. This model makes it possible to study interactions between quantum light and qubits in complex waveguide geometries, with an unprecedented number of possibly non-identical qubits, using only a personal computer.
We expect that our method will benefit applications such as quantum logic, quantum memory, quantum photon routing, and quantum communication, bringing the ambitious vision of the quantum internet closer to realization.

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Cited by

[1] Fatih Dinc and Agata M. Brańczyk, "Non-Markovian super-superradiance in a linear chain of up to 100 qubits", Physical Review Research 1 3, 032042 (2019).

[2] Kanupriya Sinha, Pierre Meystre, Elizabeth A. Goldschmidt, Fredrik K. Fatemi, S. L. Rolston, and Pablo Solano, "Non-Markovian Collective Emission from Macroscopically Separated Emitters", Physical Review Letters 124 4, 043603 (2020).

[3] Paolo Facchi, Davide Lonigro, Saverio Pascazio, Francesco V. Pepe, and Domenico Pomarico, "Bound states in the continuum for an array of quantum emitters", Physical Review A 100 2, 023834 (2019).

[4] Alexander Carmele, Nikolett Nemet, Victor Canela, and Scott Parkins, "Pronounced non-Markovian features in multiply-excited, multiple-emitter waveguide-QED: Retardation-induced anomalous population trappin", arXiv:1910.13414.

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