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arXiv:2307.16876 · SIAM Journal on Control and Optimization

Quantum Coherent and Measurement Feedback Control Based on Atoms Coupled with a Semi-infinite Waveguide

Haijin Ding, Nina H. Amini, Guofeng Zhang, John Edward Gough

Published Jan 27, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract. In this paper, we demonstrate the application of quantum feedback control in creating desired states for atomic and photonic systems utilizing a semi-infinite waveguide coupled with multiple two-level atoms. In this approach, an initially excited atom can emit one photon into the waveguide, and the photon can be reflected by either the terminal mirror of the waveguide or other atoms, establishing various feedback loops through the coherent interactions between the atom and photon. When there are no more than two excitations in the waveguide quantum electrodynamics (QED) system, the evolution of quantum states can be effectively elucidated through the lens of random graph theory. However, this process is influenced by the environment. We propose that the environment-induced dynamics in the coherent feedback loop can be eliminated by measurement-based feedback control or coherent drives. Consequently, in the atom-waveguide interactions in open quantum systems, measurement-based feedback has the potential to modulate the quantum steady states. Additionally, the homodyne detection noise during the measurement process can induce errors upon quantum states, which can be influenced by the coherent feedback parameter designs.

DOI
10.1137/23m1590482

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Abstract. In this paper, we demonstrate the application of quantum feedback control in creating desired states for atomic and photonic systems utilizing a semi-infinite waveguide coupled with multiple two-level atoms. In this approach, an initially excited atom can emit one photon into the waveguide, and the photon can be reflected by either the terminal mirror of the waveguide or other atoms, establishing various feedback loops through the coherent interactions between the atom and photon. When there are no more than two excitations in the waveguide quantum electrodynamics (QED) system, the evolution of quantum states can be effectively elucidated through the lens of random graph theory. However, this process is influenced by the environment. We propose that the environment-induced dynamics in the coherent feedback loop can be eliminated by measurement-based feedback control or coherent drives. Consequently, in the atom-waveguide interactions in open quantum systems, measurement-based feedback has the potential to modulate the quantum steady states. Additionally, the homodyne detection noise during the measurement process can induce errors upon quantum states, which can be influenced by the coherent feedback parameter designs.
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This thesis considers two types of applications of quantum feedback control; feedback creation of nonclassical states of light, and controlling nonclassical properties of an ensemble of atoms. An electro-optical feedback loop will create an in-loop field with nonclassical photon statistics similar to squeezed light, resulting in fluorescence line-narrowing of a two-level atom coupled to such light. We extend this theory to study a three-level atom coupled to broadband squashed light, and confirm the two-level atom line-narrowing using a more realistic non-Markovian description of the feedback loop. The second type of application utilizes continuous QND measurement of atomic ensembles. If we measure the collective spin, then the system experiences conditional spin squeezing dependent on the measurement results. We show that feedback based on these results can continuously drive the system into the same conditioned state, resulting in deterministically reproducible spin squeezing. If we measure the atom number fluctuations of a BEC, then, due to the nonlinearity of atomic self interactions, this is also information about phase fluctuations. We show that feedback based on this information can greatly reduce the collisional broadening of the linewidth of an atom laser out-coupled from the condensate.