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arXiv:2401.15231 · Journal of the Optical Society of America B

Band gap engineering and controlling transport properties of single photons in periodic and disordered Jaynes–Cummings arrays

Tiberius Berndsen, Nishan Amgain, Imran M. Mirza

Published Apr 9, 2024• 5 citations

Abstract

We theoretically study the single-photon transport properties in periodic and position-disordered Jaynes–Cummings (or JC) arrays of waveguide-coupled microtoroidal ring resonators, each interacting with a single two-level quantum emitter. Employing the real-space formalism of quantum optics, we focus on various parameter regimes of cavity quantum electrodynamics (cQED) to gain better control of single-photon propagation in such a many-body quantum optical setting. As for some of the key findings, we observe that the periodic setting leads to the formation of the band structure in the photon transmission spectra, which is most evident in the strong coupling regime of cQED. However, under resonant conditions with no losses, the application of Bloch’s theorem indicates that the width of forbidden gaps can be altered by tuning the emitter-cavity coupling to small values. Moreover, in the disordered case, we find that the single-photon transmission curves show the disappearance of band formation. However, spectral features originating from cQED interactions observed for the single atom-cavity problem remain robust against weak-disordered conditions. The results of this work may find application in the study of quantum many-body effects in the optical domain as well as in different areas of quantum computation and quantum networking.

DOI: 10.1364/josab.520000

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We theoretically study the single-photon transport properties in periodic and position-disordered Jaynes–Cummings (or JC) arrays of waveguide-coupled microtoroidal ring resonators, each interacting with a single two-level quantum emitter. Employing the real-space formalism of quantum optics, we focus on various parameter regimes of cavity quantum electrodynamics (cQED) to gain better control of single-photon propagation in such a many-body quantum optical setting. As for some of the key findings, we observe that the periodic setting leads to the formation of the band structure in the photon transmission spectra, which is most evident in the strong coupling regime of cQED. However, under resonant conditions with no losses, the application of Bloch’s theorem indicates that the width of forbidden gaps can be altered by tuning the emitter-cavity coupling to small values. Moreover, in the disordered case, we find that the single-photon transmission curves show the disappearance of band formation. However, spectral features originating from cQED interactions observed for the single atom-cavity problem remain robust against weak-disordered conditions. The results of this work may find application in the study of quantum many-body effects in the optical domain as well as in different areas of quantum computation and quantum networking.

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Quantum interference, responsible for a number of resonant optical phenomena, always intrigues researchers because of its application in optical devices. This work studies it in multiwaveguide systems bridged by Jaynes-Cummings emitters (JCEs) based on the scattering matrix theory. Two types of quantum interference are distinguished here. The first is between the incident wave and those scattered from the JCEs, while the second is only among those scattered waves. The first type leads to the two transmission valleys at the two eigenfrequencies of the JCEs in single-waveguide--single-JCE coupled systems. However, the second type is responsible for the narrow transmission peaks in single-waveguide--multi-JCE coupled systems, locating in the above transmission valleys. This work first shows the properties of the second type of quantum interference in detail and then discusses its two applications. On the one hand, the second type of quantum interference can be used to tailor the transmission spectra to achieve the electromagnetically-induced-transparency-like line shapes with a large group delay. On the other hand, it can also lead to the single-photon jumping between two certain waveguides with a nearly

100%

chance in multiwaveguide systems by switching on or off some of the couplings of the JCEs to the waveguides. These applications with small peak widths commonly require a small loss and might have potential in quantum informatics.

Abstract Controllable single-photon scattering in a one-dimensional waveguide coupled to a Jaynes–Cummings structure containing a time-modulated two-level atom interacting with a single-mode cavity is investigated. The photon transmission and reflection amplitudes are calculated by using an effective Floquet Hamiltonian in real space. The results show that the coupling between the atom and the cavity mode can dynamically be tuned via periodically modulating the atomic transition frequency. As a consequence, the scattering behaviors of the waveguide photons can be actively manipulated, and a controllable single-photon switch with high on-off ratio could be realized. More interestingly, the switch works well within a wide frequency region, i.e., the transmission of both resonant and off-resonant waveguide photons can be effectively switched on or off with appropriate system parameters. Furthermore, the proposed dynamically tunable switching scheme is robust against atomic dissipation associated with the help of atom-cavity coupling mismatch. Such single-photon device can be used as an elementary unit for various quantum information processing.

We investigate the generation and engineering of photonic band gaps in waveguide quantum electrodynamics systems containing periodically arranged atom polymers. We first consider the configuration of a dimer array coupled to a waveguide. The results show that if the intra- and intercell phase delays are properly designed, the center and the width of the band gaps, as well as the dispersion relation of the passbands, can be modified by adjusting the intracell coupling strength. These manipulations provide ways to control the propagating modes in the waveguide, leading to some interesting effects such as slowing or even stopping a single-photon pulse. Finally, we take the case of the tetramer chain as an example to show that, in the case of a larger number of atoms in each unit cell, tunable multigap structures and more sophisticated band-gap engineering can be realized. Our proposal provides efficient ways for photonic band-gap engineering in micro- and nanoquantum systems, which may facilitate the manipulation of photon transport in future quantum networks.

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