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arXiv:2110.09375 · Chinese Optics Letters

Three methods for the single-photon transport in a chiral cavity quantum electrodynamics system

Jiang-Shan Tang, Lei Tang, Keyu Xia

Published Jan 1, 2022• 3 citations
arXivHTMLPDF

Abstract

We investigate the single-photon transport problem in the system of a whispering-gallery mode microresonator chirally coupled with a two-level quantum emitter (QE).Conventionally, this chiral QE-microresonator coupling system can be studied by the master equation and the single-photon transport methods.Here, we provide a new approach, based on the transfer matrix, to assess the single-photon transmission of such a system.Furthermore, we prove that these three methods are equivalent.The corresponding relations of parameters among these approaches are precisely deduced.The transfer matrix can be extended to a multiple-resonator system interacting with two-level QEs in a chiral way.Therefore, our work may provide a convenient and intuitive form for exploring more complex chiral cavity quantum electrodynamics systems.

DOI
10.3788/col202220.062701

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We investigate the single-photon transport problem in the system of a whispering-gallery mode microresonator chirally coupled with a two-level quantum emitter (QE).Conventionally, this chiral QE-microresonator coupling system can be studied by the master equation and the single-photon transport methods.Here, we provide a new approach, based on the transfer matrix, to assess the single-photon transmission of such a system.Furthermore, we prove that these three methods are equivalent.The corresponding relations of parameters among these approaches are precisely deduced.The transfer matrix can be extended to a multiple-resonator system interacting with two-level QEs in a chiral way.Therefore, our work may provide a convenient and intuitive form for exploring more complex chiral cavity quantum electrodynamics systems.
We investigate single photon transport in two waveguides coupled to a two-level quantum emitter (QE). With the deduced analytical scattering amplitudes, we show that under condition of the chiral coupling between the QE and the photon in the two waveguides, the QE can play the role of ideal quantum router to redirect a single photon incident from one waveguide into the other waveguide with a probability of 100% in the ideal condition. The influences of cross coupling between two waveguides and dissipations on the routing are also shown.
We study single-photon transport properties in an array of coupled microcavities, coupled to a whispering-gallery-type resonator interacting with a two-level atom. The transmission and reflection coefficients for the single photon propagating in such a coupled system are deduced. We show that the coherent transport properties of the single photon can be well controlled by the intermode backscattering, the resonator–atom coupling and the detuning between the whispering-gallery resonator and the atom. In addition, the influence of the dissipation of the whispering-gallery resonator and the two-level atoms for the realistic physical system on the transport properties are also analysed.
We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.
As a manifestation of cooperative interactions between a single photon and a cluster of atoms, single-photon superradiance has attracted considerable attention recently but has been studied insofar as that only quantum emitters are involved in the superradiance process. Here we expand the scope of investigation to study single-photon superradiance in a waveguide-quantum-electrodynamical system containing whispering-gallery-mode (WGM) resonators which are essential for many nanophotonic devices. It is shown analytically and numerically that single-photon superradiance can also occur when WGM resonators are present. The criteria for the emergence of the superradiant emission peak and the enhanced atom-light coupling strength are derived. Finally, the general case of a cascade of WGM resonators is investigated by a renormalization approach. Single-photon frequency comb generation is demonstrated via a frequency-modulated superradiant effective atom in chiral waveguide-quantum-electrodynamical systems with WGM resonators.
We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the intermode backscattering between the two degenerate whispering-gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.
It is shown that a broad class of cavity quantum electrodynamics (QED) problems---which consider the resonant propagation of a single photon interacting with quantum emitters (QEs), such as atoms, quantum dots, or vacancy centers---can be solved directly without application of the second quantization formalism. In the developed approach, the Hamiltonian is expressed through the ket-bra products of collective (photon+cavities+QEs\mathrm{photon}+\mathrm{cavities}+\mathrm{QEs}photon+cavities+QEs) states. Consequently, the SSS matrix of input-output problems is determined exactly by the Mahaux-Weidenm\"uller formula, which dramatically simplifies the analysis of complex cavity QED systems. First, this approach is illustrated for the problem of propagation of a photon resonantly interacting with NNN two-level QEs arbitrary distributed inside the optical cavity. Solution of this problem manifests the effect of cumulative action of QEs previously known for special cases. Can a similar cumulative action of QEs enhance the inelastic resonant transmission of a single photon? We solve this problem for the case of an optical cavity having two modes resonantly coupled to electronic transitions of NNN three-level QEs. It is shown that the described structure is the simplest realistic structure which enables the down-conversion of the single-photon frequency with the amplitude approaching unity in the absence of the external driving field and sufficiently small cavity losses and QE dissipation. Overall, the simplicity and generality of the developed approach suggest a practical way to identify and describe new phenomena in cavity QED.