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Physical Review A

Effects of quantum interference in multiwaveguide systems bridged by Jaynes-Cummings emitters

Zhenrui Li, Junhua Dong, Yafang Xu, Bingsuo Zou, Yongyou Zhang

Published May 19, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.105.053712

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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 100100%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.
Transfer and scattering matrix theories are derived for studying single-photon (SP) transport in optical waveguide ladders (OWLs). The OWLs consist of two one-dimensional waveguides connected by Jaynes-Cummings emitters (JCEs) and have two input and two output channels. The von Neumann entropy is introduced to describe the entanglement between the transmitted states from the two output channels. Two types of the OWLs are studied, i.e., the OWLs with two identical waveguides (i-OWLs) and those with two different waveguides (d-OWLs). When the OWLs contain only one JCE, the SP transport behavior in the i-OWLs is the same as that in the d-OWLs. When two JCEs are introduced, the quantum interference among the JCE-scattered waves can lead to the SP jumping with a 100% chance between the waveguides for the i-OWLs, while this is hard for the d-OWLs. As a result, the i-OWLs can serve as a SP router with respect to the d-OWLs. When the number of JCEs increases to a large value (e.g., 16), the transmission probabilities of the two output channels both tend to be 0.25 for the i-OWLs, but zero for d-OWLs. Correspondingly, the entanglements approximate a constant of 1 for the i-OWLs, but of zero for the d-OWLs. It shows that a large number of JCEs can suppress the influence of other system parameters including the SP frequency and JCE loss. Therefore, the i-OWLs with a large number of the JCEs show potential for a SP splitter and entanglement generator.
Scattering and correlation properties of a two-photon (TP) pulse are studied in a four-terminal waveguide system, i.e., two one-dimensional waveguides connected by a Jaynes-Cummings emitter (JCE). The wave function approach is utilized to exactly calculate the real-time dynamic evolution of the TP transport. When the width of the incident TP Gaussian pulse is much larger than the photon wavelength, the TP transmission spectra approach that of the corresponding single photon cases and are almost independent of the pulse width. On the contrary, as the pulse width is comparable to the photon wavelength, the TP transmission and correlation both show strong dependence on the pulse width. The resonant scattering due to the JCE and the photon interference together determine the TP correlation. When the distance between the TPs is small, the TP correlations between any two terminals for the scattered TP pulse are much different from those for the incident TP pulse and therefore, such a four-terminal waveguide system provides a way to control the TP correlation.
Transmission and correlation properties of a two-photon pulse are studied in a one-dimensional waveguide (1DW) in the presence of three types of quantum emitters: two-level atom (TLA), side optical cavity (SOC), and Jaynes-Cummings model (JCM). Since there are many plane-wave components for a two-photon pulse, a nonlinear waveguide dispersion is used instead of the linearized one. The two-photon transmission spectra become flatter with decreasing the pulse width. With respect to the $\ensuremath{\delta}$ coupling between the 1DW and quantum emitter the transmission dips show a blueshift for the non-$\ensuremath{\delta}$ one and the blueshift first increases and then decreases with increasing the width of the coupling. The TLA and JCM can induce an effective photon-photon interaction that depends on the distance between the two photons, while the SOC cannot. We show that the 1DW coupled with the TLA or JCM is able to evaluate the overlap of the two photons and that the non-$\ensuremath{\delta}$ coupling has potential for controlling the two-photon correlation.
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.
We investigate the two-photon scattering properties of a Jaynes-Cummings (JC) nonlinearity consisting of a two-level system (qubit) interacting with a single-mode cavity, which is coupled to two waveguides, each containing a single incident photon wave packet initially. In this scattering setup, we study the interplay between the Hong-Ou-Mandel (HOM) effect arising due to quantum interference and effective photon-photon interactions induced by the presence of the qubit. We calculate the two-photon scattering matrix of this system analytically and identify signatures of interference and interaction in the second-order auto- and cross-correlation functions of the scattered photons. In the dispersive regime, when qubit and cavity are far detuned from each other, we find that the JC nonlinearity can be used as an almost linear, in situ tunable beam splitter giving rise to ideal Hong-Ou-Mandel interference, generating a highly path-entangled two-photon NOON state of the scattered photons. The latter manifests itself in strongly suppressed waveguide cross-correlations and Poissonian photon number statistics in each waveguide. If the two-level system and the cavity are on resonance, the JC nonlinearity strongly modifies the ideal HOM conditions leading to a smaller degree of path entanglement and sub-Poissonian photon number statistics. In the latter regime, we find that photon blockade is associated with bunched autocorrelations in both waveguides, while a two-polariton resonance can lead to bunched as well as antibunched correlations.
Abstract We investigate the single-photon transport properties in a hybrid waveguide quantum electrodynamics system, in which a one-dimensional waveguide is simultaneously coupled to a cavity and a driven Λ-type three-level atom. The cavity and the atom are also coupled to each other. We show that when the waveguide is coupled to the cavity and the atom at the same point, double electromagnetically induced transparency (EIT) can be observed from the system. The physical mechanism of the double EIT effect has been given by setting up the eigenstate structure for the whole system. When the waveguide is coupled to the cavity and the atom at different points, we demonstrate that the single-photon transmission spectra can be effectively controlled by adjusting the relative separation between the cavity and the atom. Moreover, this non-zero relative separation can lead to the occurrence of the controllable nonreciprocal scattering effect. These results have potential applications in realization of photonic coherent control.