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Chinese Physics B

Quantum routing of few photons using a nonlinear cavity coupled to two chiral waveguides

Jian-Shuang Liu, Ya Yang, Jing Lu, Lan Zhou

Published Jul 8, 2022• 4 citations
Publisher

Abstract

We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.

DOI
10.1088/1674-1056/ac7f8f

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We investigate few-photon scattering properties in two one-dimensional waveguides chirally coupled to a nonlinear cavity. The quantum states of scattered few photons are solved analytically via a real-space approach, and the solution indicates the few-photon reflection and transmission properties. When inputting two photons of equal energy to resonate with the cavity, the propagation characteristics of the two photons will be interesting, which is different from the previous anti-bunching effects with a quantum emitter. More importantly, when the total energy of the two incident photons equals the energy of a nonlinear cavity accommodating two photons, influence of the bound state will become larger to result in disappearance of antibunching effect. However, the bound state has no effect on probability of routing to another waveguide.
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Abstract A quantum router is one of the essential elements in the quantum network. Conventional routers only direct a single photon from one quantum channel into another. Here, we propose a few-photon router. The active element of the router is a single qubit chirally coupled to two independent waveguides simultaneously, where each waveguide mode provides a quantum channel. By introducing the operators of the scatter-free space and the controllable space, the output state of the one-photon and two-photon scattering are derived analytically. It is found that the qubit can direct one and two photons from one port of the incident waveguide to an arbitrarily selected port of the other waveguide with unity, respectively. However, two photons cannot be simultaneously routed to the same port due to the anti-bunch effect.
We study the coherent transport of one or two photons in a one-dimensional waveguide chirally coupled to a nonlinear resonator. Analytic solutions of the one-photon and two-photon scattering is derived. Although the resonator acts as a non-reciprocal phase shifter, light transmission is reciprocal at one-photon level. However, the forward and reverse transmitted probabilities for two photons incident from either the left side or the right side of the nonlinear resonator are nonreciprocal due to the energy redistribution of the two-photon bound state. Hence, the nonlinear resonator acts as an optical diode at two-photon level.
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 the problem of two-photon routing in waveguide QED ladders where a few two-level quantum emitters (QEs) are simultaneously coupled with two chiral waveguides. We analyze the routing probability in two regimes, namely, under a purely plane wave approximation (scattering case) and in the presence of photon-photon bound state formation. Within the scattering case, we examine the two-photon routing in the presence of up to five QEs, considering two possibilities separately: ideal-symmetric coupling and the critical coupling scenario. We examine the photon routing up to the two QEs for the bound state situation and compare the photon redirection efficiency with the corresponding scattering case. Our findings show the potential of utilizing chiral light-matter interactions in multi-photon and multi-emitter-based quantum networking protocols where interlinking among spatially distant nodes is required.
We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present an analytic solution for the quantum states of the two transmitted and reflected photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerges after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in relative coordinates, which is a feature that might be interpreted as a two-photon bound state in this waveguide-cavity system.