Photon transport and blockade based on non-Markovian interactions between a microring resonator and waveguide

TL;DR

This work analyzes photon transport and blockade in a waveguide coupled to a microring resonator at two points, introducing non-Markovian dynamics from the finite delay $L/c$ between couplings. It develops a non-Markovian input-output and scattering-matrix framework to characterize single- and two-photon transport, revealing how the delay and asymmetric couplings modify transmission via $t_\omega$ and induce two-photon interference through Kerr nonlinearity $\chi$. Extending to driven resonators, it derives a master equation with effective rates and an effective Hamiltonian, enabling blockade control through intracavity state manipulation under a classical drive $\epsilon$ and non-Markovian feedback. The study highlights tunable photon blockade and state preparation in microring photonics, with implications for scalable, room-temperature quantum photonic information processing and networking.

Abstract

We investigate photon transport and blockade based on the architecture where a waveguide is coupled to a microring resonator at two distinct points. This two-point coupling configuration between the waveguide and resonator gives rise to non-Markovian dynamics, which is induced by the photon transmission delay in the waveguide between the two coupled points. On one hand, by designing the non-Markovian coupling parameters between the waveguide and resonator, single or two-photon transport and the resulting photon blockade effect can be manipulated according to the output photonic states at the end of waveguide. This non-Markovian process can be evaluated by scattering matrices and second order correlation functions related to the distance between two coupled points. On the other hand, when classical driving fields are applied upon the resonator with interactions between its clockwise and counterclockwise modes, the blockade effect of the output field can be determined by the intracavtiy eigenstates. Then the correlations of the output field as well as the intracavity states can be modulated by the non-Markovian coupling between the microring resonator and waveguide.

Figures (5)

• Figure 1: Microring resonator coupled to a waveguide at two distinct points.
• Figure 2: Single-photon transport evaluated by $\left| t_{\omega} -1\right|$ in Eq. (\ref{['con:SinglePhotontw']}). In (a), $g_2/\kappa_a = 0$, the single-photon transport is influenced by the relative relationship among $g_1$, $\kappa_a$ and $\omega_a$. In (b), $g_1/\kappa_a =g_2/\kappa_a = 1$, the non-Markovian single-photon transport is influenced by $L$.
• Figure 3: Second order correlation function $\ln \left[ g_{\rm out}^{(2)}(0)\right]$ of the output field is influenced by input photon frequencies and other parameters when $\kappa_a = 1$MHz and $\chi = 0.1$MHz. In (a) and (b), $g_1 = g_2 = 1$MHz. In (c) and (d), $g_2 = 2g_1 = 4/3$MHz. In (a) and (c), $\omega_a L/c = \pi$. In (b) and (d), $\omega_1 + \omega_2 = 2\omega_a$.
• Figure 4: Second order correlation function $\ln \left[ g_{\rm out}^{(2)}(0)\right]$ influenced by Kerr nonlinearity when $g_0 = 1$MHz, $\kappa_a = 0.2$MHz and $\zeta = 0.5$MHz.
• Figure 5: The photon states in the resonator with $g_0 = 1$MHz, $\chi = 4$MHz, $\kappa_a = 0.2$MHz and $\zeta = 0.5$MHz. As for the non-Markoivan parameter settings, $\omega_aL/c = \pi/3$ in (a) and (c), while $\omega_aL/c = \pi$ in (b) and (d). As for the classical driving field, $\epsilon = 1$MHz in (a) and (b), while $\epsilon = 4$MHz in (c) and (d).