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arXiv:2404.17510 · Physical Review Research

Kerr nonlinearity induced nonreciprocity in dissipatively coupled resonators

Qingtian Miao, G. S. Agarwal

Published Jul 3, 2024• 14 citations
arXivHTMLPDF

Abstract

Nonlinearity-induced nonreciprocity is studied in a system comprising two resonators coupled to a one-dimensional waveguide when the linear system does not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the coupled system and includes the dissipative coupling between the waveguide and resonators, along with the input-output relations. We consider a large number of scenarios which can lead to nonreciprocity. We pay special attention to the case when the linear system does not exhibit nonreciprocal behavior. In this case, we show how very significant nonreciprocal behavior can result from Kerr nonlinearities. We find that the bistability of the nonlinear system can aid in achieving large nonreciprocity. Additionally, we bring out nonreciprocity in the excitation of each resonator, which can be monitored independently. Our results highlight the profound influence of nonlinearity on nonreciprocal behavior, offering an avenue for controlling light propagation in integrated photonic circuits. Nonlinearity-induced nonreciprocity would lead to significant nonreciprocity in quantum fluctuations when our system is treated quantum mechanically. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033020

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Nonlinearity-induced nonreciprocity is studied in a system comprising two resonators coupled to a one-dimensional waveguide when the linear system does not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the coupled system and includes the dissipative coupling between the waveguide and resonators, along with the input-output relations. We consider a large number of scenarios which can lead to nonreciprocity. We pay special attention to the case when the linear system does not exhibit nonreciprocal behavior. In this case, we show how very significant nonreciprocal behavior can result from Kerr nonlinearities. We find that the bistability of the nonlinear system can aid in achieving large nonreciprocity. Additionally, we bring out nonreciprocity in the excitation of each resonator, which can be monitored independently. Our results highlight the profound influence of nonlinearity on nonreciprocal behavior, offering an avenue for controlling light propagation in integrated photonic circuits. Nonlinearity-induced nonreciprocity would lead to significant nonreciprocity in quantum fluctuations when our system is treated quantum mechanically. Published by the American Physical Society 2024
Nonreciprocal light propagation plays an important role in modern optical systems, from photonic networks to integrated photonics. We propose a nonreciprocal system based on a resonance-frequency-tunable cavity and intensity-adaptive feedback control. Because the feedback-induced Kerr nonlinearity in the cavity is dependent on the incident direction of light, the system exhibits nonreciprocal transmission with a transmission contrast of 0.99 and an insertion loss of 1.5 dB. By utilizing intensity-adaptive feedback control, the operating intensity range of the nonreciprocal system is broadened to 20 dB, which relaxes the limitation of the operating intensity range for nonlinear nonreciprocal systems. Our protocol paves the way to realize high-performance nonreciprocal propagation in optical systems and can also be extended to microwave systems.
The nonreciprocal photon transmission between two optical modes which are nonlinearly coupled in a cross-Kerr type is investigated by using a damped auxiliary optical mode as their common engineered reservoir. The optical nonreciprocity is created by quantum interference between the nonlinear coupling induced by the cross-Kerr nonlinearity and the dissipative coupling mediated by the adiabatic elimination of the auxiliary optical mode. The photon transmission probabilities in forward and backward directions for the relative phase $\ensuremath{\varphi}$ between the two couplings are symmetric about the resonance with the probabilities for the phase $\ensuremath{\pi}\ensuremath{-}\ensuremath{\varphi}$, and are exchange symmetric with those in the case of the phase $2\ensuremath{\pi}\ensuremath{-}\ensuremath{\varphi}$. By tuning the dissipative coupling, in addition to the photon nonreciprocity being improved, the nonreciprocal photon amplification is produced. Meanwhile, it is found that not only can the cross-Kerr nonlinearity lead to a broadband optical nonreciprocity, but also it effectively produces the optical squeezing in the present scheme. The combination of the photon nonreciprocity with the optical squeezing will be useful in the realization of the quantum information processing with noise reduction.
On-chip optical nonreciprocal devices are vital components for integrated photonic systems and scalable quantum information processing. Nonlinear optical isolators and circulators have attracted considerable attention because of their fundamental interest and their important advantages in integrated photonic circuits. However, optical nonreciprocal devices based on Kerr or Kerr-like nonlinearity are subject to dynamical reciprocity when the forward and backward signals coexist simultaneously in a nonlinear system. Here, we theoretically propose a method for realizing on-chip nonlinear isolators and circulators with dynamic nonreciprocity. Dynamic nonreciprocity is achieved via the chiral modulation on the resonance frequency due to coexisting self- and cross-Kerr nonlinearities in an optical ring resonator. This work showing dynamic nonreciprocity with a Kerr nonlinear resonator can be an essential step toward integrated optical isolation.
In our recent research1, it was suggested that counter-propagating laser beams in a Kerr-nonlinear medium can induce intensity-dependent nonreciprocity which consists in different changes of refractive indecies for both of the waves. Under some conditions, this can result in such directionally asymmetrical effects as (i) directional bistability in a nonlinear ring resonator which allows one to switch the direction of propagation of a dominant mode and (ii) enhancement of the Sagnac effect in a rotating ring resonator.
Nonreciprocal optical devices play a pivotal role in modern optical systems and advanced quantum technologies. Nonreciprocal devices based on optical nonlinearity have garnered significant attention due to their compatibility with on-chip photonics fabrication techniques. However, when the opposite-propagating continuous waves are incident to such nonlinear nonreciprocal devices simultaneously, achieving dynamic nonreciprocity has remained a formidable challenge. In addition, the devices relying on nonlinear resonators suffer from limited bandwidths. In this paper, we theoretically propose a method for achieving an on-chip isolator and quasicirculator by employing a nonlinear Mach-Zehnder interferometer. Harnessing the chirality between self- and cross-Kerr nonlinearities in the nonlinear arm of the interferometer, our device achieves remarkable dynamic nonreciprocity. We obtain an isolation contrast of $\ensuremath{\geqslant}0.9$ for the optical isolator and fidelity of $\ensuremath{\geqslant}0.97$ for the optical quasicirculator, and a broad bandwidth of 20nm20\phantom{\rule{3.33333pt}{0ex}}\text{nm}20nm for both. Our protocol paves a way to realize a broadband on-chip nonlinear nonreciprocal device.
This article delves into the intricacies of nonreciprocity in a system composed of two superconducting qubits operating in a transmon regime and coupled to a 1-D waveguide. Nonreciprocity, characterized by asymmetric signal transmission, is a phenomenon of increasing interest in quantum technologies, as it enables one-way signal propagation and isolation. Our investigation derives the conditions to obtain nonreciprocity in a qubit-loaded waveguide and discusses how common approximations may impact the observed nonreciprocal effects, highlighting crucial factors that must be considered in designing such systems. By employing realistic system parameters, we unveil significant effects on the system dynamics when higher energy levels are included in the transmon regime. This leads to a reduction of nonreciprocity compared to the ideal scenario, with the transmission ratio falling below the two-level approximation limit of2/32/32/3. Additionally, the statistical properties of the system undergo significant changes, particularly in the coherent functions for transmitted and reflected signals. The emergence of additional population transfer channels and the critical role of quantum correlations between qubits underscore the necessity of careful modeling. Our findings have implications for quantum device engineering, offering insights that can enhance the design of more efficient quantum technology and advanced quantum communication systems.