When two measurable quantities of a system remain the same under variation of some system parameter, the system is said to possess symmetry. A sudden collapse of this symmetry under some small perturbations is termed spontaneous symmetry breaking. Symmetry breaking has found its presence in different domains in physics, ranging from spontaneous breaking of gauge symmetry to more contemporary models of continuous symmetry breaking in Rydberg arrays, the introduction of entanglement asymmetry, and its role in quantum phase transitions.

Optical microresonators made of materials having Kerr nonlinearity have garnered much interest in the last two decades due to their capability to demonstrate nonlinear optical interactions at low powers. These resonators have remarkable applications in optical frequency combs, telecommunications, spectroscopy, optical clock, and sub-wavelength distance measurements. Besides, fundamental physical phenomena, such as spontaneous symmetry breaking have been observed in such resonators^[1,2]. Initial experiments demonstrated symmetry breaking of counter-propagating light field intensities in Kerr resonators enabling them to develop all-optical isolators and logic gates. Additionally, breaking the symmetry between co-propagating light fields with mutually orthogonal polarizations has led to the creation of microresonator-based polarization controllers, random number generators, and vectorial frequency combs.

There has been a recent explosion of research on systems containing multiple coupled resonators due to their capability to provide new dimensions to control emerging soliton states compared to single resonator systems. The latest research mainly focus on the soliton dynamics in coupled resonator optical waveguide (CROW) systems. However, their homogeneous response, rich in potential nonlinear effects, remained largely uncharted, until recently discussed in detail in the research work^[3] published in Photonics Research, Volume 12, Issue 10, 2024. [Alekhya Ghosh, Arghadeep Pal, Lewis Hill, Graeme N. Campbell, Toby Bi, Yaojing Zhang, Abdullah Alabbadi, Shuangyou Zhang, Pascal Del'Haye, "Controlled light distribution with coupled microresonator chains via Kerr symmetry breaking," Photonics Res. 12, 2376 (2024)]

One-dimensional CROW systems usually consist of a finite number of resonators (say N) arranged in a chain, as illustrated in Figure 1(a). These systems are modeled using much-celebrated coupled Lugiato-Lefever equations (LLE), which are derived from the nonlinear Schrodinger equation. The linear coupling between the resonators controls how many photons can hop between them. Input fields are provided to the resonators at the ends of the chain, the inter-resonator coupling then populates the resonators within the chain with photons. Within the regime of linear optics, the light field intensities circulating in the resonators follow a symmetry depending on the coupling arrangement. The resonator in the chain remains symmetric to the resonator in terms of circulating optical power. This symmetry holds at low input power levels in Kerr-microresonators, as shown in Figure 1(b). However, with increasing input power, we start to observe interesting nonlinear effects. The nonlinear Kerr-effect in each resonator breaks the above-mentioned symmetry, giving us an arbitrary distribution of optical power among the resonators in the chain. This novel symmetry breaking mechanism leverages a way to control the power distribution in the CROW system. Figure 1(c) illustrates this effect.

Figure 1. (a) CROW configuration: N identical Kerr ring resonators are linked in sequence. Input fields are provided to end resonators. (b) Circulating optical powers in the resonators in symmetric regime. Resonators with identical coupling condition ( resonator and resonator) have same optical powers circulating in them. (c) Arbitrary power distribution across the resonators in the symmetry broken regime.

Controllable power distribution in a coupled resonator chain holds significant potential in the areas of all-optical computing, signal processing, data routing, and tailoring soliton dynamics. Different arrangements of bright-dark resonators in the CROW system, achievable via tuning the input power, can be used as different binary states. Therefore, the system can be used as an optical analog-to-digital converter where an analog optical input is transformed into a digital binary bit-string and multi-bit logical operations can be performed on them. Furthermore, by incorporating additional arrangements to connect inputs to all the resonators in the chain, loading and unloading bit-strings to the resonators would be easily achievable with the optical nonlinearity providing a method to perform logical operations on the stored data. Additionally, reference^[4] explores various dynamical fast-time solutions in CROW systems. These solutions, such as solitons, are influenced by the interplay of the dispersion profiles and nonlinear gains in the systems. The power redistribution achievable in CROW systems can significantly alter the intensity-dependent nonlinear gains in the resonators, thereby impacting the fast-time dynamics. Consequently, by exploiting the Kerr effect and coupling between resonators one can gain precise control over the fast-time dynamics in these systems. "These research results are in particular interesting for nonlinear optical networks that could be used for machine learning and neuromorphic computing" highlights Alekhya Ghosh, the lead author on this study.

In the following research papers, the microphotonics research group at MPL is investigating the symmetry breaking dynamics in different complex arrangements of resonators. A recent study^[5] by the team on symmetry breaking in coupled two-rod resonator systems has been accepted in Photonics Research for publication, [Arghadeep Pal, Alekhya Ghosh, Shuangyou Zhang, Lewis Hill, Haochen Yan, Hao Zhang, Toby Bi, Abdullah Alabbadi, and Pascal Del Haye, "Linear and Nonlinear Coupling of Light in Twin-Resonators with Kerr Nonlinearity," (2024)]. Moving forward, the team will explore controlled soliton dynamics by utilizing the power redistribution method.