A single photonic cavity with two independent physical synthetic dimensions (1909.04828v1)

Abstract: The concept of synthetic dimensions, which has enabled the study of higher-dimensional physics on lower-dimensional physical structures, has generated significant recent interest in many branches of science ranging from ultracold-atomic physics to photonics, since such a concept provides a versatile platform for realizing effective gauge potentials and novel topological physics. Previous experiments demonstrating this concept have augmented the real-space dimensionality by one additional physical synthetic dimension. Here we endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We experimentally observe a wide variety of rich physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and chiral currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.

• The paper introduces a dual synthetic dimension framework in a single photonic cavity, demonstrating effective spin-orbit coupling and the emergence of chiral edge states.
• The methodology uses a modulated ring resonator to couple clockwise and counter-clockwise modes, enabling pseudospin-resolved quasimomentum mapping via time-resolved band spectroscopy.
• The results establish a scalable platform for simulating higher-dimensional topological phenomena, holding promise for advancements in quantum information processing.

Analysis of Photonic Cavities with Dual Synthetic Dimensions

The concept of synthetic dimensions in photonics has opened promising avenues for the exploration of higher-dimensional quantum and classical physics through systems that are inherently lower in their dimensional topology. In this article, the authors present an innovative approach wherein a single photonic ring resonator incorporates two independent synthetic dimensions—frequency and pseudospin. This dual synthetic dimension framework significantly diverges from prior systems that typically employed a single extra dimension.

The controlled experimental setting utilizes a ring resonator modulated to enable mutual interactions between clockwise (CW) and counter-clockwise (CCW) circulating modes. This setup leads to the formation of a synthetic Hall ladder encompassing both frequency and pseudospin dimensions. Using this configuration, the paper explores complex phenomena such as effective spin-orbit coupling, magnetic fields, spin-momentum locking, and chiral current behaviors, which were observed and reported for the first time solely within synthetic dimension spaces.

Key Numerical Results and Methodologies:

• The Hamiltonian governing the system utilizes coupling coefficients that vary temporally and spatially, leading to a controllable modulation of the effective magnetic field. The synchronous coupling between different modes is achieved through an integrated modulator that facilitates these operations.
• Time-resolved band structure spectroscopy was employed, enabling the direct readout of psuedospin-resolved quasimomentum space, and demonstrated the presence of chiral edge states, akin to those predicted and observed in 2D quantum Hall systems.

The findings suggest that such a platform can circumvent the necessity for physically complex higher-dimensional experimental setups by harnessing synthetic dimensions. From a theoretical viewpoint, the primary implications of this work reflect the feasibility of simulating higher-dimensional topologically non-trivial phenomena using a remarkably simplified apparatus.

Implications and Future Outlook:

Practically, this dual-dimensional implementation offers a scalable path towards fabricating devices capable of exploring complex quantum behaviors and could be transformative for fields like quantum information processing where such topological properties are crucial.

Further research could exploit additional degrees of freedom, such as orbital angular momentum, and leverage new nanophotonic components to enhance system capabilities. Additionally, studying synthetic dimension-driven dynamics on-chip using novel materials or integrating similar systems into real-space photonic circuits could foster advancements in practical quantum devices.

Overall, this work sets the stage for future experimental and theoretical efforts aimed at realizing multiple synthetic dimensions in various physical contexts, offering a fertile ground for new discoveries in both fundamental and applied physics. Such exploration into topologically protected systems and synthetic gauge fields may prove instrumental in the ongoing evolution of photonic technologies.