Photonic Gauge Potential in One Cavity with Synthetic Frequency and Orbital Angular Momentum Dimensions

Abstract

We explore a single degenerate optical cavity supporting a synthetic two dimensional space, which includes the frequency and the orbital angular momentum axes of light. We create the effective gauge potential inside this synthetic space and show that the system exhibits topologicallyprotected one-way edge states along the OAM axis at the boundaries of the frequency dimension. In this synthetic space, we present a robust generation and manipulation of entanglement between the frequency and OAM of photons. Our work shows that a higher dimensional synthetic space involving multiple degrees of freedom of light can be achieved in a "zero" dimensional spatial structure, pointing towards a unique platform to explore topological photonics and to realize potential applications in optical communications and quantum information processing.

Higher-order topological insulators in synthetic dimensions

“…(2)]. The field distribution significantly deviates from that for the corner mode excitation based on the RWA (in g), but corner localization is still observed for moderate modulation strengths A 1 /K < 1. k Simulations highlighting the difference in the field distributions obtained using the full solution and the RWA upon exciting a corner site in the trivial regime [A 0 /A 1 = γ/λ = 1.1] under ultrastrong modulation [A 1 /K = 1] strong coupling to a ring with a radius M ω times smaller than that of the main rings to induce a strong local change in the FSR every M ω modes 23 . Alternatively, one can engineer the dispersion of the ring waveguide to strongly perturb the FSR beyond the M ω modes 13 , which makes the modulation in Eq.…”

“…A prime focus of research on synthetic dimensions has been the pursuit of conventional topological phases in simple structures, such as the study of the 2D quantum Hall effect in a 1D real-space array [13][14][15][16][17] or the study of 3D topological physics in a 2D planar array 18,19 . Additionally, researchers have studied two or more simultaneous synthetic dimensions to implement higher-dimensional physics in essentially 0D systems [20][21][22][23][24] . Since the concept of synthetic dimensions is well suited to the study of topological physics in high-dimensional lattices, a natural question is whether HOTIs can be realized in synthetic space.…”

Topological phases in ring resonators: recent progress and future prospects

“…For example, one can introduce long-range couplings along the synthetic frequency dimension by using modulation frequencies that are multiples of the FSR, enabling emulation of the two-dimensional Haldane model using three rings [119]. Moreover, in a single resonator, one can combine two internal degrees of freedom of light such as frequency and OAM to construct a twodimensional synthetic lattice [120]. In such synthetic lattices, the effective magnetic field can be naturally introduced through the additional coupling waveguides, thereby creating topologically protected one-way edge states.…”

Discrete diffraction and Bloch oscillations in non-Hermitian frequency lattices induced by complex photonic gauge fields

“…In this work, we extend the concept of non-Hermitian lattice to frequency dimension and achieve various non-Hermitian transport phenomena, suggesting also a method to probe the NHSE by means of frequency Bloch oscillations. Synthetic dimension refers to an artificial lattice formed by coupling a set of modes with equally spaced parameters like frequency, time or momentum [49][50][51][52][53][54][55][56][57][58], making it possible to emulate higher-dimensional physics in lower-dimensional physical structures. Here we apply complex index modulation to introduce photonic transitions in a slab waveguide and create a frequency lattice.…”