Measuring topological invariants is an essential task in characterizing topological phases of matter. They are usually obtained from the number of edge states due to the bulk-edge correspondence or from interference since they are integrals of the geometric phases in the energy band. It is commonly believed that the bulk band structures could not be directly used to obtain the topological invariants. Here, we implement the experimental extraction of Zak phase from the bulk band structures of a Su-Schrieffer-Heeger (SSH) model in the synthetic frequency dimension. Such synthetic SSH lattices are constructed in the frequency axis of light, by controlling the coupling strengths between the symmetric and antisymmetric supermodes of two bichromatically driven rings. We measure the transmission spectra and obtain the projection of the time-resolved band structure on lattice sites, where a strong contrast between the non-trivial and trivial topological phases is observed. The topological Zak phase is naturally encoded in the bulk band structures of the synthetic SSH lattices, which can hence be experimentally extracted from the transmission spectra in a fiber-based modulated ring platform using a laser with telecom wavelength. Our method of extracting topological phases from the bulk band structure can be further extended to characterize topological invariants in higher dimensions, while the exhibited trivial and non-trivial transmission spectra from the topological transition may find future applications in optical communications.

Experimental measurement of dynamic band structure exhibits the evolution of the wave vector in a synthetic lattice.

The moiré lattice has recently attracted broad interest in both solid-state physics and photonics where exotic phenomena in manipulating the quantum states are explored. In this work, we study the one-dimensional (1D) analogs of “moiré” lattices in a synthetic frequency dimension constructed by coupling two resonantly modulated ring resonators with different lengths. Unique features associated with the flatband manipulation as well as the flexible control of localization position inside each unit cell in the frequency dimension have been found, which can be controlled via the choice of flatband. Our work therefore provides insight into simulating moiré physics in 1D synthetic frequency space, which holds important promise for potential applications toward optical information processing.

Non-Hermitian topological photonics plays a key role in bridging topological matter with gain and loss engineering in optics. Here we report the experimental observation of the break of chiral currents in a Hall ladder from the non-Hermiticity by constructing synthetic frequency dimension in two rings, where currents on both legs of the ladder co-propagate in the same direction. The origin of such phenomena is resulted from the interplay between the effective magnetic flux and the on-site gain and loss. Such non-Hermitian co-propagating currents exhibit characteristics of unidirectional frequency conversion in both rings, and moreover, different from the counterpart in Hermitian systems, can provide a method to probe the signatures of the non-Hermitian skin effect from steady-state bulk dynamics. Our model is further extended to models including next-nearest-neighbor couplings, pointing to a way for observing the non-Hermitian signature with higher winding number, and provides a new control knob for light manipulation with the topological dissipation engineering.

The moiré superlattices attract growing interest for holding exotic physics due to their fascinating properties from electronics to photonics. Much attention has been focused on the localization effect for waves in the flat band regime or the delocalization effect from the strongly dispersive band feature. Here, we study the weakly dispersive band in between the two above scenarios in a one-dimensional synthetic frequency moiré superlattice and observe the wave packet distributions therein toward novel frequency comb generation. Mode spacing in the spectral wave packet is reduced compared to the free spectral range of individual rings due to the mode couplings from the unequal sublattice periods of the synthetic moiré lattice. We unveil that the optimal compact frequency comb generation occurs in the weakly dispersive regime holding simultaneously uniform power distribution and broad frequency spanning in our experiment, benefiting from the interplay between the band flatness and power uniformity of mode distribution. Our results study the fundamental physics of the weakly dispersive moiré band in the synthetic frequency dimension and also show a new way for the future compact frequency comb generation in on-chip devices with small footprint size.