Floquet Topological Phases in One-Dimensional Nonlinear Photonic Crystals

Topological electromagnetic waves in dispersive and lossy plasma crystals

Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on dielectric materials with weak dispersions, this study focuses on topological phases in dispersive materials and presents a numerical study of Chern insulators in gaseous-phase plasma cylinder cells. We develop a numerical framework to address the complex material dispersion arising from the plasma medium and external magnetic fields and identify Chern insulator phases that are experimentally achievable. Using this numerical tool, we also explain the flat bands commonly observed in periodic plasmonic structures, via local resonances, and how edge states change as the edge termination is periodically modified. This work opens up opportunities for exploring band topology in new materials with non-trivial dispersions and has potential radio frequency (RF) applications, ranging from plasma-based lighting to plasma propulsion engines.

Direct extraction of topological Zak phase with the synthetic dimension

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.

Floquet Quadrupole Photonic Crystals Protected by Space-Time Symmetry

High-order topological phases, such as those with nontrivial quadrupole moments [1,2], protect edge states that are themselves topological insulators in lower dimensions. So far, most quadrupole phases of light are explored in linear optical systems, which are protected by spatial symmetries [3] or synthetic symmetries [1,2,4-7]. Here we present Floquet quadrupole phases in driven nonlinear photonic crystals that are protected by space-time screw symmetries [8]. We start by illustrating space-time symmetries by tracking the trajectory of instantaneous optical axes of the driven media. Our Floquet quadrupole phase is then confirmed in two independent ways: symmetry indices at high-symmetry momentum points and calculations of the nested Wannier bands. Our Letter presents a general framework to analyze symmetries in driven optical materials and paves the way to further exploring symmetry-protected topological phases in Floquet systems and their optoelectronic applications.

Thermal control of the topological edge flow in nonlinear photonic lattices

The chaotic evolution resulting from the interplay between topology and nonlinearity in photonic systems generally forbids the sustainability of optical currents. Here, we systematically explore the nonlinear evolution dynamics in topological photonic lattices within the framework of optical thermodynamics. By considering an archetypical two-dimensional Haldane photonic lattice, we discover several prethermal states beyond the topological phase transition point and a stable global equilibrium response, associated with a specific optical temperature and chemical potential. Along these lines, we provide a consistent thermodynamic methodology for both controlling and maximizing the unidirectional power flow in the topological edge states. This can be achieved by either employing cross-phase interactions between two subsystems or by exploiting self-heating effects in disordered or Floquet topological lattices. Our results indicate that photonic topological systems can in fact support robust photon transport processes even under the extreme complexity introduced by nonlinearity, an important feature for contemporary topological applications in photonics.

The nonlinear evolution dynamics in topological photonic lattices is systematically investigated within the framework of optical thermodynamics. This approach allows for the precise prediction of topological currents even under the extreme complexity introduced by nonlinearity.

Non-Floquet engineering in periodically driven dissipative open quantum systems

Floquet engineering plays a key role in realizing novel dynamical topological states. The conventional Floquet engineering, however, only applies to time-periodic non-dissipative Hermitian systems, and for the open quantum systems, non-Hermitian processes usually occur. So far, it remains unclear how to characterize the topological phases of time-periodic open quantum systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to solve the problem and illustrate it by a continuously time-periodic non-Hermitian bipartite chain. In non-Floquet theory, a temporal non-unitary transformation is exercised on the Floquet states, and the transformed Floquet spectrum restores the form of the Wannier-Stark ladder. Besides, we also show that different choices of the starting points of the driving period can result in different localization behavior, effects of which can reversely be utilized to design quantum detectors of phases in dissipative oscillating fields. Our methods are capable of describing topological features in dynamical open quantum systems with various driving types and can find its applications to construct new types of dynamical topological materials.