Photonic Floquet topological insulators in atomic ensembles

Abstract

We demonstrate the feasibility of realizing a photonic Floquet topological insulator (PFTIs) in an atomic ensemble. The interference of three coupling fields will split energy levels periodically, to form a periodic refractive index structure with honeycomb profile that can be adjusted by different frequency detunings and intensities of the coupling fields. This in turn will affect the appearance of Dirac cones in the momentum space. When the honeycomb lattice sites are helically ordered along the propagation direction, gaps open at Dirac points, and one obtains a PFTI in an atomic vapor. An obliquely incident beam will be able to move along the zigzag edge of the lattice without scattering energy into the PFTI, due to the confinement of edge states. The appearance of Dirac cones and the formation of PFTI can be shut down by the third-order nonlinear susceptibility and opened up by the fifth-order one.

Generating Lieb and super-honeycomb lattices by employing the fractional Talbot effect

“…But, if the nondiffracting property of such beams is broken, then they may display the Talbot effect during propagation in free space. Incidentally, these beams may not only display the Talbot effect, but it has been reported that the beams prepared by the multi-beam interference method can also be used to investigate topological and optical-quantum analogue phenomena [23,24]. It is well known that the periodic beam structures may exhibit surprising patterns (i.e., the fractional Talbot images) in the realization of the Talbot effect.…”

Edge States in Dynamical Superlattices

“…One of the manifestations of such effects is the appearance of topologically protected edge states that are typically unidirectional (in the 2D systems) and that demonstrate immunity to backscattering on disorder and other structural lattice defects due to topological protection. In modulated periodic photonic systems, frequently called Floquet insulators [3,15,22,23], longitudinal variations of underlying potential were shown to lead to appearance of the effective external time-dependent "magnetic fields" that qualitatively change the behaviour of the system and allow to design a new class of devices employing topologically protected transport, including photonic interconnects, delay lines, isolators, couplers, and other structures [23]. Periodically modulated photonic lattices were employed for realization of discrete quantum walks [24,25], and allowed observation of Floquet topological transitions with matter waves [26,27].…”

PT symmetry in a fractional Schrödinger equation

“…In particular, the spectra of ‐symmetric systems possess a critical point, above which the eigenvalues of the system become complex and therefore the symmetry is broken. It is also known that in topological photonics , Dirac cones in the energy zones can be deformed by the symmetry, which results in the complex eigenvalues becoming distributed in a circular fashion. Based on these unique properties, enabled by symmetry, some novel on‐chip optical devices such as optical isolators and coherent perfect absorbers have been proposed.…”