Floquet engineering of optical nonlinearities: a quantum many-body approach

Abstract

Subjecting a physical system to a time-periodic drive can substantially modify its properties and applications. This Floquet-engineering approach has been extensively applied to a wide range of classical and quantum settings in view of designing synthetic systems with exotic properties. Considering a general class of two-mode nonlinear optical devices, we show that effective optical nonlinearities can be created by subjecting the light field to a repeated pulse sequence, which couples the two modes in a fast and time-periodic manner. The strength of these drive-induced optical nonlinearities, which include an emerging four-wave mixing, can be varied by simply adjusting the pulse sequence. This leads to topological changes in the system's phase space, which can be detected through light intensity and phase measurements. Our proposal builds on an effective-Hamiltonian approach, which derives from a parent quantum many-body Hamiltonian describing driven interacting bosons. As a corollary, our results equally apply to Bose-Einstein condensates in driven double-well potentials, where pair tunneling effectively arises from the periodic pulse sequence. Our scheme offers a practical route to engineer and finely tune exotic nonlinearities and interactions in photonics and ultracold quantum gases.

Period-doubled Floquet Solitons

“…Some recent examples of nonlinear topological effects include the formation of Floquet solitons in a topological bandgap [26][27][28], topological edge solitons [29][30][31], nonlinearity-induced local topological edge states [32], and nonlinear Thouless pumping [33,34]. In this context, we also highlight recent works on interacting Floquet polaritons [35], modulation-induced nonlinearity in magnetic insulators [36] and optical devices [37].…”

Nonlinear topological symmetry protection in a dissipative system

“…Indeed, the Kerr nonlinearity stems from interaction processes among photons, in direct analogy with the nonlinearity inherent to Bose-Einstein condensates and described by the Gross-Pitaevskii equation [37]. We also present an effective Hamiltonian approach, similar to that used for the Floquet engineering of quantum mat-ter [38][39][40], to explain aspects of the emergence of the symmetry in our system. Finally, our work could have relevance to the symmetry restoration techniques used in mean-field approaches of quantum many-body systems in nuclear, atomic, and molecular physics [41].…”