[Paper Review] Floquet engineering of optical nonlinearities: a quantum many-body approach

Nathan Goldman|arXiv (Cornell University)|Mar 10, 2022

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper proposes a quantum many-body approach to Floquet engineering of optical nonlinearities in two-mode systems via periodic pulse sequences, inducing effective four-wave mixing and tunable nonlinear interactions. By mapping the driven bosonic system to an effective Hamiltonian, the scheme enables topological phase transitions detectable through intensity and phase measurements, applicable to both photonic devices and ultracold quantum gases with engineered pair tunneling.

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.

Motivation & Objective

• To develop a theoretical framework for generating effective optical nonlinearities in two-mode systems using time-periodic pulse sequences.
• To establish a connection between driven optical systems and quantum many-body physics, particularly in the context of interacting bosons.
• To demonstrate that drive-induced nonlinearities, including four-wave mixing, can be tuned by adjusting pulse sequences.
• To show that topological phase transitions emerge in the system's phase space, detectable via measurable optical quantities.
• To extend the applicability of the scheme to both photonic devices and ultracold Bose-Einstein condensates in double-well potentials.

Proposed method

• The study employs a parent quantum many-body Hamiltonian describing two species of interacting bosons subjected to a periodic pulse sequence.
• The effective Hamiltonian is derived using a Floquet approach, mapping the driven system into a time-averaged effective description.
• The system is analyzed using Schwinger boson operators to express intra-mode (Hubbard) and inter-mode (cross) interactions in terms of angular momentum operators.
• Key interactions such as pair tunneling and four-wave mixing are identified through the effective Hamiltonian's structure, particularly via terms like $ \hat{J}_z^2 $, $ \hat{J}_y^2 $, and their combinations.
• Theoretical analysis connects the driven system to the nonlinear Schrödinger (Gross-Pitaevskii) equation, enabling mapping to photonic and ultracold atomic systems.
• Phase space topology is probed via measurable quantities such as light intensity and phase, enabling experimental detection of topological transitions.

Experimental results

Research questions

• RQ1 Can periodic pulse sequences induce effective optical nonlinearities in two-mode systems without intrinsic nonlinearity?
• RQ2 How do the parameters of the pulse sequence control the strength and nature of the emergent nonlinear interactions?
• RQ3 What topological features emerge in the phase space of the driven system, and how are they detectable via optical measurements?
• RQ4 To what extent can the same framework describe both photonic devices and ultracold quantum gases with engineered interactions?
• RQ5 How does the effective Hamiltonian derived from the many-body model capture the emergence of four-wave mixing and pair tunneling?

Key findings

• Effective four-wave mixing is generated in the system through a periodic pulse sequence, with its strength tunable by adjusting pulse parameters.
• The system exhibits topological phase transitions in its phase space, which are detectable via changes in light intensity and phase measurements.
• The effective Hamiltonian derived from the many-body model reproduces the nonlinear Schrödinger equation with tunable nonlinear interactions, including pair tunneling.
• The emergence of pair tunneling in Bose-Einstein condensates is shown to arise from the same periodic driving mechanism, linking photonic and ultracold atomic systems.
• Theoretical expressions for interactions in terms of Schwinger operators reveal that $ \hat{J}_z^2 $ and $ \hat{J}_y^2 $ encode intra-mode and inter-mode interactions, respectively, with their combination yielding effective nonlinear terms.
• The framework is extendable to driven-dissipative systems such as microresonators, provided dissipation is incorporated within the Floquet formalism.