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Thermalization and Entanglement of Quantum Light in a Nonlinear Multimode System

Michael Birk, Mark D. Lyubarov, Ron Ruimy, Matan Even Tzur, Fan O. Wu, Oren Cohen, Mordechai Segev, Ido E. Kaminer, Pavel Sidorenko

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We study how thermodynamic behavior in classical nonlinear optical multimode systems presents itself in quantmn many-body settings, and find multimode entanglement arising in the thermalization process.
DOI
10.1364/cleo_fs.2023.fth4b.2

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Thermalization of isolated quantum systems is an intriguing phenomenon at the forefront of contemporary physics. In this work, we demonstrate that nonlinear multimode optical platforms can be harnessed to induce effective quantum interactions between photons. Through numerical experiments where quantum beams propagate alongside classical light within multimode nonlinear optical systems, we reveal the thermalization of fundamental quantum light states--specifically single- and two-photon states. This thermalization is clearly manifested by the emergence of Rayleigh-Jeans and Boltzmann statistical distributions. Beyond providing a deeper understanding of how classical nonlinearities can be used to investigate quantum many-body dynamics, our findings will enable the exploration of a broader range of complex quantum phenomena, including aspects of quantum phase transitions, within readily accessible classical optical settings.
The past few years have witnessed a resurgence of interest in multimode structures, predominantly driven by the ever-increasing demand for higher information capacities. This renaissance, in turn, incited a flurry of activities in the general area of nonlinear multimode optics. The sheer complexity associated with the presence of hundreds or thousands of nonlinearly interacting modes that collectively act as a many-body system, has led to new opportunities in observing a multitude of novel optical effects that would have been otherwise impossible in single mode settings. In this talk, a thermodynamic theory capable of describing complex, highly multimoded, nonlinear optical systems is presented. It is shown that the mode occupancies in such nonlinear multimode arrangements follow a universal behavior that always tends to maximize the system’s entropy at steady-state. This thermodynamic response takes place irrespective of the type of nonlinearity involved and can be utilized to either heat or cool an optical multimode system. Aspects associated with adiabatic compressions and expansions will be discussed along with the possibility for all-optical Carnot cycles.
Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon-photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh-Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.