Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1405.5821 · Physical Review B

Chemical potential for light by parametric coupling

Mohammad Hafezi, Prabin Adhikari, Jacob M. Taylor

Published Nov 19, 2015• 67 citations
arXivHTMLPDF

Abstract

Usually photons are not conserved in their interaction with matter. Consequently, for the thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semiconductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. In particular, we show that the photonic system equilibrates to the temperature of the bath, with a tunable chemical potential that is set by the frequency of the parametric coupler. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott insulator--superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources, and even electronlike circuits with light.

DOI
10.1103/physrevb.92.174305

Related papers

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Huizhong Ren, Georgios G. Pyrialakos, Qi Zhong +3 more

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.

Light Science & Applications•May 12, 2025•4 citations

Sisyphus Thermalization of Photons in a Double Quantum Dot

Michael J. Gullans, J. Stehlik, Y.-Y. Liu +3 more

A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

Physical Review Letters•Dec 3, 2015•2 citations

Photon Thermalization in Driven Open Quantum Systems

Chiao-Hsuan Wang

Light is a paradigmatic quantum field, with individual excitations---photons---that are the most accessible massless particles known. However, their lack of mass and extremely weak interactions mean that typically the thermal description of light is that of blackbody radiation. As the temperature of the light decreases, the overall number of photons approaches zero. Therefore, efforts for quantum optics and optical physics have mostly focused on driving systems far from equilibrium to populate sufficient numbers of photons. While lasers provide a severe example of a nonequilibrium problem, recent interests in the near-equilibrium physics of so-called photon gases, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one re-examine near-equilibrium cases. In this thesis, we consider peculiar driven open quantum system scenarios where near-equilibrium dynamics can lead to equilibration of photons with a finite number, following a thermal description closer to that of an ideal gas than to blackbody radiation. Specifically, we show how laser cooling of a well-isolated mechanical mode or atomic motion can provide an effective bath which enables control of both the chemical potential and temperature of the resulting grand canonical ensemble of photon. We then theoretically demonstrate that Bose condensation of photons can be realized by cooling an ensemble of two-level atoms inside a cavity. Finally, we find that the engineered chemical potential for light not only admits future applications in many-body quantum simulations, facilitates preparation of near-equilibrium photonic states, but also enables an analogous voltage bias for photonic circuit elements.

Bulletin of the American Physical Society•Jan 1, 2018•0 citations

Quantum phase transitions of light in the Dicke-Bose-Hubbard model

Soi-Chan Lei, Ray‐Kuang Lee

We extend the idea of quantum phase transitions of light in an atom-photon system with a Dicke-Bose-Hubbard model for an arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for an arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.

arXiv:0709.1352•Physical Review A•Mar 12, 2008•36 citations

Phase Transition of Light in Cavity QED Lattices

Marco Schirò, Mykola Bordyuh, Barış Öztop +1 more

Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.

arXiv:1205.3083•Physical Review Letters•Aug 3, 2012•127 citations

THE ROLE OF CHEMICAL PHOTON SOURCES FOR EMERGING QUANTUM COMMUNICATION TECHNOLOGIES

Ravuri Hema Krishna

Purpose-The purpose of this study is to review the origin and physical properties of chemical photons produced through chemical reactions and electronically excited molecular states, and to assess their potential relevance and feasibility for use in quantum communication systems.Design/Methodology/Approach-This paper presents a comprehensive literature-based review of chemically generated photon sources, including chemiluminescence, biophoton emission, and molecular fluorescence.It compares these sources with conventional quantum photonic technologies such as lasers, spontaneous parametric down-conversion, and quantum dots, while examining recent advances in molecular photonics and nanochemistry aimed at enhancing photon quality and controllability.Findings-The analysis reveals that chemical photon sources exhibit unique emission mechanisms, spectral tunability, and low-energy excitation pathways.While they currently face challenges in coherence, single-photon purity, and stability, emerging chemical engineering strategies demonstrate promising improvements toward quantum-grade performance.Practical Implications-Chemically The Role of Chemical Photon Sources for Emerging Quantum Communication Technologies

•Feb 3, 2026•0 citations
Usually photons are not conserved in their interaction with matter. Consequently, for the thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semiconductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. In particular, we show that the photonic system equilibrates to the temperature of the bath, with a tunable chemical potential that is set by the frequency of the parametric coupler. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott insulator--superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources, and even electronlike circuits with light.
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.
A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.
Light is a paradigmatic quantum field, with individual excitations---photons---that are the most accessible massless particles known. However, their lack of mass and extremely weak interactions mean that typically the thermal description of light is that of blackbody radiation. As the temperature of the light decreases, the overall number of photons approaches zero. Therefore, efforts for quantum optics and optical physics have mostly focused on driving systems far from equilibrium to populate sufficient numbers of photons. While lasers provide a severe example of a nonequilibrium problem, recent interests in the near-equilibrium physics of so-called photon gases, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one re-examine near-equilibrium cases. In this thesis, we consider peculiar driven open quantum system scenarios where near-equilibrium dynamics can lead to equilibration of photons with a finite number, following a thermal description closer to that of an ideal gas than to blackbody radiation. Specifically, we show how laser cooling of a well-isolated mechanical mode or atomic motion can provide an effective bath which enables control of both the chemical potential and temperature of the resulting grand canonical ensemble of photon. We then theoretically demonstrate that Bose condensation of photons can be realized by cooling an ensemble of two-level atoms inside a cavity. Finally, we find that the engineered chemical potential for light not only admits future applications in many-body quantum simulations, facilitates preparation of near-equilibrium photonic states, but also enables an analogous voltage bias for photonic circuit elements.
We extend the idea of quantum phase transitions of light in an atom-photon system with a Dicke-Bose-Hubbard model for an arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for an arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
Purpose-The purpose of this study is to review the origin and physical properties of chemical photons produced through chemical reactions and electronically excited molecular states, and to assess their potential relevance and feasibility for use in quantum communication systems.Design/Methodology/Approach-This paper presents a comprehensive literature-based review of chemically generated photon sources, including chemiluminescence, biophoton emission, and molecular fluorescence.It compares these sources with conventional quantum photonic technologies such as lasers, spontaneous parametric down-conversion, and quantum dots, while examining recent advances in molecular photonics and nanochemistry aimed at enhancing photon quality and controllability.Findings-The analysis reveals that chemical photon sources exhibit unique emission mechanisms, spectral tunability, and low-energy excitation pathways.While they currently face challenges in coherence, single-photon purity, and stability, emerging chemical engineering strategies demonstrate promising improvements toward quantum-grade performance.Practical Implications-Chemically The Role of Chemical Photon Sources for Emerging Quantum Communication Technologies