Emergence of unidirectionality and phase separation in optically dense emitter ensembles

Year: 2025

Authors: Kusmierek K.J., Schemmer M., Mahmoodian S., Hammerer K.

Autors Affiliation: Leibniz Univ Hannover, Inst Theoret Phys, Appelstr 2, D-30167 Hannover, Germany; Ist Nazl Ott Consiglio Nazl Ric CNR INO, I-50019 Sesto Fiorentino, Italy; Univ Firenze, European Lab Nonlinear Spect LENS, I-50019 Sesto Fiorentino, Italy; Univ Sydney, Inst Photon & Opt Sci IPOS, Sch Phys, Sydney, NSW 2006, Australia; Univ Sydney, Ctr Engn Quantum Syst, Sch Phys, Sydney, NSW 2006, Australia.

Abstract: The transmission of light through an ensemble of two-level emitters in a one-dimensional geometry is commonly described by one of two emblematic models of quantum electrodynamics (QED): the driven-dissipative Dicke model or the Maxwell-Bloch equations. Both exhibit distinct features of phase transitions and phase separations, depending on system parameters such as optical depth and external drive strength. Here, we explore the crossover between these models via a parent spin model from bidirectional waveguide QED, by varying positional disorder among emitters. Solving mean-field equations and employing a second-order cumulant expansion for the unidirectional model-equivalent to the Maxwell-Bloch equations-we study phase diagrams, the emitter’s inversion, and transmission depending on optical depth, drive strength, and spatial disorder. We find in the thermodynamic limit the emergence of phase separation with a critical value that depends on the degree of spatial order but is independent of Doppler broadening effects. Even far from the thermodynamic limit, this critical value marks a special point in the emitter’s correlation landscape of the unidirectional model and is also observed as a maximum in the magnitude of inelastically transmitted photons. We conclude that a large class of effective one-dimensional systems without tight control of the emitters spatial ordering can be effectively modeled using a unidirectional waveguide approach.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 7 (4)      Pages from: 43267-1  to: 43267-17

More Information: We are grateful to S. Felicetti, C. Lidl, A. Rauschen-beutel, T. Roscilde, P. Schneeweiss, and J. Volz for stimul-ating discussions. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foun-dation) under SFB 1227 DQ-mat Project No. A09-274200144 and Germany’s Excellence Strategy-EXC-2123 QuantumFrontiers-390837967. S.M. acknowledges support from the Australian Research Council (ARC) via the Future Fellowship, Emergent many-body phenomena in engineered quantum optical systems, Project No. FT200100844. M.S. acknowledges support via the Italian Ministry of University and Research, in the framework of the National Recovery and Resilience Plan (NRRP) for funding project MSCA 0000048.
KeyWords: Doppler effect; Electrodynamics; Light transmission; Optical properties; Optical waveguides; Phase diagrams; Phase separation; Phase transitions; Quantum electronics; Transmissions
DOI: 10.1103/dzpg-9wv3