Signatures of optical phase transitions in superradiant and subradiant atomic arrays

Christopher D Parmee,Janne Ruostekoski

doi:10.1038/s42005-020-00476-1

Abstract

Resonant light interacting with matter supports different phases of a polarisable medium, and optical bistability where two phases coexist. Such phases have previously been actively studied in cavities. Here, we identify signatures of optical phase transitions and optical bistability mapped onto scattered light in free-space planar arrays of cold atoms. Methods on how to explore such systems in superradiant and extreme subradiant states are proposed. The cooperativity threshold and intensity regimes for the intrinsic optical bistability, supported by resonant dipole-dipole interactions alone, are derived in several cases of interest analytically. Subradiant states require lower intensities, but stronger cooperativity for the existence of non-trivial phases than superradiant states. The transmitted light reveals phase transitions and bistability that are predicted by mean-field theory as large jumps in coherent and incoherent signals and hysteresis. In the quantum solution, traces of phase transitions are identified in enhanced quantum fluctuations of excited level populations.

Highlights

Resonant light interacting with matter supports different phases of a polarisable medium, and optical bistability where two phases coexist
Beyond the low light intensity (LLI) regime with multiple excitations, atomic arrays start experiencing saturation, and the rich phenomenology of long-range interactions and collective behaviour can lead to the full many-body quantum solutions deviating from the semiclassical models that neglect quantum fluctuations[20]
We find that multiple mean-fieldtheoretical stable phases, including ones with spontaneous symmetry breaking and persistent oscillations, and optical bistability are identifiable in the transmitted light as large jumps in coherent and incoherent signals and hysteresis upon sweeping of the laser frequency

Summary

Introduction

Resonant light interacting with matter supports different phases of a polarisable medium, and optical bistability where two phases coexist. Resonant emitters in regular planar arrays have attracted considerable attention from classical circuit resonators forming metamaterials[1] and metasurfaces[2] to plasmonics[3] and quantum systems, such as superconducting SQUID rings[4] and cold atoms[5] Such surfaces can be utilised for manipulation of electromagnetic fields, including phase-holography[6] and sensing[7]. By studying light emission from radiatively strongly coupled atoms in planar arrays of subwavelength spacing, we identify optical signatures of phase transitions in collective atomic excitations. We propose methods on how to drive such eigenmodes by manipulating the atomic level shifts and consider two examples: a uniform mode that was recently experimentally studied in subradiant transmission measurements[5], which at smaller lattice spacings, considered here, becomes superradiant, and an extreme subradiant checkerboard eigenmode that can exist outside the light cone, decoupled from the environment

Methods

Results

Conclusion