Signatures of optical phase transitions in superradiant and subradiant atomic arrays

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.

Bistable optical transmission through arrays of atoms in free space

“…Intrinsic bistability was thought to be unachievable for atoms in the optical regime, but recent theoretical studies of many-body systems suggest that interaction-mediated bistability is more generic and possible in a variety of systems with short-and long-range interactions [22][23][24]. In particular, we recently demonstrated [25] that intrinsic bistability and optically-induced phases emerge in arrays of atoms at sufficiently high densities, due to resonant light-mediated dipole-dipole (DD) interactions and that these could be identified in coherently and incoherently scattered light.…”

“…However, modes with q lying near to or outside the light cone cannot directly be excited by incident light due to the rapid phase variation required, and instead must be driven by applying symmetry-breaking fields to the lattice [25]. Such a symmetry-breaking level shifts could be generated, for example, by ac Stark shifts [97] of lasers.…”

“…(15) can have up to three real solutions, of which two are dynamically stable, resulting in optical bistability. Cases where solutions become unstable can result in the emergence of a typically rich phase diagram of different solutions, exhibiting a dependence on the intensity and laser frequency [25].…”

“…We formulate a theory for optical bistability of free-space atomic arrays that in general depends on the underlying LLI mode, expanding our earlier analysis of Ref. [25]. In some cases, the theory can be solved even analytically, with sufficiently small atomic separations (ka) < (π/3) 1/2 needed for bistability of spatially uniform modes.…”

“…In particular, a Mott-insulator state of 87 Rb atoms was now studied [37] in an optical lattice with near unit filling, where a subradiant eigenmode with a spatially uniform phase profile was driven by the incident field in the limit of low light intensity (LLI), and observed in a narrowed transmission resonance for light. Collective interaction of light with closely related arrays of atoms has attracted considerable theoretical interest [25,.…”