We determine the transmission of light through a planar atomic array beyond the limit of low light intensity that displays optical bistability in the mean-field regime. We develop a theory describing the intrinsic optical bistability, which is supported purely by resonant dipole-dipole interactions in free space, showing how bistable light amplitudes exhibit both strong cooperative and weak single-atom responses and how they depend on the underlying low light intensity collective excitation eigenmodes. Similarities of the theory with optical bistability in cavities are highlighted, while recurrent light scattering between atoms takes on the role of cavity mirrors. Our numerics and analytic estimates show a sharp variation in the extinction, reflectivity, and group delays of the array, with the incident light completely extinguished up to a critical intensity well beyond the low light intensity limit. Our analysis paves a way for collective nonlinear optics with cooperatively responding dense atomic ensembles.
We determine the transmission of light through a planar atomic array beyond the limit of low light intensity that displays optical bistability in the mean-field regime. We develop a theory describing the intrinsic optical bistability, which is supported purely by resonant dipole-dipole interactions in free space, showing how bistable light amplitudes exhibit both strong cooperative and weak single-atom responses and how they depend on the underlying low light intensity collective excitation eigenmodes. Similarities of the theory with optical bistability in cavities are highlighted, while recurrent light scattering between atoms takes on the role of cavity mirrors. Our numerics and analytic estimates show a sharp variation in the extinction, reflectivity, and group delays of the array, with the incident light completely extinguished up to a critical intensity well beyond the low light intensity limit. Our analysis paves a way for collective nonlinear optics with cooperatively responding dense atomic ensembles.
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.
Understanding strong cooperative optical responses in dense and cold atomic ensembles is vital for fundamental science and emerging quantum technologies. Methodologies for characterizing light-induced quantum effects in such systems, however, are still lacking. Here we unambiguously identify significant quantum many-body effects, robust to position fluctuations and strong dipole-dipole interactions, in light scattered from planar atomic ensembles, by comparing full quantum simulations with a semiclassical model neglecting quantum fluctuations. We find pronounced quantum effects at high atomic densities, light close to saturation intensity, and around subradiant resonances. Such conditions also maximize spin-spin correlations and entanglement between atoms, revealing the microscopic origin of light-induced quantum effects. In several regimes of interest, our approximate model reproduces light transmission remarkably well, permitting analysis of otherwise numerically inaccessible large ensembles, in which we observe many-body analogues of resonance power broadening, vacuum Rabi splitting, and significant suppression in cooperative reflection from atomic arrays.
Abstract Understanding strong cooperative optical responses in dense and cold atomic ensembles is vital for fundamental science and emerging quantum technologies. Methodologies for characterizing light-induced quantum effects in such systems, however, are still lacking. Here we unambiguously identify significant quantum many-body effects, robust to position fluctuations and strong dipole–dipole interactions, in light scattered from planar atomic ensembles by comparing full quantum simulations with a semiclassical model neglecting quantum fluctuations. We find pronounced quantum effects at high atomic densities, light close to saturation intensity, and around subradiant resonances. Such conditions also maximize spin–spin correlations and entanglement between atoms, revealing the microscopic origin of light-induced quantum effects. In several regimes of interest, our approximate model reproduces light transmission remarkably well, permitting analysis of otherwise numerically inaccessible large ensembles, in which we observe many-body analogues of resonance power broadening, vacuum Rabi splitting, and significant suppression in cooperative reflection from atomic arrays.
We study strong, light-mediated, resonant dipole-dipole interactions in two-dimensional planar lattices of cold atoms. We provide a detailed analysis for the description of the dipolar point emitter lattice plane as a ``superatom'' whose response is similar to electromagnetically induced transparency but which exhibits an ultranarrow collective size-dependent subradiant resonance linewidth. The superatom model provides intuitively simple descriptions for the spectral response of the array, including the complete reflection, full transmission, narrow Fano resonances, and asymptotic expressions for the resonance linewidths of the collective eigenmodes. We propose a protocol to transfer almost the entire radiative excitation to a single correlated subradiant eigenmode in a lattice and show that the medium obtained by stacked lattice arrays can form a cooperative magnetometer. Such a magnetometer utilizes similar principles as magnetometers based on the electromagnetically induced transparency. The accuracy of the cooperative magnetometer, however, is not limited by the single-atom resonance linewidth but the much narrower collective linewidth that results from the strong dipole-dipole interactions.
Collective coupling between dipoles can dramatically modify the optical response of a medium. Such effects depend strongly on the geometry of the medium and the polarization of the light. Using a classical coupled dipole model, here we investigate the simplest case of one-dimensional arrays of interacting atomic dipoles driven by a weak laser field. Changing the polarization and direction of the driving field allows us to separately address superradiant, subradiant, redshifted, and blueshifted eigenmodes, as well as observe strong Fano-like interferences between different modes. The cooperative eigenvectors can be characterized by the phase difference between nearest-neighbor dipoles, ranging from all oscillating in phase to all oscillating out of phase with their nearest neighbors. Investigating the eigenvalue behavior as a function of atom number and lattice spacing, we find that certain eigenmodes of an infinite atomic chain have the same decay rate as a single atom between two mirrors. The effects we observe provide a framework for collective control of the optical response of a medium, giving insight into the behavior of more complicated geometries, as well as providing further evidence for the dipolar analog of cavity QED.
Spontaneous pattern formation from a uniform state is a widely studied nonlinear optical phenomenon that shares similarities with non-equilibrium pattern formation in other scientific domains. Here we show how a single layer of atoms in an array can undergo nonlinear amplification of fluctuations, leading to the formation of intricate optical patterns. The origin of the patterns is intrinsically cooperative, eliminating the necessity of mirrors or cavities, although introduction of a mirror in the vicinity of the atoms significantly modifies the scattering profiles. The emergence of these optical patterns is tied to a bistable collective response, which can be qualitatively described by a long-wavelength approximation, similar to a nonlinear Schrödinger equation of optical Kerr media or ring cavities. These collective excitations have the ability to form singular defects and unveil atomic position fluctuations through wave-like distortions.