We study the collective optical response of an atomic ensemble confined within a single-mode optical cavity by stochastic electrodynamics simulations that include the effects of atomic position correlations, internal level structure, and spatial variations in cavity coupling strength and atom density. In the limit of low light intensity, the simulations exactly reproduce the full quantum field-theoretical description for cold stationary atoms and at higher light intensities we introduce semiclassical approximations to atomic saturation that we compare with the exact solution in the case of two atoms. We find that collective subradiant modes of the atoms, with very narrow linewidths, can be coupled to the cavity field by spatial variation of the atomic transition frequency and resolved at low intensities, and show that they can be specifically driven by tailored transverse pumping beams. We show that the cavity optical response, in particular both the subradiant mode profile and the resonance shift of the cavity mode, can be used as a diagnostic tool for the position correlations of the atoms and hence the atomic quantum many-body phase. The quantum effects are found to be most prominent close to the narrow subradiant mode resonances at high light intensities. Although an optical cavity can generally strongly enhance quantum fluctuations via light confinement, we show that the semiclassical approximation to the stochastic electrodynamics model provides at least a qualitative agreement with the exact optical response outside the subradiant mode resonances even in the presence of significant saturation of the atoms.
We study the collective optical response of an atomic ensemble confined within a single-mode optical cavity by stochastic electrodynamics simulations that include the effects of atomic position correlations, internal level structure, and spatial variations in cavity coupling strength and atom density. In the limit of low light intensity, the simulations exactly reproduce the full quantum field-theoretical description for cold stationary atoms and at higher light intensities we introduce semiclassical approximations to atomic saturation that we compare with the exact solution in the case of two atoms. We find that collective subradiant modes of the atoms, with very narrow linewidths, can be coupled to the cavity field by spatial variation of the atomic transition frequency and resolved at low intensities, and show that they can be specifically driven by tailored transverse pumping beams. We show that the cavity optical response, in particular both the subradiant mode profile and the resonance shift of the cavity mode, can be used as a diagnostic tool for the position correlations of the atoms and hence the atomic quantum many-body phase. The quantum effects are found to be most prominent close to the narrow subradiant mode resonances at high light intensities. Although an optical cavity can generally strongly enhance quantum fluctuations via light confinement, we show that the semiclassical approximation to the stochastic electrodynamics model provides at least a qualitative agreement with the exact optical response outside the subradiant mode resonances even in the presence of significant saturation of the atoms.
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal-level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low-light-intensity limit for atoms with a single electronic ground state, the full quantum field-theoretical representation of the model can be solved exactly by means of classical stochastic electrodynamics simulations for stationary atoms that represent cold atomic ensembles. Simulations for the optical response of atoms in a quantum degenerate regime require one to synthesize a stochastic ensemble of atomic positions that generates the corresponding quantum statistical position correlations between the atoms. In the case of multiple ground levels or at light intensities where saturation becomes important, the classical simulations require approximations that neglect quantum fluctuations between the levels. We show how the model is extended to incorporate corrections due to quantum fluctuations that result from virtual scattering processes. In the low-light-intensity limit, we illustrate the simulations in a system of atoms in a Mott-insulator state in a two-dimensional optical lattice, where recurrent scattering of light induces strong interatomic correlations. These correlations result in collective many-atom subradiant and superradiant states and a strong dependence of the response on the spatial confinement within the lattice sites.
We study propagation of low-intensity light in a medium within a one-dimensional (1D) model electrodynamics. It is shown that the coupled theory for light and matter fields may be solved, in principle exactly, by means of stochastic simulations that account for both collective linewidths and line shifts, and for quantum statistical position correlations of the atoms. Such simulations require that one synthesize atomic positions that have correlation functions appropriate for the given type of atomic sample. We demonstrate how one may simulate both a Bose-Einstein condensate (BEC) and a zero-temperature noninteracting Fermi-Dirac gas. Results of simulations of light propagation in such quantum degenerate gases are compared with analytical density expansions obtained by adapting the approach of Morice, Castin, and Dalibard [Phys. Rev. A 51, 3896 (1995)] to the 1D electrodynamics. A BEC exhibits an optical resonance that narrows and stays somewhat below the atomic resonance frequency as collective effects set in with increasing atom density. The first two terms in the analytical density expansion are in excellent agreement with numerical results for a condensate. While fermions display a similar narrowing and shift of the resonance with increasing density, already in the limit of very dilute gas the linewidth is only half of the resonance linewidth of an isolated atom. We attribute this to the regular spacing between the atoms, which is enforced by the Pauli exclusion principle. The analytical density expansion successfully predicts the narrowing, and also gives the next term in the density expansion of the optical response in semiquantitative agreement with numerical simulations.
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.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
Atoms subject to weak coherent incident light can be treated as coupled classical linear oscillators, supporting subradiant and superradiant collective excitation eigenmodes. We identify the limits of validity of this linear classical oscillator model at increasing intensities of the drive by solving the quantum many-body master equation for coherent and incoherent scattering from a chain of trapped atoms. We show that deviations from the linear classical oscillator model depend sensitively on the resonance linewidths υα of the collective eigenmodes excited by light, with the intensity at which substantial deviation occurs scaling as a power law of υα. The linear classical oscillator model then becomes inaccurate at much lower intensities for subradiant collective excitations than superradiant ones, with an example system of seven atoms resulting in critical incident light intensities differing by a factor of 30 between the two cases. By individually exciting eigenmodes, we find that this critical intensity has a υα2.5 scaling for narrower resonances and more strongly interacting systems, while it approaches a υα3 scaling for broader resonances and when the dipole-dipole interactions are reduced. The υα3 scaling also corresponds to the semiclassical result whereby quantum fluctuations between the atoms have been neglected. We study both the case of perfectly mode-matched drives and the case of standing-wave drives, with significant differences between the two cases appearing only at very subradiant modes and positions of Fano resonances.
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.