Light scattering by a periodic atomic array is studied when the atoms couple with the mode of a high-finesse optical resonator and are driven by a laser. When the von-Laue condition is not satisfied, there is no coherent emission into the cavity mode, and the latter is pumped via inelastic scattering processes. We consider this situation and identify conditions for which different nonlinear optical processes can occur. We show that these processes can be controlled by suitably tuning the strength of laser and cavity coupling, the angle between laser and cavity axis, and the array periodicity. We characterize the coherence properties of the light when the system can either operate as degenerate parametric amplifier or as a source of antibunched light. Our study permits us to identify the individual multiphoton components of the nonlinear optical response of the atomic array and the corresponding parameter regimes, thereby in principle allowing one to control the nonlinear optical response of the medium.
Light scattering by a periodic atomic array is studied when the atoms couple with the mode of a high-finesse optical resonator and are driven by a laser. When the von-Laue condition is not satisfied, there is no coherent emission into the cavity mode, and the latter is pumped via inelastic scattering processes. We consider this situation and identify conditions for which different nonlinear optical processes can occur. We show that these processes can be controlled by suitably tuning the strength of laser and cavity coupling, the angle between laser and cavity axis, and the array periodicity. We characterize the coherence properties of the light when the system can either operate as degenerate parametric amplifier or as a source of antibunched light. Our study permits us to identify the individual multiphoton components of the nonlinear optical response of the atomic array and the corresponding parameter regimes, thereby in principle allowing one to control the nonlinear optical response of the medium.
The interaction between Bose Einstein condensates (BECs) and coherent light fields is treated within the framework of nonlinear wave mixing and studied using techniques developed in the fields of nonlinear and quantum optics. We focus in particular on two situations involving a BEC driven by a strong off-resonant 'pump' laser. First, we consider the case where the laser light is scattered into a single mode of an optical ring cavity. We then consider the case where the light is scattered into the continuum of vacuum modes of the electric field. The first problem is an extension of recent theoretical and experimental work on the so-called collective atomic recoil laser (CARL), whereas the second corresponds to a recent condensate-superradiance experiment performed at MIT. In the cavity situation, we develop a CARL model in which both the atomic and optical fields are treated fully quantum mechanically. We first show that the previous CARL model, which treats the atomic motion classically, breaks down at the recoil temperature due to the effects of matter-wave diffraction. We then show that when combined with a BEC the CARL can be viewed as a device which parametrically amplifies atomic and optical fields. The existence of entanglement and non-classical intensity correlations between the amplified atomic and optical fields is demonstrated, as well as the ability to manipulate the quantum statistical properties of the matter and light waves by injecting a weak laser field into the optical cavity to trigger the device. By replacing the cavity mode with a continuum of modes, we are able to formulate a quantum theory of condensate superradiance in which the scattered light field is eliminated in the Markov approximation. This model shows that condensate depletion leads to mode competition which prevents light scattering in all but the preferred direction(s). The outcome of the mode-competition is highly sensitive to the quantum fluctuations which trigger the phenomenon, resulting in large run-to-run variations in the angular pattern of the superradiant light pulse, an effect which is observed experimentally.
We show theoretically that two atomic dipoles in a resonator constitute a nonlinear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We identify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics might be observed as a result of self-organization of laser-cooled atoms in resonators.
This thesis summarizes the research work we did in the past years, which focuses on the theoretical study of quantum effects of ordered atomic structures interacting with the quantum electric field of an optical resonator. Within this work we investigated the quantum properties of the light at the cavity output, emitted by this kind of system, and the quantum state of the atoms confined by the light fields of the cavity mode. Following one possible partition, we have organized the thesis in two parts. The first part of the thesis is devoted to the quantum properties of the light at the output of optical cavities, in which atoms are confined. After a brief introduction on the basics of atom-photon interactions, we show theoretically, that two atomic dipoles in a resonator can behave as a quantum non-linear medium, whose response can be controlled through the interactomic distance of the atoms inside the resonator. We identify the parameter regime, for which the system operates as a parametric amplifier, based on the atoms' collective dipole cascade emission. Moreover we also determine the corresponding field squeezing spectrum at the cavity output. These dynamics could be observed as a result of self-organization processes of laser-cooled atoms in resonators. The second part of the thesis studies the quantum ground state of an ultracold atomic gas trapped inside an optical resonator by the mechanical effects of atom-photon interactions. Due to the strong coupling regime, the ultracold atomic gas feels a quantum potential, where the fluctuations at the single photon level may be relevant in determining the trapping conditions. This potential depends on the atomic distribution, which at the same time determines the intracavity field amplitude. Here, after a brief introduction on ultracold atoms in optical lattices, we study the low temperature physics of an ultracold atomic gas in the quantum potential formed inside a pumped cavity, by mapping the dynamics to an effective Bose-Hubbard model. We predict the existence of non-compressible states of the atomic gas, and determine a phase diagram as a function of the cavity parameters. Novel effects are encountered, such as the existence of overlapping stability regions corresponding to competing insulator-like states when the laser pumps the cavity, to provide one example out of many. At the end of the thesis a concluding chapter presents some general outlooks to this thesis work.
We consider the coupling of light, via an optical cavity, to two-dimensional atomic arrays whose lattice spacing exceeds the wavelength of the light. Such “superwavelength” spacing is typical of optical tweezer arrays. While subwavelength arrays exhibit strong atom-photon coupling, characterized by high optical reflectivity in free space, the coupling efficiency of superwavelength arrays is reduced due to collective scattering losses to high diffraction orders. We show how a moderate-finesse cavity can overcome these losses. As the scattering losses peak at certain discrete values of the lattice spacing, the spacing can be optimized to achieve efficient atom-photon coupling in the cavity. Our cavity-QED theory properly accounts for collective dipolar interactions mediated by the lossy, non-cavity-confined photon modes and for finite-size effects of both the array and the light field. These findings pave the way to harnessing the versatility of tweezer arrays for efficient atom-photon interfaces in applications of quantum computing, networking, and nonlinear optics. Published by the American Physical Society 2024
We study the quantum dynamics of an array of coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. In this configuration atomic excitation is suppressed even for strong driving fields, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of this interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest when the atoms are ordered in a wavelength spaced lattice placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. We analyze the mechanical forces in the regime where the interference condition is fulfilled, and show that the atomic pattern is mechanically stable whenever the driving frequency is red detuned with respect to the cavity frequency, irrespective of the atomic transition frequency
We theoretically investigate light scattering from an array of atoms into the guided modes of a waveguide. We observe that the scattering of a plane-wave laser field into the waveguide modes is dramatically enhanced for angles that deviate from the geometric Bragg angle. This modified Bragg condition arises from the dispersive interactions between the guided light and the atoms. We analytically identify various parameter regimes in which the scattering rate features a qualitatively different dependence on the atom number, such as linear, quadratic, oscillatory, or constant behavior. In combination with rigorous numerical calculations, we demonstrate that these scalings are independent of a possible asymmetry of the atom-light coupling. Finally, we show that our findings are robust against voids in the atomic array, facilitating their experimental observation and potential applications. Our work sheds light on collective light scattering and the interplay between geometry and interaction effects, with implications reaching beyond the optical domain.