Microscopic models based on multilevel atoms are central to optimizing nonlinear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work, we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of interatomic correlations and collective decay over the photons created in this nonlinear process is then explored. We identify three regions of operation: (i) laser-dominated, (ii) intermediate, and (iii) dipole-dominated. The dependence of single- and two-photon correlations is studied in detail for each region by varying atomic orientations and laser parameters consistent with current experiments involving atomic gases. Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning—with general features that can be obtained in an isolated atom scheme—to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photon correlations. Signatures of these processes are identified for existing experimental realizations. The intuition obtained from this connection helps to uncover relevant parameters that could be exploited for quantum control protocols based on dispersive and dissipative cooperative effects in multilevel systems.
Microscopic models based on multilevel atoms are central to optimizing nonlinear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work, we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of interatomic correlations and collective decay over the photons created in this nonlinear process is then explored. We identify three regions of operation: (i) laser-dominated, (ii) intermediate, and (iii) dipole-dominated. The dependence of single- and two-photon correlations is studied in detail for each region by varying atomic orientations and laser parameters consistent with current experiments involving atomic gases. Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning—with general features that can be obtained in an isolated atom scheme—to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photon correlations. Signatures of these processes are identified for existing experimental realizations. The intuition obtained from this connection helps to uncover relevant parameters that could be exploited for quantum control protocols based on dispersive and dissipative cooperative effects in multilevel systems.
We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction combined with atom-field coupling can introduce additional interatomic correlations acting as a phase synchronizing factor. For the case of weakly interacting atoms with $J<\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, where J is the interparticle coupling constant and ${\ensuremath{\omega}}_{0}$ is the atomic frequency, dynamical regimes of cooperative relaxation of atoms are analyzed in the Born-Markov approximation both numerically and using the mean field approximation. We show that interparticle correlations induced by the direct interaction result in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation which differs from superradiance in nature. For superradiant transition, the synchronizing effect of interatomic interaction is found to manifest itself in enhancement of superradiance. When the interaction is strong and $J>\ensuremath{\hbar}{\ensuremath{\omega}}_{0}$, one-particle one-photon transitions are excluded and transition to the regime of multiphoton relaxation occurs. Using a simple model of two atoms in a high-Q single mode cavity we show that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effects of dipole-dipole interaction and solitonic mechanism of relaxation are discussed.
High optical nonlinearities can be achieved at the single photon level by coupling the photon states to strongly interacting Rydberg excitations under the conditions of electromagnetically induced transparency. The nonlinear response in Rydberg quantum optics comes as a direct result of the long range dipole-dipole interactions via Rydberg blockade and interaction induced dephasing. In this thesis, Rydberg quantum optics experiments are performed with two spatially separated mediums with a nonlinear response at the single photon level. Two ultracold rubidium atomic clouds are tightly confined by a pair of in-vacuo aspheric lenses such that only a few Rydberg excitations can exist in each one of the clouds simultaneously. The long range character of the dipole-dipole interactions leads to the generation of quantum states of light. The effective photon-photon interactions are directly observed as an anti-correlation in the simultaneous photon retrieval as a result of the non resonant van der Waals interactions. The collective Rydberg excitations, stored in the non-overlapping mediums, experience an additional spatial non-uniform phase. In addition, we experimentally characterize the cooperative optical response of a cold atomic medium at a single photon level. This aims to exploit the enhancement of the spontaneous emissions decay rate (superradiance) as a dependence of the number of atoms involved in the ensemble. The observed atomic response in two different regimes gives a further understanding of the system dynamics and unlocks a promising potential route towards the implementation in scalable, multichannel quantum optical devices.
We develop a general dressed-state framework for computing fluorescence spectra, probe absorption spectra, and photon-photon correlations of light scattered by ensembles of Nat two-level atoms with arbitrary Jg→Je transitions driven by intense coherent fields. The approach employs a full vectorial treatment of the electromagnetic field, handles any atomic geometries, illumination directions, and polarizations, and yields optical observables as explicit sums of Lorentzian lines whose positions, widths, and weights are directly tied to the eigenvalues and eigenvectors of the Lindbladian. The framework is implemented in an open-source Python package and benchmarked against exact single- and two-atom calculations. We identify geometries in which the full vectorial description is essential, and the scalar approximation fails qualitatively. Applying the method to pairs of atoms with a Jg=0→Je=1 transition, we show that elastic and inelastic scattered intensities collapse onto universal master curves controlled by a single collective saturation parameter built from the dominant superradiant mode, across several orders of magnitude in drive strength and interatomic distance. We identify collective phenomena that require a description beyond this single-mode picture. Extending the analysis to atoms with ground-state degeneracy, we find that most collective features carry over, while two qualitatively new effects emerge: an incoherent spontaneous Raman channel that modifies the scaling of inelastic emission, and a slow timescale in the time-delayed correlations g(2)(τ) governed by the competition between Raman scattering and subradiant decay, controlled by a single dimensionless parameter. These results provide both physical insight and practical computational tools for engineering collective optical responses in few-atom systems such as optical tweezer arrays.
The collective scattering of light by a large number of coupled scatterers yields a rich many-body physics, yet treating such a problem in the quantum regime is a challenge.In this thesis, we consider a large atomic cloud in free space and driven by a monochromatic light, where the vacuum modes induce long-range dipole-dipole interactions.In order to study clouds of hundreds of particles, higher order correlation terms are neglected, keeping only quantum correlations between pair of atoms: this allows to reduce the number of degrees of freedom from 2 2N in the full quantum model to N 2 .Most of the works in the literature on dipole-dipole interactions have been performed in the linear optics limit, and our techniques allow to compare classical to beyond-semi-classical results.In particular, superradiance and subradiance have been reported in the decay dynamics of the cloud.Differently, by considering a system in the ground state and switching on the pump, we show that superradiance is also present in the Rabi oscillations at a rate obtained from using a single-dipole model for the radiated intensity.A frequency shift in the Rabi oscillations is also reported, which can be interpreted, in a linear dispersion theory, as a signature of a collective multimode vacuum Rabi splitting.While the classical dipoles model captures correctly the dynamics in the low-intensity regime, it fails for higher saturation, where semi-classical methods can be applied successfully.In particular, we observe a quantum subradiant decay in the intensity of the radiated field in the saturated regime.Furthermore, considering the decay dynamics starting from an initially strongly driven cloud, we observed that the states with n < N/2 excited atoms decays much slower than the ones with n > N/2: in other words, the upper part of the Dicke ladder is characterized by a superradiant emission, and the lower part by a subradiant one.Finally, investigating the fluorescence spectrum, we obtained quantum cooperative effects that modify the steady-state spectrum: additional sidebands at twice the Rabi frequency for the system driven at resonance and, out of resonance, an asymmetry in the peaks at the generalized Rabi frequency, and for all detection angles.We also present preliminary results of a sensor model that can capture the time evolution of the spectrum in the decay dynamics, a situation that the quantum regression theorem fails to describe.Several of these results were discussed in parallel with experimental data obtained by an experimental group of collaborators, and others aim to guide future experiments.
We present an analysis of four-wave parametric amplification resulting from the nonlinear response of a two-level atomic system. The atomic dipole moment induced by weak optical fields at frequencies ${\ensuremath{\omega}}_{3}$ and ${\ensuremath{\omega}}_{4}$ in the presence of an optical field of arbitrary intensity at frequency ${\ensuremath{\omega}}_{1}$, where ${\ensuremath{\omega}}_{3}+{\ensuremath{\omega}}_{4}=2{\ensuremath{\omega}}_{1}$, is obtained by solving the density-matrix equations of motion with phenomenological damping constants. The resulting nonlinear polarization can induce loss or three-photon gain in either weak wave and can act to parametrically couple these waves. The spatial evolution of the weak-field amplitudes is obtained by finding approximate solutions to the Helmholtz wave equations using the nonlinear polarization for the source terms. These solutions predict large gain for either or both of the weak waves under experimentally attainable conditions. Depending on the circumstance, this gain can be attributed solely to the three-photon gain, solely to the parametric coupling, or to an interplay between these effects. In addition, the solutions show an enhancement in the gain when $|{\ensuremath{\omega}}_{3}\ensuremath{-}{\ensuremath{\omega}}_{1}|=|{\ensuremath{\omega}}_{4}\ensuremath{-}{\ensuremath{\omega}}_{1}|={\ensuremath{\Omega}}^{\ensuremath{'}}$, where ${\ensuremath{\Omega}}^{\ensuremath{'}}$ is the generalized Rabi frequency associated with the driving of the atoms by the wave at frequency ${\ensuremath{\omega}}_{1}$.
An ensemble of atoms coupled to the radiation field exhibits collective behaviours when the interatomic separation is comparable to the wavelength of photons emitted by the atoms. The collective coupling of the atoms with the electromagnetic field gives rise to coherent exchange interactions between the atoms. In addition, the spontaneous decay of photons from the ensemble becomes a collective process that can happen at a much faster (superradiant) or slower (subradiant) rate than that of a single atom. These processes affect the way that fluorescence light is scattered from the system when it is driven by a laser. However, little is known about the response of a dense atomic gas beyond the linear regime of very weak driving, due to the involved complexity of the problem. The first part of this thesis investigates how the presence of strong laser driving affects properties of the far-field fluorescence light emitted by the ensemble, such as the power spectrum and second order coherence. Depending on the strength of the driving laser and the particular arrangement of the atoms, the laser can modify considerably how the collective behaviours of the atomic ensemble are manifested in the fluorescence. The relative strengths of the coherent interaction and collective decay process are intrinsically linked to the way that the atoms couple to the radiation field; one cannot be changed without modifying the other. Altering the environment by, for example, placing the atoms near a surface or a waveguide, can change this relation significantly from that for atoms in free space. Therefore, modified environments represent a platform for the generation of otherwise inaccessible regimes of collective behaviour, with potential applications in quantum state engineering. The second part of this thesis provides a numerical investigation into how the collective properties of a dense atomic system can be manipulated by placing the atoms close to planar surfaces or an optical nanofiber. These structures modify the light-matter coupling by altering the electric field experienced by the atoms. It is shown that surfaces of metallic and dielectric materials can be used to either enhance or suppress the collective behaviours, depending on the particular system arrangement. In particular, the coupling of atoms with bound surface modes, such as the surface plasmon polaritons that are formed at an air-metal interface, is demonstrated to have a strong effect on the interactions. An optical nanofiber supports a set of fundamental guided modes, that propagate along the fiber. If the atoms are suitably polarised, then they will emit primarily into the guided modes travelling in one direction. By calculating and analysing the collective decay states of a chain of atoms placed near a nanofiber, it is demonstrated that the atom-fiber coupling leads to the formation of a superradiant mode that is preserved at large atomic separations. The presence of chiral emission is shown to introduce phase gradients to the collective modes.