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Theoretical studies of optical non-linear effects in ultracold Rydberg gases

Andrey Grankin 1
1 Laboratoire Charles Fabry / Optique Quantique
LCF - Laboratoire Charles Fabry
Abstract : Photons appear as reliable information messengers since they interact very weakly with their environment. Unfortunately, they interact so weakly with each other that the direct implementation of optical two-qubit gates is impossible. The propagation through atomic nonlinear media however allows one to achieve effective photon-photon interactions. The technique of electromagnetically induced transparency (EIT) allows one to induce a strong resonant non-linearity -- not strong enough to be noticeable in the quantum domain though, on one of the transitions of a three-level ladder system. To enhance the nonlinear effects and reach the quantum regime, it was recently proposed to combine the EIT approach with the excitation blockade induced by the strong dipole-dipole interactions between Rydberg atoms. By putting the medium in a cavity, one imposes multiple passes to the light therefore increasing the optical nonlinearity. This kind of setup was studied both theoretically and experimentally in the dispersive regime and for a relatively weak nonlinearity, for which a classical treatment of the field is still valid. In this dissertation, we investigate the optical nonlinear effects induced by a Rydberg medium in the quantum regime.In chapter 1, we present our system, its dynamical equations and recall the definition and basic properties of the intensity correlation function g^{left(2right)}that we use to characterize the action of nonlinearity on the photonic field. In chapter 2, we consider the so-called dispersive regime, i.e. when the intermediate state is far detuned and can be adiabatically eliminated. We employ the Rydberg bubble approximation in which the system effectively consists in an ensemble of two-level superatoms coupled to the cavity mode, described by the driven Tavis-Cummings model. We compute analytically and numerically the g^{left(2right)}function of the transmitted light, which, depending on the cavity parameters, is shown to be either bunched or antibunched. In chapter 3, we present an alternative treatment of the system, which allows us to investigate the resonant regime. In the low-feeding limit, we analytically derive the correlation function g^{left(2right)}left(tauright)for the transmitted and reflected lights, based on the factorization of the lowest perturbative order of operator product averages. We then propose an effective non-linear three-boson model for the coupled atom-cavity system. Finally, we investigate the resonant regime and observe novel features of the correlation function g^{left(2right)}showing the interplay of impedance matching conditions and dipole-dipole interactions. In chapter 4, we analyze the system in the Schwinger-Keldysh formalism. Applying Wick's theorem, we perturbatively expand correlation functions with respect to both, feeding and dipole-dipole interactions Hamiltonians and perform a complete resummation with respect to the latter. By this method we recover the results of Chap. 3 in an analytic form. We also go beyond and derive analytic expressions for the elastic and inelastic components of the cavity transmission spectrum. We identify a polaritonic resonance structure in this spectrum, to our knowledge unreported so far, that we physically interpret. In chapter 5, we describe a novel scheme for high fidelity photonic controlled-phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. This protocol can be implemented with cavities of moderate finesse allowing for highly efficient processing of quantum information encoded in photons.
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Submitted on : Friday, September 16, 2016 - 3:35:07 PM
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  • HAL Id : tel-01367711, version 1

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Andrey Grankin. Theoretical studies of optical non-linear effects in ultracold Rydberg gases. Optics [physics.optics]. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLO006⟩. ⟨tel-01367711⟩

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