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arXiv:1502.06429 · Physical Review A

Quantum-optical nonlinearities induced by Rydberg-Rydberg interactions: A perturbative approach

Andrey Grankin, E. Brion, Erwan Bimbard, Rajiv Boddeda, Imam Usmani, Alexei Ourjoumtsev, Philippe Grangier

Published Oct 29, 2015• 22 citations
arXivHTMLPDF

Abstract

In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical nonlinearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant thus generalizing our previous results. We can thus investigate quantitatively new features associated with the resonant behavior of the system. We also propose an effective nonlinear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.

DOI
10.1103/physreva.92.043841

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•Jan 1, 2014•1 citation
In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical nonlinearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant thus generalizing our previous results. We can thus investigate quantitatively new features associated with the resonant behavior of the system. We also propose an effective nonlinear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system.
We theoretically investigate the quantum statistical properties of light transmitted through an atomic medium with strong optical nonlinearity induced by Rydberg–Rydberg van der Waals interactions. In our setup, atoms are located in a cavity and nonresonantly driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of the weak signal field and a strong control beam. To characterize the transmitted light, we compute the second-order correlation function . The simulations we obtained on the specific case of rubidium atoms suggest that the bunched or antibunched nature of the outgoing beam can be chosen at will by tuning the physical parameters appropriately.
We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples electronic states of a pair of atoms dressed by a strong control field. We calculate the optical response for the three-level system by explicitly including the dynamics of the intermediate state. We find an analytical expression for the third-order susceptibility for a weak classical probe field. The nonlinear absorption displays the strongest resonant behavior on two-photon resonance where the detuning of the probe field equals the Rabi frequency of the control field. The nonlinear dispersion of the medium exhibits various spatial shapes depending on the interaction strength. Based on the developed model, we propose a realistic experimental scenario to observe the resonance by performing transmission measurements.
Abstract We experimentally characterize the optical nonlinear response of a cold atomic medium placed inside an optical cavity, and excited to Rydberg states. The excitation to S and D Rydberg levels is carried out via a two-photon transition in an electromagnetically induced transparency configuration, with a weak (red) probe beam on the lower transition, and a strong (blue) coupling beam on the upper transition. The observed optical nonlinearities induced by S states for the probe beam can be explained using a semi-classical model with van der Waals’ interactions. For the D states, it appears necessary to take into account a dynamical decay of Rydberg excitations into a long-lived dark state. We show that the measured nonlinearities can be explained by using a Rydberg bubble model with a dynamical decay.
The realization of nonlinear optical effects at the single photon level would be a significant step forward for quantum information processing and communications. In particular, a strong dispersive and non-dissipative nonlinearity could enable the implementation of a two-photon phase gate. One possible strategy to reach such huge nonlinearities is to convert photons into strongly interacting particles, like collective excitations involving Rydberg atoms. Interactions between Rydbergs in fact lead to a “blockade” phenomenon, where each Rydberg atom blocks the excitation of its neighbors, which can result in strong nonlinearities. Here, we use an ensemble of cold Rydberg atoms inside an optical cavity to create large dispersive nonlinearities on a weak probe beam far detuned from a D2-line transition in87Rb atoms [1]. The used three-level ladder scheme, with a second control field detuned from resonance on the upper transition towards a Rydberg level, is shown in Fig.1a). A simple explanation of the nonlinear effect is the following: if a very weak probe beam is injected into the cavity in the presence of the blue light on the two-photon transition, it experiences the single-atom three-level dispersion described by the real part of the three-level susceptibility χ-3level. This corresponds to a certain shift of the transmitted cavity peak (Fig. 1b)).
The influence of van der Waals (vdW) interaction on the nonlinear optical properties of Rydberg atoms is investigated within a three-level cascade scheme established using two probe and control laser fields. It is demonstrated that vdW interaction can induce reverse saturable absorption (RSA) in the Rydberg atoms in the two-photon resonance condition, enabling controllable optical limiting behavior. Furthermore, the presence of vdW interaction facilitates a switch between saturable absorption and RSA and vice versa beyond the two-photon resonance condition, thereby enabling intrinsic optical bistability in the system.
Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reflected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations.