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arXiv:1209.1948 · Physical Review Letters

Observation and Measurement of Interaction-Induced Dispersive Optical Nonlinearities in an Ensemble of Cold Rydberg Atoms

Valentina Parigi, Erwan Bimbard, Jovica Stanojevic, Andrew J. Hilliard, Florence Nogrette, Rosa Tualle-Brouri, Alexei Ourjoumtsev, Philippe Grangier

Published Dec 4, 2012• 137 citations
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Abstract

We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.

DOI
10.1103/physrevlett.109.233602

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We observe and measure dispersive optical nonlinearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical nonlinearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
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)).
We investigate dispersive optical nonlinearities that arise from a Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the nonlinear response to a weak optical probe in the presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be evaluated in a steady-state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple ``universal scaling'' formula to determine the dispersive optical nonlinearity of the medium. We also develop a technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that only involve two-body correlations, which can be solved numerically. All average populations and coherences are then obtained straightforwardly.
The combination of electromagnetically induced transparency with the nonlinear interaction between Rydberg atoms provides an effective interaction between photons. In this Letter, we investigate the storage of optical pulses as collective Rydberg atomic excitations in a cold atomic ensemble. By measuring the dynamics of the stored Rydberg polaritons, we experimentally demonstrate that storing a probe pulse as Rydberg polaritons strongly enhances the Rydberg mediated interaction compared to the slow propagation case. We show that the process is characterized by two time scales. At short storage times, we observe a strong enhancement of the interaction due to the reduction of the Rydberg polariton group velocity down to 0. For longer storage times, we observe a further, weaker enhancement dominated by Rydberg induced dephasing of the multiparticle components of the state. In this regime, we observe a nonlinear dependence of the Rydberg polariton coherence time with the input photon number. Our results have direct consequences in Rydberg quantum optics and may enable the test of new theories of strongly interacting Rydberg systems.
By coupling a probe transition to a Rydberg state using electromagnetically induced transparency (EIT) we map the strong dipole-dipole interactions onto an optical field. We characterize the resulting cooperative optical nonlinearity as a function of probe strength and density. We demonstrate good quantitative agreement between the experiment and an N-atom cooperative model for N=3 atoms per blockade sphere and the n=60 Rydberg state. The measured linewidth of the EIT resonance places an upper limit on the dephasing rate of the blockade spheres of <110 kHz.
We present a theory of electromagnetically induced transparency in a cold ensemble of strongly interacting Rydberg atoms. Long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our model is computationally very efficient and is in quantitative agreement with the results of the recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010)].