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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

CLEO®/Europe — IQEC 2013 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 May 1, 2013• 0 citations
Publisher

Abstract

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)).

DOI
10.1109/cleoe-iqec.2013.6801609

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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.
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, 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 calculations reproduce and interpret the results of recent experiments.
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.
Transmission properties of a weak probe field traveling through a sample of interacting cold 87Rb atoms driven into the three-level ladder configuration, which is a typical Rydberg electromagnetically induced transparency (EIT) system, are investigated. Rydberg atoms are considered to be a perfect platform in the research fields of quantum optics and quantum information processing due to some exaggerated properties of Rydberg atoms with high principal quantum number, especially, the dipole-dipole interaction between Rydberg atoms leads to the so-called dipole blockade effect accommodating at most one Rydberg excitation within a mesoscopic volume. The dipole blockade effect may be mapped onto the spectrum of EIT, and the EIT exhibits the cooperative optical nonlinearity which is usually characterized by two indicators, i.e., the probe intensity and the photonic correlation. The cooperative optical nonlinearity is also found here in the phase of transmission spectrum, and the phase can be regarded as the third indicator of nonlinearity in Rydberg EIT. However, there are tremendous differences between the phase and probe transmission (photonic correlation) though they both originate from the conditional polarization. Specifically, the phase is not sensitive to neither the incident probe intensity nor the initial photonic correlation at the resonant probe frequency under the condition of the Autler-Townes (AT) splitting where two other indicators exhibit significant cooperative nonlinearity. The nonlinearity in phase spectrum occurs only in the regime between the resonant probe frequency and the AT splitting and especially is remarkable at the frequency where the probe field is classical. Finally, influence of the principal quantum number and the atomic density on the transmitted phase are examined. In the nonlinear regime, the absolute value of the phase becomes smaller and smaller as the principal quantum number and the atomic density are raised. This indicates that the nonlinearity is strengthened by increasing them. The probe phase provides an attractive supplement to study in depth the cooperative optical nonlinearity in Rydberg EIT and offers us the considerable flexibility to manipulate the propagation and evolution of a quantum light field.