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arXiv:1106.1360 · Physical Review Letters

Electromagnetically Induced Transparency with Rydberg Atoms

David Petrosyan, Johannes Otterbach, Michael Fleischhauer

Published Nov 14, 2011• 247 citations
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Abstract

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)].

DOI
10.1103/physrevlett.107.213601

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Acta Physica Sinica•Jan 1, 2019•2 citations
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)].
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.
We present an improved superatom model for examining nonlinear optical responses of cold Rydberg atoms in the regime of electromagnetically induced transparency (EIT). By going beyond the weak-probe approximation, we find that several higher-order collective states should be included to correctly describe the coherent Rydberg excitation of superatoms. Otherwise, numerical results based on the simple ladder system of superatoms will contribute wrong predictions on light intensity and photon correlation of the transmitted probe field. In particular, a great photon-bunching effect will be improperly expected somewhere out of the EIT window in one dilute atomic sample. The essence of this improved superatom model lies in that it can provide reliable predictions on the nonlinear Rydberg-EIT phenomena even in dense atomic samples and may be extended to realize lossless conditional light interactions in appropriate multilevel systems exhibiting dipole blockade.
Abstract Cavity electromagnetically induced transparency (EIT) is revisited via the input probe field intensity. A strongly interacting Rydberg atomic medium ensemble is considered in a cavity, where atoms behave as superatoms (SAs) under the dipole blockade mechanism. Each atom in the strongly interacting Rydberg atomic medium ( 87 Rb) follows a three-level cascade atomic configuration. A strong control and weak probe field are employed in the cavity with the ensemble of Rydberg atoms. The features of the reflected and transmitted probe light are studied under the influence of the input probe field intensity. A transparency peak (cavity EIT) is revealed at a resonance condition for small values of input probe field intensity. The manipulation of the cavity EIT is reported by tuning the strength of the input probe field intensity. Further, the phase and group delay of the transmitted and reflected probe light are studied. It is found that group delay and phase in the reflected light are negative, while for the transmitted light they are positive. The magnitude control of group delay in the transmitted and reflected light is investigated via the input probe field intensity.
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.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
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.