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arXiv:1404.0311 · Physical Review Letters

Electromagnetically Induced Transparency in an Entangled Medium

Weibin Li, Daniel Viscor, Sebastian Hofferberth, Igor Lesanovsky

Published Jun 18, 2014• 66 citations
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Abstract

We theoretically investigate light propagation and electromagnetically induced transparency in a quasi-one-dimensional gas in which atoms interact strongly via exchange interactions. We focus on the case in which the gas is initially prepared in a many-body state that contains a single excitation and conduct a detailed study of the absorptive and dispersive properties of such a medium. This scenario is achieved in interacting gases of Rydberg atoms with two relevant S states that are coupled through exchange. Of particular interest is the case in which the medium is prepared in an entangled spin-wave state. This, in conjunction with the exchange interaction, gives rise to a nonlocal susceptibility that--in comparison to conventional Rydberg electromagnetically induced transparency--qualitatively alters the absorption and propagation of weak probe light, leading to nonlocal propagation and enhanced absorption.

DOI
10.1103/physrevlett.112.243601

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We theoretically investigate light propagation and electromagnetically induced transparency in a quasi-one-dimensional gas in which atoms interact strongly via exchange interactions. We focus on the case in which the gas is initially prepared in a many-body state that contains a single excitation and conduct a detailed study of the absorptive and dispersive properties of such a medium. This scenario is achieved in interacting gases of Rydberg atoms with two relevant S states that are coupled through exchange. Of particular interest is the case in which the medium is prepared in an entangled spin-wave state. This, in conjunction with the exchange interaction, gives rise to a nonlocal susceptibility that--in comparison to conventional Rydberg electromagnetically induced transparency--qualitatively alters the absorption and propagation of weak probe light, leading to nonlocal propagation and enhanced absorption.
We theoretically investigate the linear susceptibility and propagation of light in a three-dimensional (3-D) Rydberg gas under conditions of electromagnetically induced transparency. Rydberg atoms with two relevant S states are coupled via exchange interactions. When the gas is initially prepared in an entangled spin-wave state, this coupling induces a strong, nonlocal susceptibility whereby the photon field at one point of the medium acts as a source at a distant position. The nonlocal propagation occurs not only in the propagation direction but also in the paraxial direction. We discuss the absorption features and numerically simulate the 3-D propagation of probe laser light. Combined with the long-range exchange interaction, we show that the 3-D Rydberg gas is an ideal medium for studying nonlocal wave phenomena, in which the strength, range, and sign of the nonlocal interaction kernel can be widely tuned.
A three-level atomic medium can be made transparent to a resonant probe field in the presence of a strong control field acting on an adjacent atomic transition to a long-lived state, which can be represented by a highly excited Rydberg state. The long-range interactions between the Rydberg state atoms then translate into strong, non-local, dispersive or absorptive interactions between the probe photons, which can be used to achieve deterministic quantum logic gates and single photon sources. Here we show that long-range dipole–dipole exchange interaction with one or more spins—two-level systems represented by atoms in suitable Rydberg states—can play the role of control field for the optically dense medium of atoms. This induces transparency of the medium for a number of probe photons n p not exceeding the number of spins n s , while all the excess photons are resonantly absorbed upon propagation. In the most practical case of a single spin atom prepared in the Rydberg state, the medium is thus transparent only to a single input probe photon. For larger number of spins n s , all n p ≤ n s photon components of the probe field would experience transparency but with an n p -dependent group velocity.
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 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.
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.
A three-level atomic medium can be made transparent to a resonant probe field in the presence of a strong control field acting on an adjacent atomic transition. We show that long-range dipole-dipole exchange interaction with one or more spins -- two-level systems represented by atoms in suitable Rydberg states -- can play the role of control field for the optically-dense medium of atoms. This induces transparency of the medium for a number of probe photons npn_pnp​ not exceeding the number of spins nsn_sns​, while all the excess photons are resonantly absorbed upon propagation. In the case of a single spin atom prepared in the Rydberg state, the medium is thus transparent only to a single input probe photon. For larger number of spins nsn_sns​, all np≤nsn_p \leq n_snp​≤ns​ photon components of the probe field experience transparency but with an npn_pnp​-dependent group velocity.