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Journal of Physics B Atomic Molecular and Optical Physics

Electromagnetically induced transparency in thermal Rydberg atoms: superatom model with finite Doppler broadening

Si-Yin Bai, Qian-Qian Bao, Xue-Dong Tian, Yi-Mou Liu, Jin‐Hui Wu

Published Feb 14, 2018• 7 citations
Publisher

Abstract

Abstract We study the steady optical responses of a cold atomic ensemble driven into the three-level ladder configuration involving a Rydberg state at finite temperatures. By improving the superatom model with thermal movement included, we calculate relevant atomic coherence effects and find that the residual Doppler broadening at the mK–K temperatures will weaken the nonclassical properties of transmitted probe photons. Furthermore, propagation directions of the probe and coupling fields have a great influence on various properties related to electromagnetically induced transparency. That is, the residual Doppler effect is more destructive to relevant atomic coherence effects in the co-propagation case but can be partially eliminated in the counter-propagation case.

DOI
10.1088/1361-6455/aaaf52

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Abstract We study the steady optical responses of a cold atomic ensemble driven into the three-level ladder configuration involving a Rydberg state at finite temperatures. By improving the superatom model with thermal movement included, we calculate relevant atomic coherence effects and find that the residual Doppler broadening at the mK–K temperatures will weaken the nonclassical properties of transmitted probe photons. Furthermore, propagation directions of the probe and coupling fields have a great influence on various properties related to electromagnetically induced transparency. That is, the residual Doppler effect is more destructive to relevant atomic coherence effects in the co-propagation case but can be partially eliminated in the counter-propagation case.
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 For multi-level systems in hot atomic vapors the interplay between the Doppler shift due to atomic motion and the wavenumber mismatch between driving laser fields strongly influences transmission and absorption properties of the atomic medium. In a three-level atomic ladder-system, Doppler broadening limits the visibility of electromagnetically-induced transparency (EIT) when the probe and control fields are co-propagating, while EIT is recovered under the opposite condition of counter-propagating geometry and k p < k c , with k p and k c being the wavenumbers of the probe and control fields, respectively. This effect has been studied and experimentally demonstrated as an efficient mechanism to realize non-reciprocal probe light transmission, which may enable applications as magnetic-field free optical isolators. Here, we describe the basics of this effect and discuss a simple picture for the underlying mechanism. We illustrate how the non-reciprocity scales with wavelength mismatch and show how to experimentally demonstrate the effect in a simple Rydberg-EIT system using thermal Rubidium atoms.
The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.
The influence of Doppler broadening on a four-level N-type atomic system has been investigated in the presence of spontaneous generating coherence. The atomic system interacting with three electromagnetic fields and includes the nonradiative decay, the effect of co- and counter-propagation of the fields is considered. The probe susceptibility behaviors can be modified by Doppler broadening via nonperturbative treatments of the density matrix elements solution in the absence and presence of the spontaneous generating coherence. Some interesting features are enhanced for the spectral behaviors and controllability of electromagnetically induced transparency, which were found to be in good agreement to some experimental results without including Zeeman sublevels to the system.
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.
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.