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Physical Review A

Polarization-selective optical nonlinearities in cold Rydberg atoms

Jin‐Hui Wu, M. Artoni, Giuseppe Carlo La Rocca

Published Dec 3, 2015• 9 citations
Publisher

Abstract

We study the interaction between a probe and a trigger weak fields in a sample of cold rubidium atoms in the presence of a coupling and a dressing strong fields. Dipole Rydberg blockade may occur and can be set to depend on the probe and trigger polarizations giving rise to diverse regimes of electromagnetically induced transparency (EIT) with a concomitant small probe and trigger absorption and dispersion. This is shown to be relevant to the implementation of polarization conditional probe and trigger cross nonlinearities in cold Rydberg atoms.

DOI
10.1103/physreva.92.063805

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We study the interaction between a probe and a trigger weak fields in a sample of cold rubidium atoms in the presence of a coupling and a dressing strong fields. Dipole Rydberg blockade may occur and can be set to depend on the probe and trigger polarizations giving rise to diverse regimes of electromagnetically induced transparency (EIT) with a concomitant small probe and trigger absorption and dispersion. This is shown to be relevant to the implementation of polarization conditional probe and trigger cross nonlinearities in cold Rydberg atoms.
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.
We study the transmission properties of a probe field passing through a sample of NNN-type cold atoms possessing a high Rydberg state. Due to the conditioned dipole blockade of Rydberg excitation, this atomic sample might exhibit a nonlinear optical response in terms of electromagnetically induced transparency (EIT) as manifested by the sensitivity of the transmitted probe intensity and correlation to input probe intensity and correlation. It is of particular interest that the nonlinear EIT response can be opposite (either normal or abnormal) in two different regions of probe detuning, which is a striking feature of the four-level N system of interacting atoms. The realization of both normal and abnormal nonlinear EIT effects in one atomic sample is expected to have wider applications in manipulation of photonic statistics of weak light signals, e.g., to attain prominent photonic bunching and/or antibunching in a dynamic quantum delay or memory process.
We study the optical response of cold rubidium atoms driven into the four-level Y configuration exhibiting two high Rydberg levels in the regime of electromagnetically induced transparency (EIT). Atoms excited to either Rydberg level interact with each other just via self-blockade potentials (I) or also via cross blockade potentials (II). Numerical results show a few interesting quantum phenomena on the transmitted properties of a weak probe field owing to controlled single and double Rydberg blockade. In case (I), it is viable to switch between single-photon outputs with vanishing (invariable) two-photon (three-photon) correlation and photon-pair outputs with vanishing (invariable) three-photon (two-photon) correlation. Such output switch can be easily done by modulating frequencies and intensities of two strong coupling fields to create a degenerate EIT window or two separated EIT windows. In case (II), we find that two-photon and three-photon correlations decrease together at a degenerate EIT window center while increasing together between two separated EIT windows. Such consistent changes are observed because both correlations are modified by the identical polarizability degradation though depending on single and double Rydberg blockade, respectively.
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.
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.