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arXiv:1106.2001 · Physical Review Letters

Nonlocal Nonlinear Optics in Cold Rydberg Gases

S. Sevinçli, Nils Henkel, Cenap Ates, Thomas Pohl

Published Oct 3, 2011• 206 citations
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Abstract

We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulas for the third-order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with the enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modulational instabilities in a self-defocusing medium.

DOI
10.1103/physrevlett.107.153001

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We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulas for the third-order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with the enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modulational instabilities in a self-defocusing medium.
Abstract Rydberg atoms, characterized by their giant polarizability and strong long-range interactions, provide an ideal platform for exploring optical nonlinearities. By coupling light to ensembles of Rydberg atoms, one can map the strong and nonlocal interactions between Rydberg atoms and light fields. A particularly important scheme for realizing such nonlinearity is electromagnetically induced transparency (EIT). This article presents a review of the research progress in nonlinear optics based on Rydberg-EIT systems, particularly nonlinear light propagation in Rydberg atomic gases. We first introduce the fundamental properties of Rydberg atoms and the physical mechanism of EIT-enhanced nonlinearity, emphasizing how the Rydberg blockade effect endows the system with a giant nonlocal Kerr nonlinearity. Subsequently, we discuss some typical nonlinear optical phenomena in such a system with focusing and defocusing nonlocal nonlinearities. In the focusing regime, we discuss spatial solitons, vortex solitons, soliton cloning, soliton molecules, optical bullets, and self-induced transparency solitons. Other topics are also discussed. In the defocusing regime, we analyze pattern formation and shock wave dynamics. Finally, we provide an outlook on the future development of this field toward quantum control, hybrid-system integration, and novel functional devices.
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.
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.
We develop an efficient Monte Carlo approach to describe the optical response of cold three-level atoms in the presence of electromagnetically induced transparency (EIT) and strong atomic interactions. In particular, we consider a Rydberg-EIT medium where one involved level is subject to large shifts due to strong van der Waals interactions with surrounding Rydberg atoms. Agreement with much more involved quantum calculations is excellent, demonstrating its applicability over a wide range of densities and interaction strengths. The calculations show that nonlinear absorption due to Rydberg-Rydberg atom interactions exhibits universal behavior.
We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.
Nonlinear and nonlocal effects are discussed in the interaction of laser fields with thermal Rydberg atoms in an electromagnetically induced transparency configuration. We assume that the system's steady state adiabatically follows the time variation in the dipole-dipole interactions due to the atomic motion and use a continuum description for the atomic medium. Based on these approximations, we obtain an analytical form for the nonlocal nonlinear atomic response of the thermal medium and study it for different parameter cases. We further propose a generalized model to describe the modulational instability (MI) in absorptive nonlinear media, in order to understand the propagation dynamics in the thermal Rydberg medium. Interestingly, this model predicts that at short propagation distances, each wave component exhibits the MI effect in absorptive nonlinear media, unlike in the purely dispersive case.