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arXiv:1512.03577 · Physical Review A

Nonlocal nonlinear response of thermal Rydberg atoms and modulational instability in an absorptive nonlinear medium

Lida Zhang, Jörg Evers

Published Sep 1, 2016• 6 citations
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Abstract

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.

DOI
10.1103/physreva.94.033402

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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.
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 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 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.
The thesis is devoted to the theoretical studies of coherent control and manipulation of classical or quantum light via nonlocal effects. At the classical level, controllable light propagation dynamics in the paraxial regime is investigated. The specific type of nonlocal linear effects induced in thermal atomic vapor is explored to achieve diffractionless and lossless propagation, uniform phase modulation, and frequency conversion with diffractionless image duplication for laser beams with arbitrarily encoded spatial profiles. Next, the study is extended to investigate propagation dynamics in the presence of nonlocal nonlinear effects generated in thermal interacting Rydberg atoms, which mainly reveals simultaneous competition between the nonlocal nonlinear absorption and the modulational instability for each wave component. Moreover, parity-time (PT) symmetric dynamics in cold Rydberg atoms are exploited, and it is shown that a phase transition from unbroken to broken PT symmetry can be induced by nonlocal nonlinear effects. At the quantum level, it is further proposed to test the quantum nonlocality of single x-ray photons in a system where very weak x-ray pulses interact with 57Fe nuclei in a thin cavity, such that a Bell-like inequality in the single-photon version is violated. All these proposals are feasible in current experimental settings.
XXX waves are a special type of wave packet that can maintain their transverse profile of XXX shape during propagation, and they are of much interest for the study of fundamental physics and practical applications. Here we present a scheme to generate nonlinear XXX waves and realize their active control by using a cold gas of Rydberg atoms via electromagnetically induced transparency (EIT). We show that, due to the EIT effect contributed by a control laser field and the strong, nonlocal Kerr nonlinearity contributed by Rydberg-Rydberg interaction between atoms, the system supports high-dimensional, nonlocal, and nonlinear optical XXX waves, which have low propagation loss, ultraslow propagation velocity, and ultralow generation power. We also show that the stability domain of such XXX waves can be greatly enlarged by increasing the nonlocality degree of the Kerr nonlinearity, and their motion trajectory can be manipulated by using an external magnetic field. Our study opens a route for generating and controlling nonlocal ultraslow nonlinear optical XXX waves, which may have promising applications in optical information processing and transmission.
Dispersive shock waves (DSWs) are fascinating wave phenomena occurring in media when nonlinearity overwhelms dispersion (or diffraction). Creating DSWs with low generation power and realizing their active controls is desirable but remains a longstanding challenge. Here, we propose a scheme to generate weak-light DSWs and realize their manipulations in an atomic gas involving strongly interacting Rydberg states under the condition of electromagnetically induced transparency. We show that for a two-dimensional Rydberg gas, weak nonlocality of optical Kerr nonlinearity can significantly change and induce a singular behavior of the edge speed and hence an instability of the DSWs, which, however, can be suppressed by increasing the degree of the Kerr nonlocality. We also show that in a three-dimensional Rydberg gas, DSWs can be created and propagate stably when the system works in the intermediate nonlocality regime. Different from the DSWs reported before, the DSWs found here have extremely low generation power. Moreover, such DSWs can be actively controlled; in particular, they can be stored and retrieved with high efficiency and fidelity through switching off and on a control laser field. The results reported here are useful not only for unveiling intriguing physics of DSWs but also for finding promising applications of nonlinear and nonlocal Rydberg media.