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arXiv:1012.2247 · Journal of Modern Optics

Cross-phase modulation and population redistribution in a periodic tripod medium

K. Słowik, Andrzej Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, G.C. La Rocca

Published Jun 10, 2011• 3 citations
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Abstract

The cross-Kerr effect is studied for two weak beams, probe and trigger, propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam in a regime of electromagnetically induced transparency. The nonlinear phase shifts for both transmitted and reflected probe beams induced by the trigger's presence are found to depend on the probe detuning, the control beam's intensity, the relaxation rates and, in particular, on the redistribution of the population among the atomic levels. Such a quantitative analysis indicates that the transmitted and reflected probe beam components and their respective phase shifts can be easily controlled and optimized.

DOI
10.1080/09500340.2011.586476

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The cross-Kerr effect is studied for two weak beams, probe and trigger, propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam in a regime of electromagnetically induced transparency. The nonlinear phase shifts for both transmitted and reflected probe beams induced by the trigger's presence are found to depend on the probe detuning, the control beam's intensity, the relaxation rates and, in particular, on the redistribution of the population among the atomic levels. Such a quantitative analysis indicates that the transmitted and reflected probe beam components and their respective phase shifts can be easily controlled and optimized.
The cross-Kerr effect is studied for two pulses propagating in an atomic medium in a tripod configuration, dressed by a strong standing wave coupling beam. Nonlinear phase shifts for both transmitted and reflected beams are calculated taking into account the redistribution of the population among the atomic levels which allows one to study the phase shifts in a wide range of pulse detunings. The influence of other parameters, e.g., the intensity of the control field and the relaxation rates, on the cross-Kerr effect is also examined in detail.
Cross-Kerr nonlinearities are analyzed for two light beams propagating in an atomic medium in the tripod configuration, dressed by a strong standing-wave laser field that induces periodic optical properties. The reflection and transmission spectra as well as the phases of both the reflected and transmitted components of the two beams are analyzed theoretically with nonlinearities up to third order being taken into account. Ranges of parameters are sought in which the cross-Kerr effect can be used as the basis of the phase gate.
In the present paper we consider a simultaneous propagation of two weak pulses (the 'probe' and 'trigger') in the tripod configuration atomic medium, irradiated by a strong quasi-standing control field. The latter leads to a periodic modulation of the refractive index of the medium which now becomes a photonic crystal. While propagating in such a medium both probe and trigger are split into transmitted and reflected components the nonlinear phase shifts of which are of particular interest. We calculate the nonlinear periodic susceptibilities and make numerous simulations of the propagation of the stationary pulses in different conditions. We calculate the phases of the outgoing fields and find the optimal values of parameters characterizing the system, i.e. when the nonlinear phase shifts of both transmitted and reflected probe and trigger components are large. We show a convenient way of controlling the process by shifting the frequency of the incoming probe. We plot the transmission and reflection spectra for different values of parameters of the system, which could be used as a flexible beam splitter, for which the phases and intensities of outgoing beams can be independently changed.
We investigate, both theoretically and experimentally, the cross-Kerr nonlinearity generated in a four-level tripod system in the 87Rb D1 line. The system exhibits simultaneous electromagnetically induced transparency (EIT) windows for two weak (probe and trigger) fields and the enhanced cross-Kerr nonlinearity by EIT. The cross-Kerr nonlinear phase shifts for probe (trigger) field are measured at several different intensities of trigger (probe) field. The results show that large cross-phase modulation (XPM) coefficients can be achieved at low light intensities.
We report experimental observations on the simultaneous electromagnetically induced transparency (EIT) effects for probe and trigger fields (double EIT) as well as the enhanced cross-phase modulation (XPM) between the two fields in a four-level tripod EIT system of the D1 line of 87Rb atoms. The XPM coefficients (larger than 2 x 10(-5) cm2/W) and the accompanying transmissions (higher than 60%) are measured at a slight detuning of the probe field from the exact EIT-resonance condition. The system and enhanced cross-Kerr nonlinearities presented here can be applied to quantum information processes.
We study the interaction of a weak probe field, having two orthogonally polarized components, with an optically dense medium of four-level atoms in a tripod configuration. In the presence of a coherent driving laser, electromagnetically induced transparency is attained in the medium, dramatically enhancing its linear as well as nonlinear dispersion while simultaneously suppressing the probe field absorption. We present the semiclassical and fully quantum analysis of the system. We propose an experimentally feasible setup that can induce large Faraday rotation of the probe field polarization and therefore be used for ultrasensitive optical magnetometry. We then study the Kerr nonlinear coupling between the two components of the probe, demonstrating a novel regime of symmetric, extremely efficient cross-phase modulation, capable of fully entangling two single-photon pulses. This scheme may thus pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding, and teleportation.