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Cross-Phase Modulation and Population Redistribution in a Periodic Tripod Medium

Karolina Słowik, Jarosław Zaremba, M. Artoni, G. C. La Rocca

Published Aug 17, 2016• 3 citations
OpenAlex

Abstract

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.

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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.
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.
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 the experimental observations on the simultaneous EIT effects for probe and trigger fields (double EIT) as well as the large 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*10-5cm2/W) and the accompanying transmissions (higher than 60%) are measured at slightly detuning of the probe field from the exact EIT resonance condition. The presented system can be applied in the recently proposed quantum information processing with weak cross-Kerr nonlinearities.
Quantum theory of self-phase and cross-phase modulation of ultrashort light pulses in the Kerr medium is developed, taking into account the response time of an electronic nonlinearity. The corresponding algebra of time-dependent Bose operators is elaborated. It is established that the spectral region of the pulse where the quadrature fluctuation level is lower than the shot-noise one depends on the value of the nonlinear phase shift, the intensity of another pulse and the relaxation time of the nonlinearity. It is shown that the frequency of the pulse spectrum at which the suppression of fluctuations is maximum can be controlled by adjusting the other pulse intensity.