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arXiv:physics/0604135 · Journal of Physics B Atomic Molecular and Optical Physics

Tuneable nonlinearity in atomic response to a bichromatic field

Ashok Vudayagiri, Surya P. Tewari

Published Sep 12, 2006• 4 citations
arXivHTMLPDF

Abstract

An atomic response to a probe beam can be tailored by creating coherences between atomic levels with the help of another beam. Changing parameters of the control beam will change the nature of coherences and hence the nature of the atomic response as well. Such a change can depend upon intensities of both probe and control beams in a nonlinear fashion. We present a situation where this nonlinearity in dependence can be precisely controlled, to obtain different variations as desired. We also present a detailed analysis of how this nonlinear dependence arises and show that this is an interesting effect of several coherent population trap states that exist and a competition among them to trap the atomic population.

DOI
10.1088/0953-4075/39/18/021

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An atomic response to a probe beam can be tailored by creating coherences between atomic levels with the help of another beam. Changing parameters of the control beam will change the nature of coherences and hence the nature of the atomic response as well. Such a change can depend upon intensities of both probe and control beams in a nonlinear fashion. We present a situation where this nonlinearity in dependence can be precisely controlled, to obtain different variations as desired. We also present a detailed analysis of how this nonlinear dependence arises and show that this is an interesting effect of several coherent population trap states that exist and a competition among them to trap the atomic population.
We present a theoretical description of the interaction of optical waves due to the resonant nonlinear response of an atomic system. We emphasize how the resonant nature of the nonlinear coupling is modified by the shifting of the atomic energy levels as a consequence of the dynamic Stark effect and show the equivalent role played by population pulsations in determining the nature of the nonlinear coupling. A general formalism is developed to treat these effects and is explicitly applied to several examples of current interest, including single-beam saturation spectroscopy, pump–probe saturation spectroscopy, modulation spectroscopy, degenerate four-wave mixing for phase conjugation, and instabilities in the beam propagation through resonant media.
In a three-level closed Λ system with incoherent pumping, both the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role in inducing different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). These two coherences can interfere destructively and constructively giving rise to different nonlinear processes (EIT, EIA, AWI) when the strength of these two coherences is comparable. Therefore the system can switch over from one nonlinear process to the other and the desired response of the system can be achieved by controlling the system parameters. It has been shown that this switching can occur by changing the relative strength of Rabi frequencies for the coherent and probe fields and the mode of incoherent pumping (unidirectional and bidirectional) for a chosen SGC parameter. Further control over the response can be achieved by changing the phase between two radiation fields. But the dependence on phase is different when both the coherences contribute than that obtained only from SGC. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis and any restrictions over the system parameters (e.g. spontaneous decay widths on probe and coherent transitions are equal) have been avoided to make it applicable to various atomic and molecular systems. However the approximate expressions can be derived from these exact values. Numerical values obtained by solving the density matrix equations agreed well with these exact analytical values.
Refractive index and absorption experienced by a probe field propagating through a three-level atomic medium can be effectively manipulated by the bistable behavior of a control field. The probe field couples the lower transition of the atom in a ladder configuration and experiences normal or anomalous dispersion depending on the control field being in the upper or lower bistable state, respectively. We also obtain nonlinear dynamical instability in the form of periodic self-pulsing as the lower bistable branch becomes unstable, quite unlike earlier demonstrations of an unstable regime in the upper branch. Consequently, the susceptibility experienced by the probe field varies periodically in time as dictated by the control field self-pulsing.
This paper examines spatially dependent absorption and gain of a weak probe field in a 3-level atomic Λ-system with spontaneously generated coherence and incoherent pump, using an optical vortex beam as the control field. The inhomogeneous phase distribution between the probe and vortex fields modulates the transverse distribution of the system's optical response. A flexible control over the azimuthal modulation in the transverse plane can be achieved by changing such parameters as the orbital angular momentum and the optical transition detuning. The vortex parameters can also be used to affect the population distribution of the atomic system's upper state. This method for achieving precise control over the optical response characteristics contributes to advances in optical information and communication, quantum devices and sensing.
The control of the optical properties of a medium by atomic coherence and quantum interference effects is an important area of research, not only for its fundamental aspects in the understanding of radiation and matter interaction, but also for its potential applications in the design of optical devices. Atomic coherence can emerge in a medium through the coupling of a strong coherent field to an atomic transition. This coupling affects the optical properties of the medium in a very interesting ways. For example, it may yield light amplification without population inversion. Also, it can modify the traditional dispersion of an optical medium in such a way that maximum variations of the refractive index occur around a spectral region of vanishing absorption. In the first part of this work we investigate some fundamental aspects of this coherent dynamics. We investigate how this non-inversion gain is affected by the presence of atomic motion. The coherent interaction between atom and radiation can lead to the interference between optical paths of decay. We report on an atomic setting where the interference structures depend upon the phase of the coherent field, an new effect which is absent in other resonance fluorescent phenomena. As a potential application, we investigate a novel approach for the modulation of optical signal. This approach consists of injecting atomic coherence in the medium in order to tailor its optical properties so it is a more suitable medium for modulation.