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Physica Scripta

Electromagnetically induced transparency for Λ-like systems with a structured continuum and broad-band coupling laser

Quoc Khoa Doan, Van Cao Long, W. Leoński

Published Feb 1, 2012• 8 citations
Publisher

Abstract

In this paper, electric susceptibility of a laser-dressed atomic medium is calculated for a model Λ-like system which includes two lower states and a structured continuum. It is assumed that the laser control field applied in the experiment of electromagnetically induced transparency can be decomposed into two parts: a deterministic (coherent) part and a randomly fluctuating chaotic component (white noise). The exact formulae determining the dispersion and absorption spectra of the medium susceptibility are derived by solving a set of coupled stochastic integro-differential equations. The results show that the position and width of the transparency window change dramatically in comparison with the case when the noise of the control laser is absent.

DOI
10.1088/0031-8949/2012/t147/014008

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Physical Review A•Sep 1, 1997•18 citations
In this paper, electric susceptibility of a laser-dressed atomic medium is calculated for a model Λ-like system which includes two lower states and a structured continuum. It is assumed that the laser control field applied in the experiment of electromagnetically induced transparency can be decomposed into two parts: a deterministic (coherent) part and a randomly fluctuating chaotic component (white noise). The exact formulae determining the dispersion and absorption spectra of the medium susceptibility are derived by solving a set of coupled stochastic integro-differential equations. The results show that the position and width of the transparency window change dramatically in comparison with the case when the noise of the control laser is absent.
We discuss the electromagnetically induced transparency (EIT) phenomenon for a model in which a structured continuum is described by a so-called double Fano structure; instead of one autoionizing (AI) state, two such states are embedded in a flat continuum. Such a Fano structure is the upper level of a Λ-like three-level system and is coupled to two lower ones by an external laser field involving δ-correlated, Gaussian, Markov process (white noise), simulating realistic conditions of the experiment. For such a system we derived and solved a set of coupled stochastic integrodifferential equations in the stationary regime, obtaining exact formulas determining the electric susceptibility of the system. Dispersion and absorption spectra of the medium susceptibility were calculated and compared with those already discussed in the literature. We have shown that the presence of an additional AI level considerably changes the structure of transparency windows and how noisy excitation influences the EIT processes.
A Λ-like model of atomic levels involving two auto-ionizing states is considered. The levels are irradiated by two external electromagnetic fields, a strong driving and a weak probing ones. The analytical formula for medium susceptibility shows an additional electromagnetically induced transparency window caused by the second auto-ionizing level. Characteristics of both transparency windows are analyzed depending on parameters of auto-ionizing levels and the external driving field. Manipulation of these characteristics seems to be very effective because of their large sensitivity with respect to the parameters involved in the problem. This manipulation becomes even more feasible when considered model is implemented in so-called laser-induced continuum structure.
Using density matrix eqution, the absorption and dispersion properties of a A-type four-level system driven by coherent fields are investigated. The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state, three, double or single electromagnetically induced transparency (EIT) can appear explicitly in this system. And the explanations of these phenomena are given by using the dressed states. In the three EIT, the location of transparent windows can be manipulated by controlling the detuning of the driving field. What's more, it is also found that the medium shows a large refractive index at each transparency window, and the group velocity of the probe laser can be enhanced.
Summary form only given. The destructive quantum interference of resonantly excited transitions within a lambda-system in case of two photon resonance leads to a medium, which is coherently prepared in a superpositional dark state. The corresponding distinct enhancement of radiation transmission is well known as electromagnetically induced transparency. Interaction of quantized fields with such a medium yields a correlation of quantum phase fluctuations of the fields even for independent cw lasers. The experiments are done on the Na D/sub 1/ line by means of a temperature stabilized sodium vapor cell. One frequency component is modulated by a broad spectrum of phase fluctuations of about 50 MHz width by means of an electrooptical phase modulator driven by a noise generator. A transfer of noise to the other frequency components within a lambda- or a closed double-lambda transition scheme during transmission through the dark state medium is observed using the heterodyne spectroscopy. The verified exponential decay of the width of the beat signal in dependence on the medium optical density proofs the noise transfer and hence the correlation of phase fluctuations between the corresponding frequency components. This behaviour as well as the different limits of decay for lambda- (towards the transparency linewidth) and closed double-lambda (towards zero) scheme is in good qualitative agreement with the theory.
Summary form only given. The destructive quantum interference of resonantly excited transitions within a lambda-system in case of two photon resonance leads to a medium, which is coherently prepared in a superpositional dark state. The corresponding distinct enhancement of radiation transmission is well known as electromagnetically induced transparency. Interaction of quantized fields with such a medium yields a correlation of quantum phase fluctuations of the fields even for independent cw lasers. The experiments are done on the Na D/sub 1/ line by means of a temperature stabilized sodium vapor cell. One frequency component is modulated by a broad spectrum of phase fluctuations of about 50 MHz width by means of an electrooptical phase modulator driven by a noise generator. A transfer of noise to the other frequency components within a lambda- or a closed double-lambda transition scheme during transmission through the dark state medium is observed using the heterodyne spectroscopy. The verified exponential decay of the width of the beat signal in dependence on the medium optical density proofs the noise transfer and hence the correlation of phase fluctuations between the corresponding frequency components. This behaviour as well as the different limits of decay for lambda- (towards the transparency linewidth) and closed double-lambda (towards zero) scheme is in good qualitative agreement with the theory.
This paper deals with electromagnetically induced transparency (EIT), i.e., a significant suppression of absorption at a material transition (in the form of a dip in an absorption spectrum), due to a strong laser field, coupling the excited level with an auxiliary excited (unpopulated) level. A comprehensive theory of EIT is developed for the cases of coherent and Markovian phase- and amplitude-phase-fluctuating coupling fields. For a coherent coupling field, a shift of the absorption minimum from the two-photon resonance is revealed in the off-resonance case. Two models of amplitude-phase fluctuating fields are considered: the chaotic field and the uncorrelated-jump field. Closed analytical expressions for EIT line shape are derived and exact limits of different regimes of EIT are obtained, the emphasis being on the near-resonance case. The main conclusion is that an amplitude-phase-fluctuating field can induce significant transparency, though reduced in comparison to a phase-fluctuating field of the same average intensity and bandwidth. EIT decreases with the increase of the bandwidth for all stochastic models considered. EIT with a chaotic field is generally less pronounced than EIT with an uncorrelated-jump field of the same intensity and bandwidth, the difference increasing with the field intensity. The possibility of experimental verification of the results obtained is discussed.