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International Laser Science Conference

Intensity dependence of the polarization tensor in a quantum treatment

N. Chencinski, Andrei N. Weiszmann

Published Jan 1, 1986• 0 citations
Publisher

Abstract

Recently one of the authors published a paper concerning the exact quantum mechanical description of pressure-induced four-wave mixing in which the exact expression of the transition probability was found.1 In this approach, a formal solution for the problem of multifield interacting with a single multilevel atom is presented by treating the fields fully quantized and the states in a dressed atomic picture. If we think of the four-wave mixing experiments as a case where the ω a , ω b , and ω c waves are sent into the medium with the fourth wave at ω p generated by the mixing, the output amplitude should be proportional to the component of the polarization fluctuating at the frequency of ω p . Based on these results, we obtained an exact quantum mechanical expression for the polarization tensor. This paper intends to explore the photon number (intensity) dependence of the polarization tensor (susceptibility) and give a comparison of the line shapes for low and high intensity of the incoming three beams. Specifically, the corresponding terms for the 31st, 32nd and 33rd terms in the Bloembergen classical expression for the susceptibility tensor will be investigated in detail.2 For no dissipation we will plot and analyze the amplitude of the polarization component at ω p .

DOI
10.1364/ils.1986.thl16

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Recently one of the authors published a paper concerning the exact quantum mechanical description of pressure-induced four-wave mixing in which the exact expression of the transition probability was found.1 In this approach, a formal solution for the problem of multifield interacting with a single multilevel atom is presented by treating the fields fully quantized and the states in a dressed atomic picture. If we think of the four-wave mixing experiments as a case where the ω a , ω b , and ω c waves are sent into the medium with the fourth wave at ω p generated by the mixing, the output amplitude should be proportional to the component of the polarization fluctuating at the frequency of ω p . Based on these results, we obtained an exact quantum mechanical expression for the polarization tensor. This paper intends to explore the photon number (intensity) dependence of the polarization tensor (susceptibility) and give a comparison of the line shapes for low and high intensity of the incoming three beams. Specifically, the corresponding terms for the 31st, 32nd and 33rd terms in the Bloembergen classical expression for the susceptibility tensor will be investigated in detail.2 For no dissipation we will plot and analyze the amplitude of the polarization component at ω p .
It is shown that in order to obtain a correct interpretation of experiments on four-photon nonlinear spectroscopy within the absorption line, it is necessary to allow not only for a coherent four-photon process due to a resonant electronic nonlinearity but also for a similar process involving generation of optically induced diffraction gratings followed by the diffraction of one of the probe beams from these gratings. It is also necessary to allow for the contribution of highly excited molecular states to the resonant electronic nonlinearity. General expressions are derived and investigated for the cubic susceptibility in an isotropic medium. It is found that all nonzero components of this tensor may be expressed in terms of a single scalar function of the interacting wave frequencies. The explicit form of this function is determined in the lowest order of perturbation theory.
The four-wave mixing susceptibility χ(3)(ω1, ω1, -ω2) of a system of two-level atoms driven by weak external fields of frequencies ω1 and ω2 in a high-Q cavity is evaluated in the presence of atomic collisions. That susceptibility exhibits resonances corresponding to dipole-allowed transitions between the first two excited manifolds of the dressed states and the ground state and also the collision-induced Bloembergen resonances. The resonances corresponding to transitions between the first two manifolds of excited states that characterize the quantum and nonlinear nature of the atom–field interaction are, however, flattened in the absence of collisions. The collisions thus induce the quantum effects in four-wave mixing in a high-Q cavity.
Polarization properties of pure four-wave mixing (FWM) and dressed-FWM processes in a two-level system and a cascade three-level atomic system are theoretically and experimentally investigated. The relative intensities and polarization characteristics of the FWM signals in different laser polarization configurations and different level systems are experimentally investigated and compared. Also, the results are theoretically explained by different transition paths combinations. In the dressed-FWM processes, we study the dependence of dressing effect on the incident field's polarization. The FWM signal generated by a linearly polarized pumping field is suppressed more by the dressing field than the one generated by a circularly polarized pumping field. However, an opposite effect was observed when the probe field's polarization is changed. The multidressing mechanisms are used to explain these effects. In addition, the interference and polarization dependence of the coexisting FWM signals in the same atomic system are discussed.
The spectrum of light emitted by a single atom in a thermal bath interacting with three electromagnetic fields is calculated using the dressed-atom picture. The emission spectrum consists of an elastic Raman-like component and dephasing-induced redistribution components that are inelastic in nature. In contrast to coherent four-wave mixing [as given by chi((3))], in which a pressure-induced elastic component (PIER 4) has been predicted and observed, the single-atom response does not contain any elastic pressure-induced components. We derive explicit expressions for the single atom and for the PIER 4 spectra that are not restricted to the impact limit.
In this paper, we continue our development of the quantum theory of nondegenerate multiwave mixing in an atomic medium [Phys. Rev. A 37, 2017 (1988)]. In our development, the atomic variables are eliminated using a frequency-domain approach employing a slowly varying amplitude approximation that is more rigorous than the usual adiabatic approximation. We then specialize to the case of four-wave interaction with two strong pump beams and obtain noise correlations of the atomic polarization that are applicable to nondegenerate four-wave mixing. The noise correlations include the effect of atomic collisions that is crucial to the atomic-vapor experiments. After making the usual rotating-wave approximation, the atomic-polarization equations give us a set of temporal coupled-mode equations for the c-number variables corresponding to the annihilation operators. We then further specialize to the single-beam case in which all the relevant modes of interest are collinear and obtain a paired set of coupled-mode equations. In order to apply the theory to experiments employing traveling-wave interaction geometries, in the following paper of this series we will present a formalism to treat the spatial propagation of a quantum field.