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Journal of Experimental and Theoretical Physics

Influence of a polar ambient medium on multiphoton resonances in dipole molecules

Viktor A Kovarskii, O. B. Prepelitsa

Published Jan 1, 2000• 0 citations
Publisher

Abstract

The influence of fluctuations of a polar ambient medium on multiphoton resonances in dipole molecules interacting with an external electromagnetic field is studied. It is shown that the electric fields created by the fluctuating dipole moments of the medium strongly influence the fulfillment of the multiphoton resonance conditions. Cases of slow and fast fluctuations of the polar ambient medium are considered separately. It is established that the temperature dependence of the multiphoton resonance probability is non-Arrhenius because of the influence of the fluctuations on the profile of the potential barrier. For fast fluctuations it is predicted that the rate of the multiphoton transition will decrease as the intensity of the fluctuations of the polar ambient medium increases.

DOI
10.1134/1.559090

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The influence of fluctuations of a polar ambient medium on multiphoton resonances in dipole molecules interacting with an external electromagnetic field is studied. It is shown that the electric fields created by the fluctuating dipole moments of the medium strongly influence the fulfillment of the multiphoton resonance conditions. Cases of slow and fast fluctuations of the polar ambient medium are considered separately. It is established that the temperature dependence of the multiphoton resonance probability is non-Arrhenius because of the influence of the fluctuations on the profile of the potential barrier. For fast fluctuations it is predicted that the rate of the multiphoton transition will decrease as the intensity of the fluctuations of the polar ambient medium increases.
An interaction of an atomic/molecular medium with two strong electric fields E L (t) and E M (t) is investigated. The frequency omega L of the first (laser) field E L (t) is close to a transition frequency omega 21 between an upper (2) and a lower (1) atomic levels while the second field E M (t) is of a much lower frequency omega M << omega 21 . The medium is a dipole gas characterized by a nonzero averaged value of electric dipole moment in the states 1 and/or 2. As analytical solution of equations for the density matrix of a dipole atom/molecule interacting with the fields E L (t) and E M (t) is found using the second approximation of the averaging method by Krylov-Bogoliubov-Mitropolskii. The solution obtained is valid in a much broader range of field strengths than an analogous solution that could have been found by the usual time-dependent perturbation theory. Using the solution obtained for the density matrix, polarization of a dipole gas interacting with the fields E L (t) and E M (t) is analytically calculated. This analytical expression for polarization of such media can be utilized for study of various nonlinear optical phenomena. One of the phenomena is a generation of waves at frequencies omega L +or-p omega M and (p+1) omega M (where p=1,2,3,...) in a dipole gas. Another phenomenon is an amplification of the incident wave of the lower frequency omega M due to a stimulated scattering in a dipole gas.
Degenerate four-wave-mixing phase conjugation is analyzed in the case of two-photon transitions between levels having unequal dipole moments. The theoretical treatment is based upon a nonperturbative solution of the density matrix and does not require the rotating-wave approximation. We give an analytical expression for the polarization component oscillating at the field frequency for a medium excited by stationary waves. In the weak-probe-beam limit, the contributions in the direction of the probe and conjugated beams are evaluated. For instance, by using this two-photon process, instead of the usual single-photon one which is independent of the permanent dipole moments even in the strong-field limit, it is shown that lower intensities are sufficient to reach higher reflectivities. The influences of the permanent dipole moments, relaxation rates, and field frequency are also discussed.
The interaction of two continuous wave electric fields (lasers) with a two-level molecule, that has a nonzero difference d, between the permanent dipoles of the two states involved in a multiphoton two-color transition, is studied in the rotating wave approximation and by using exact methods. Analytical rotating wave approximation results for the time-dependent populations of the molecular states and for the resonance profiles are derived and used to help discuss the effects of permanent dipole moments in the two-color absorption problem. Several examples of multiphoton, two-color, two-level resonance profiles calculated in the rotating wave approximation and by using exact techniques, are employed for illustrative purposes. They are used to help quantify the conditions for the validity of the two-color rotating wave approximation, which are considerably more restrictive than the analogous conditions for the one-color rotating wave approximation with d≠0, and to illustrate the interpretive and predictive nature of the rotating wave approximation results. For example, there are many multiphoton, two-color transitions that are available if a molecule possesses permanent dipoles (d≠0). The analytic rotating wave approximation expression for the molecule-two laser coupling can often be used to reliably estimate the field parameters of the two lasers that are required to optimize a given transition relative to others.
We investigate the influence of different electric moments on the shift and dephasing of molecules in a matter wave interferometer. Firstly, we provide a quantitative comparison of two molecules that are non-polar yet polarizable in their thermal ground state and that differ in their stiffness and response to thermal excitations . While C 25 H 20 is rather rigid, its larger derivative C 49 H 16 F 52 is additionally equipped with floppy side chains and vibrationally activated dipole moment variations. Secondly, we elucidate the role of a permanent electric dipole moment by contrasting the quantum interference pattern of a (nearly) non-polar and a polar porphyrin derivative. We find that a high molecular polarizability and even sizeable dipole moment fluctuations are still well compatible with high-contrast quantum interference fringes. The presence of permanent electric dipole moments, however, can lead to a dephasing and rapid degradation of the quantum fringe pattern already at moderate electric fields. This finding is of high relevance for coherence experiments with large organic molecules, which are generally equipped with strong electric moments.
A rotating-wave approximation (RWA) for the single-photon and multiphoton resonance profiles for a two-level molecule interacting with both sinusoidal and static electric fields is derived. Included is a useful expression for the coupling between the molecule and the applied sinusoidal field which exhibits the effects of both diagonal dipole matrix elements (permanent dipole moments) and the applied static electric field. Comparisons of the RWA results with exact two-level calculations provide qualitative information concerning the validity of the RWA as a function of molecular and field parameters. These examples are also used to illustrate the interpretive nature of the RWA results for the resonance profiles and some of the effects of permanent dipoles and static fields on the profiles. Of particular interest are examples involving Boltzmann rotationally averaged spectra as a function of temperature where it is shown that minima in the spectra occurring for high temperatures can be reduced or removed completely if the temperature or applied static field is reduced.
It has been shown that nonlinear near-field optical resonances occur in diatomic nanostructures consisting of identical or different two-level atoms in the presence of a radiation field when the dipole-dipole interaction is taken into account. The frequencies of these resonances depend strongly on the intensity of the external optical radiation, on the initial conditions, on the polarization of the external field with respect to the axis of the nanostructure, and on the interatomic distance. The interatomic interaction is taken into account beyond perturbation theory. For this reason, the effective polarizabilities of the atoms of the nanostructure are expressed in terms of the polynomials of both the interatomic distance and the electric field strength of the external optical wave. A “falling tower” effect that is caused by the nonlinear behavior of the local dipole moments of atoms in the nanostructure is predicted.