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Journal of Physics B Atomic and Molecular Physics

Radiative transitions at the doublet splitting frequency in the resonant Stark effect

Helen S. Freedhoff, Martin E. Smithers

Published Aug 1, 1975• 7 citations
Publisher

Abstract

Preliminary studies have been made of a system which consists of a molecule placed in an intense electromagnetic field resonant with a molecular transition frequency, and a probe field containing frequencies in the neighbourhood of the resulting dynamic Stark splitting frequency 2 epsilon . In these studies, only a single decay process was considered. Both emission and absorption of radiation by the system are predicted at frequencies near 2 epsilon , provided that the molecule has different permanent dipole moments in its lower and its upper states. A correct treatment, which allows for a cascade of emitted photons, is expected to bring about some quantitative changes in the shape of the predicted spectrum, but to leave unchanged the basic prediction of transitions at frequency 2 epsilon .

DOI
10.1088/0022-3700/8/11/002

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Effects Of Permanent Dipoles And Static Fields On Molecular Spectra

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An analytic expression for the absorption spectra of a two-level molecule or atom is derived, within the rotating wave approximation (RWA), which includes the effects of permanent dipole moments and static electric fields. The derivation is for the interaction of the system with a plane-polarized sinusoidal electromagnetic field (EMF) in the semi-classical electric dipole approximation. The RWA resonance profile, and a series of exactly calculated two-level model spectra, are used to investigate some single- and multi-photon spectral effects due to permanent dipoles and static fields, relative to the atomic problem (no permanent dipoles). These effects include the occurrence of even as well as odd photon transitions. Permanent dipole moments can cause narrowing of the resonances, oscillatory fringes around the resonances as a function of frequency, and decreases in the molecule-EMF coupling, relative to the atomic results. Comparisons with exact two-level model spectra are used to study the validity of the RWA results and indicate that several features, such as dynamic backgrounds and shifts of the resonance frequencies from the weak EMF limits of {dollar}\\omega\\sbsp{lcub}\\rm res{rcub}{lcub}\\rm N{rcub}{dollar} = {dollar}\\Delta{dollar}E/N, N = 1,2,3, dots, are missing in the RWA spectra as the coupling increases.;Perturbative corrections to the RWA absorption spectra and the full widths at half maxima for the resonances are derived, neglecting static fields, and used to investigate and explain the effects missing in the RWA; the RWA resonance profile is a zeroth plus first order result obtainable from a time-independent Floquet Hamiltonian secular equation. The usefulness and validity of the perturbative corrections are investigated and it is concluded that these corrections are not useful computationally past second order. However, the corrections are useful in understanding some of the deficiencies of the RWA. These include the shifts of the N-photon resonance positions to low frequency, with respect to {dollar}\\Delta{dollar}E/N, that can occur for molecules with non-zero permanent dipoles; the shift is always to high frequency for atoms. A series of exact model calculations, for "giant dipole" molecules, is also used to discuss the effects of permanent dipole moments on spectra and to establish comparisons with the recent literature on the subject.

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Electromagnetically induced transparency in a molecular gas

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The dynamic Stark effect on the as Q (5,4) transition of the 0 → 1 vibrational band of the ν 2 mode of ammonia 15 NH 3 was studied by the method of copropagating waves of radiation of two 13 CO 2 lasers operating at the R (18) I line. For waves with mutually orthogonal polarizations, which propagated in a waveguide cell, the intensity of the saturating radiation reached 225 W/cm 2 , and the absorption line of the probing radiation had the form of a two-hump curve with a splitting that was consistent with the Rabi frequency for the ammonia transition being investigated. At the maximum intensity of the saturating radiation, complete transparency was observed at the center of the absorption line of 15 NH 3 . When identically polarized saturating and probing waves propagating in a cell at a small angle with respect to each other were used, the splitting was more weakly manifested. The effect of a spatial inhomogeneity of the optical fields on the shape of the line of saturated absorption is discussed.

Optics and Spectroscopy•Jul 1, 2001•8 citations
Preliminary studies have been made of a system which consists of a molecule placed in an intense electromagnetic field resonant with a molecular transition frequency, and a probe field containing frequencies in the neighbourhood of the resulting dynamic Stark splitting frequency 2 epsilon . In these studies, only a single decay process was considered. Both emission and absorption of radiation by the system are predicted at frequencies near 2 epsilon , provided that the molecule has different permanent dipole moments in its lower and its upper states. A correct treatment, which allows for a cascade of emitted photons, is expected to bring about some quantitative changes in the shape of the predicted spectrum, but to leave unchanged the basic prediction of transitions at frequency 2 epsilon .
Studies are made of a system consisting of a molecule interacting with both an intense electromagnetic field resonant with a molecular transition frequency and a weak RF probe field at the Rabi frequency. An earlier study of this system (Freedhoff et al., ibid., vol.8, p.L209 (1975)) is extended to include the effects of photon cascades and of laser detuning. The method of calculation is the dressed-atom description and master-equation approach of Cohen-Tannoudji and Reynaud (1977). Unlike the earlier study, the present treatment produces quantitatively correct expressions for the emission and absorption spectra both in the visible and in the RF regions. More importantly, however, the predicted absorption intensity is greatly enhanced over that in the earlier study, and, for negative detuning of the laser, amplification of the RF signal is predicted.
Calculations based on a full master equation approach have been made of the absorption spectrum for a certain three-level system in which two states mod 2), mod 1) are strongly driven by a near resonant monochromatic laser field whose Rabi frequency is large compared with the natural lifetime width of mod 2). A third state mod 3) is coupled to the nearby state mod 2) by a static electric field. As the static field coupling increases the spectrum in the neighbourhood of the laser frequency changes from the partly emissive, partly absorptive Mollow form to an absorptive spectrum with two strong peaks. Also, the spectrum in the neighbourhood of the upper level transition frequency changes from an Autler-Townes doublet to a spectrum where a new emissive line appears at the Rabi frequency. In terms of the dressed atom model, this transition corresponds to an intradoublet transition previously forbidden in two-level atoms, though predicted to occur in certain two-level molecular systems. The spectrum is interpreted in terms of a dressed atom model. In general terms not only do the dressed atom transition frequencies correlate well with the spectral features, but there is also good agreement between the heights and widths of the spectral features and those obtained from the full master equation approach. The importance of using the full dipole operator in the basic definitions of the spectral quantities is also demonstrated.
The theory of coherent radiation emission in two-level quantum systems with permanent dipole moments at the multiphoton resonant excitation by moderately strong laser fields is presented. A simple analytic formula for the expectation value of a dipole moment operator is obtained. The spectrum corresponding to harmonic generation and low-frequency radiation on the generalized Rabi frequency is investigated both analytically and numerically. The effect of dynamic Stark shift on a dipole spectrum under direct multiphoton resonant excitation is considered.
An analytic expression for the absorption spectra of a two-level molecule or atom is derived, within the rotating wave approximation (RWA), which includes the effects of permanent dipole moments and static electric fields. The derivation is for the interaction of the system with a plane-polarized sinusoidal electromagnetic field (EMF) in the semi-classical electric dipole approximation. The RWA resonance profile, and a series of exactly calculated two-level model spectra, are used to investigate some single- and multi-photon spectral effects due to permanent dipoles and static fields, relative to the atomic problem (no permanent dipoles). These effects include the occurrence of even as well as odd photon transitions. Permanent dipole moments can cause narrowing of the resonances, oscillatory fringes around the resonances as a function of frequency, and decreases in the molecule-EMF coupling, relative to the atomic results. Comparisons with exact two-level model spectra are used to study the validity of the RWA results and indicate that several features, such as dynamic backgrounds and shifts of the resonance frequencies from the weak EMF limits of {dollar}\\omega\\sbsp{lcub}\\rm res{rcub}{lcub}\\rm N{rcub}{dollar} = {dollar}\\Delta{dollar}E/N, N = 1,2,3, dots, are missing in the RWA spectra as the coupling increases.;Perturbative corrections to the RWA absorption spectra and the full widths at half maxima for the resonances are derived, neglecting static fields, and used to investigate and explain the effects missing in the RWA; the RWA resonance profile is a zeroth plus first order result obtainable from a time-independent Floquet Hamiltonian secular equation. The usefulness and validity of the perturbative corrections are investigated and it is concluded that these corrections are not useful computationally past second order. However, the corrections are useful in understanding some of the deficiencies of the RWA. These include the shifts of the N-photon resonance positions to low frequency, with respect to {dollar}\\Delta{dollar}E/N, that can occur for molecules with non-zero permanent dipoles; the shift is always to high frequency for atoms. A series of exact model calculations, for "giant dipole" molecules, is also used to discuss the effects of permanent dipole moments on spectra and to establish comparisons with the recent literature on the subject.
The dynamic Stark effect on the as Q (5,4) transition of the 0 → 1 vibrational band of the ν 2 mode of ammonia 15 NH 3 was studied by the method of copropagating waves of radiation of two 13 CO 2 lasers operating at the R (18) I line. For waves with mutually orthogonal polarizations, which propagated in a waveguide cell, the intensity of the saturating radiation reached 225 W/cm 2 , and the absorption line of the probing radiation had the form of a two-hump curve with a splitting that was consistent with the Rabi frequency for the ammonia transition being investigated. At the maximum intensity of the saturating radiation, complete transparency was observed at the center of the absorption line of 15 NH 3 . When identically polarized saturating and probing waves propagating in a cell at a small angle with respect to each other were used, the splitting was more weakly manifested. The effect of a spatial inhomogeneity of the optical fields on the shape of the line of saturated absorption is discussed.