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Journal of the Optical Society of America B

Coupled-pendulum model of the stimulated resonance Raman effect

Philip Hemmer, Mara Goff Prentiss

Published Aug 1, 1988• 63 citations
Publisher

Abstract

A set of three classical coupled pendulums is used to model the stimulated resonance Raman interaction. This model provides a simple, intuitive, physical description of the resonance Raman process and can also be used to interpret experimental observations, including the dynamics of Raman-induced transparency, the physical nature of Ramsey fringes in separated-field excitation, and the effects of off-resonant laser excitation. The model has also been extended to suggest what might be observed for strong laser fields.

DOI
10.1364/josab.5.001613

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A set of three classical coupled pendulums is used to model the stimulated resonance Raman interaction. This model provides a simple, intuitive, physical description of the resonance Raman process and can also be used to interpret experimental observations, including the dynamics of Raman-induced transparency, the physical nature of Ramsey fringes in separated-field excitation, and the effects of off-resonant laser excitation. The model has also been extended to suggest what might be observed for strong laser fields.
In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a \ensuremath{\Lambda} system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.
Precision studies of stimulated-resonance Raman interactions in a sodium atomic beam were performed with emphasis on Ramsey’s separated-field excitation. Ramsey fringes were obtained for a field separation of up to 30 cm, and the data were consistent with theoretical predictions. Possible applications of this Raman interaction to clock development also were studied by stabilizing a microwave oscillator to a Raman–Ramsey fringe. The resulting oscillator stability of 1.5 × 10−11 for a 1000-sec averaging time compares favorably with commercial cesium clocks when differences in atom transit time and transition frequency are taken into consideration. Finally, potential sources of long-term frequency error, which are important for clock applications, were also partially investigated.
We have considered the stimulated Raman spectra arising from interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states ‖3〉 and ‖4〉 and two lower states ‖1〉 and ‖2〉, where the metastable state ‖2〉 is depleted through the action of two strong laser fields operating between the states ‖2〉↔‖4〉 and ‖2〉↔‖3〉, respectively. Using a model Hamiltonian, where all the free and interacting fields are quantized, and the Green function method in the limit of high photon densities of both laser fields, we have studied stimulated two-photon processes near the frequencies ±ω≊ω21≊ω41 −ωa≊ω31 −ωb for the ‖1〉→‖2〉 electric dipole forbidden transition describing physical processes, where one photon of the signal field with frequency ω41(ω31) is absorbed while a photon of the laser field with frequency ωa(ωb) is emitted and vice versa; ωij refers to an atomic transition frequency between the states ‖i〉 and ‖j〉. The spectral function for the stimulated two-photon processes consists of a central peak at the frequency ω=ω21, which has a delta function distribution indicating the stability of the mode in question, and three pairs of sidebands, where one pair of sidebands is induced by each laser field, respectively, while the third pair of sidebands is induced by both laser fields simultaneously. The intensities of the sidebands are always negative indicating that strong amplification (stimulated emission) takes place at the corresponding frequencies. The computed resonance and off-resonance spectra are graphically presented and discussed. When a classical description for both laser fields is used, the spectral function is found to describe one pair of sidebands, which is induced by both laser fields simultaneously; this classical result is graphically presented and compared with those obtained when the fields are quantized. It is shown that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photon fields which is lost in the classical picture. The effect of the quantum nature or, equivalently, the boson character of the photon is to split the ‘‘classical’’ spectrum described by one pair of sidebands into three pairs, whose sum of relative intensities is equal to that of the original pair derived classically.
An analysis is made of some features of spontaneous resonance Raman scattering representing a noise signal which is amplified by a strong field in a nonlinear medium. A detailed review is made of the experimental results obtained in investigations of the spectra of stimulated preresonance and resonance Raman scattering in nonlasing and lasing systems. It is shown that, depending on the experimental conditions, these spectra may be due to transitions between vibrational levels of molecules which are in the ground or first excited electronic states. The example of several compounds is used to demonstrate the information which can be derived from such spectra. Possible practical applications of studies of such spectra are indicated. The physical basis of the theory of stimulated resonance Raman scattering is discussed and conclusions are drawn on the nature and mechanism of this Raman effect.
We have calculated the excitation spectra of a single electron in the excited state of a three-level atom interacting with two off-resonant laser fields at high intensities. We have also considered the process where one laser photon is absorbed by the ground state, as well as a Raman-type process where one photon of one of the laser fields is emitted while another photon of the other laser field is absorbed simultaneously by the second excited state of the atom. The net excitation spectra of the three processes in question consist of two peaks having always positive intensities indicating induced absorption (attenuation) and a third peak which has positive, zero and negative intensities for values of the Rabi frequencies , and , respectively. When , the Raman-type process prevails over the other two, and the resulting peak has a negative intensity indicating that significant amplification is likely to occur at the corresponding frequency.