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Physical Review A

Multiphoton Raman resonances in three-level Λ atoms in two bichromatic fields

Hartmut Wallis

Published Aug 1, 1995• 11 citations
Publisher

Abstract

A subharmonic resonance occurs on irradiation of a three-level (\ensuremath{\Lambda}) system by two bichromatic fields when an integer multiple of the common frequency difference matches the Raman detuning between the two lower levels. The occurrence of these multiphoton resonances requires saturation of the Raman transition. The three-level model is applied in order to understand recent experimental studies of subharmonic Raman resonances between vibrational states of optically trapped atoms. I explain the difference between these resonances and the well-known velocity-tuned (Doppleron) resonances in two-level atoms by considering a two-state model with the excited state eliminated. I finally point out a Sisyphus cooling mechanism that is entirely dependent on an additional relaxation of the Raman coherence, comparable to collision-induced resonances.

DOI
10.1103/physreva.52.1441

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A subharmonic resonance occurs on irradiation of a three-level (\ensuremath{\Lambda}) system by two bichromatic fields when an integer multiple of the common frequency difference matches the Raman detuning between the two lower levels. The occurrence of these multiphoton resonances requires saturation of the Raman transition. The three-level model is applied in order to understand recent experimental studies of subharmonic Raman resonances between vibrational states of optically trapped atoms. I explain the difference between these resonances and the well-known velocity-tuned (Doppleron) resonances in two-level atoms by considering a two-state model with the excited state eliminated. I finally point out a Sisyphus cooling mechanism that is entirely dependent on an additional relaxation of the Raman coherence, comparable to collision-induced resonances.
We report a 1D study of optical forces on atoms in a two-frequency laser field. The light couples two ground state hyperfine structure levels to a common excited state of 85Rb^{85}\mathrm{Rb}85Rb, thus forming a \ensuremath{\Lambda} system. We observe a new type of sub-Doppler coupling with blue-tuned light that uses neither polarization gradients nor magnetic fields, efficient heating with red tuning, and the spatial phase dependence of these. We observed deflection from a rectified dipole force and determined its velocity dependence and capture range. We report velocity selective resonances associated with Raman transitions. A simplified semiclassical calculation agrees qualitatively with our measurements.
We study the behavior of a two-level atom that is driven by a bichromatic field consisting of a strong resonant component and a weaker tunable component. In addition to the splitting of the energy levels (the multiphoton AC Stark effect), we find that the weaker component also shifts the subharmonic resonances, an effect we attribute to a dynamic Stark shift. When the weaker component is tuned to a shifted resonance, no fluorescence occurs at either the frequency of the strong component or the three-photon mixing frequency. Results are obtained with numerical techniques and explained in terms of the dressed-atom model of the system.
The author considers the stimulated emission process that occurs at the difference-frequency generation of a bichromatic field interacting with a three-level atom in the Lambda configuration. In the low-intensity limit of both laser fields and at finite detunings, there are two induced excitations whose lifetimes are much longer in comparison to those of excitations spontaneously emitted by the excited states of the atom. Conditions are established under which the two-photon stimulated emission prevails, indicating that significant amplification is likely to occur at the difference-frequency generation.
We have calculated numerically the excitation spectra arising from the interaction of a two-level atom with two strong electromagnetic fields. In the limit of high photon densities, the excitation spectra are considered when one of two laser fields is at resonance while the frequency of the other laser field is varied as well as when both laser fields are off resonance. At resonance, the spectra consist of a central peak and several sidebands peaked at the frequencies ω = ω a ± m(ω a - ω b ), corresponding to the multi-frequency mixing of both laser fields where m is a positive integer. Sidebands also appear at fractional multiples of frequencies and are due to contributions arising from energy shifts induced by the laser fields. The computed spectra at resonance are discussed and compared with the observed ones. The off-resonance spectra are computed for a wide range of values of Rabi frequencies and detunings, and are presented graphically. It is found that in the off-resonance case, mixing of a larger number of light frequencies occurs from that in the resonance case. The intensity of the peaks in the off-resonance case are immensely enhanced in comparison with those at resonance. The enhancement of the intensities is in agreement with the observed ones and its occurrence is theoretically explained. It is shown that if the detunings are properly chosen then the desired peak describing the required mixing of frequencies of the laser fields can be immensely enhanced. The method may be useful to investigate multi-frequency resonances of the rotation or rotation-vibration spectra of excited states or excited states near their ionization continua.
We present a general theoretical description of laser cooling of three-level atoms in a Λ configuration in two standing waves. Detunings, intensity, and spatial phase difference of the two waves are arbitrary. We demonstrate that, for a zero spatial phase shift, sub-Doppler cooling requires equal detunings. The basic mechanism is then coherent population trapping. For different detunings sub-Doppler cooling occurs only when the spatial phases of the two standing waves are different. This effect can be traced back to a mechanism of the Sisyphus type. These schemes of sub-Doppler cooling require neither polarization gradients nor magnetic fields.