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Soviet Journal of Quantum Electronics

Two-photon light shift and two-photon Lamb dips

R. Keil, P. E. Toschek

Published Aug 31, 1978• 3 citations
Publisher

Abstract

Light-induced resonance frequency shifts of atoms and molecules under off-resonance conditions are considered. The results are reported of the application of a cross-saturation method to shifts inside a Doppler profile of an atomic helium line. Two-photon Lamb dips are reported and these require perturbation theory calculations up to the fifth approximation.

DOI
10.1070/qe1978v008n08abeh010620

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Light-induced resonance frequency shifts of atoms and molecules under off-resonance conditions are considered. The results are reported of the application of a cross-saturation method to shifts inside a Doppler profile of an atomic helium line. Two-photon Lamb dips are reported and these require perturbation theory calculations up to the fifth approximation.
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A semiclassical theory of two-photon Lamb dips is presented, when one of the radiations is in the radio-frequency region and the other is in the optical region. Perturbation solutions as well as an exact recurrence formula are discussed. For the latter case numerical results are given. The resonance line shape of the two-photon Lamb dip shows a variety of changes according to the experimental conditions. When both the optical and the rf fields are weak a line is of a dispersion form. When the rf field is increased, the line changes to a Lorentzian form. When the optical field is increased, the line is shifted and broadened. If the radio frequency is close to or less than the Doppler width of the gas, a two-photon Lamb dip is accompanied with satellite dips which correspond to molecules with nonzero velocity components along the propagation of the laser radiation. The intensity of a two-photon Lamb dip is expected to decrease rapidly with increasing radio frequency. Additional effects when the sample cell is placed inside the laser cavity are also discussed. Those results agree qualitatively with recent observations by Fruend, R\"omheld, and Oka.
Atomic or molecular energy levels are shifted by a non-resonant electromagnetic irradiation. These so-called "light-shifts" must be carefully taken into account in high resolution spectroscopy experiments since they perturb the atomic Bohr frequencies which one wants to measure or to use as frequency standards. In this paper, we present a brief survey of various types of light-shifts corresponding to different physical situations. We use a dressed atom approach allowing simple physical discussions and simple calculations. Some new suggestions are made.
The profile of a two-photon resonant absorption line of a particle subjected to a standing optical wave is calculated allowing for the quadratic Doppler effect. It is shown that the line profile is governed entirely by the ratio of the homogeneous line width to the quadratic Doppler frequency shift. An exact expression is obtained for the line profile in the second order in ν/c and the main approximations are considered. The profiles are calculated for the 1S-2S and 1S-3S transitions in the hydrogen atom.
We calculate the effect of light-induced forces on the fluorescence line shape of a two-level atom crossing at right angles two counterpropagating light beams of parallel linear polarizations $(\mathrm{lin}\ensuremath{\Vert}\mathrm{lin})$ in a common configuration for ultrahigh-precision optical spectroscopy. For an incident atomic beam with a narrow spread of transverse velocities the dipole force induces a redshift of the fluorescence maximum, while in the reverse case of a wide spread of transverse velocities the radiation-pressure force induces a blueshift of the saturation dip minimum. We then use our theory to explain the blueshift of the saturation line-center dip occurring for the closed transition $2{}^{3}{S}_{1}\ensuremath{\rightarrow}2{}^{3}{P}_{2}$ of a 4He{}^{4}\mathrm{He}4He beam. The observed shift, which is in quite good agreement with the theory, can be of the order of 1/10 of the transition natural linewidth and hence quite important for ultrahigh-precision spectroscopy measurements.
Resonant two-photon absorption is discussed for the case in which the exciting field may be intense enough and near enough to resonance to cause appreciable saturation. A single pair of levels in an otherwise quite general atom is assumed to satisfy the appropriate resonance condition, and equations are derived governing the time evolution of the associated 2 \ifmmode\times\else\texttimes\fi{} 2 submatrix of the full atomic density matrix. Atomic relaxation is treated explicitly. The analysis, which treats both inversion-symmetric and inversion-nonsymmetric cases within the same general formalism, is developed systematically, the necessary approximations receiving careful discussion. The results are analogous to those for the corresponding one-photon process, but with a shift in the resonance frequency proportional to the intensity of the exciting field. This frequency shift is not identical to the one calculated by time-independent (second-order) perturbation theory, and becomes large when the energy of an intermediate state of the atom approaches the mean of the energies of the active states.