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Journal of Physics B Atomic and Molecular Physics

The double optical resonance spectrum for arbitrary pulse shapes

P. Thornton Greenland

Published Feb 14, 1985• 17 citations
Publisher

Abstract

A uniform asymptotic expression for the double optical resonance signal is obtained for arbitrary pulse shapes. The theory, which is applicable for resonant pump pulses with a total envelope area of greater than about 10 pi , predicts a multipeak structure for the double optical resonance spectrum. This is interpreted as arising from interference between probe excitation at two different parts of the pump pulse. Related phenomena have already been observed in similar, exact, calculations for specific pulse shapes.

DOI
10.1088/0022-3700/18/3/016

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Physical Review A•Aug 14, 2009•29 citations
A uniform asymptotic expression for the double optical resonance signal is obtained for arbitrary pulse shapes. The theory, which is applicable for resonant pump pulses with a total envelope area of greater than about 10 pi , predicts a multipeak structure for the double optical resonance spectrum. This is interpreted as arising from interference between probe excitation at two different parts of the pump pulse. Related phenomena have already been observed in similar, exact, calculations for specific pulse shapes.
The theory of optical-microwave double resonance is extended to the case of the off-resonant optical field. Line shapes for fixed optical and variable microwave frequencies are calculated under various conditions by the density matrix method. Analytical expressions are given for small microwave or small optical saturation. When the off-resonance is much greater than the Doppler width of the optical transition, optical Stark effect and optical-microwave two-photon transition are the principal effects. When the signal is observed as a variation of microwave absorption, the former effect is much stronger than the latter. When the signal is detected optically, the two-photon and the stepwise transitions for small microwave saturation are the effects with the same order of magnitude, while the optical Stark effect is a secondary effect. The line shapes are also calculated numerically for arbitrary microwave and optical saturation.
Exact solutions to the problem of a two-level atom interacting with an external field with a sech time profile are used to calculate the optical-double-resonance (ODR) and time-dependent resonance-fluorescence (RF) spectra for various values of the detuning. The probe in the ODR case is assumed to have either a sech or a flat time profile. For small pulse areas the exact ODR expressions obtained are very simple. For large pulse areas the ODR spectra for a flat probe differs markedly from the equivalent spectra for a sech probe, and for any pulse area they both depend strongly on the detuning. As the detuning increases, the extreme peaks on one side increase significantly before eventually decreasing whilst the peaks on the other side decrease rapidly and monotonically. Similar features are found for the RF spectrum, but the dependence on detuning is weaker.
This paper presents a theory of lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe fields using the steady-state solutions for the 3-level density matrix. When Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, each with an angular frequency half-width half maximum equal to the relaxation rates, which are assumed to be equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed to be much larger than the pump and probe Rabi frequencies and the probe frequency is higher than that of the pump, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit width that is proportional to the pump Rabi frequency, which is commonly known as power broadening. However, the width does not equal that Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.
The nonlinear theory of stimulated Raman scattering of high-energy long laser pulses in two-level media is constructed and provides a unified global interpretation of the experiments of Dr\"uhl, Wenzel, and Carlsten [Phys. Rev. Lett. 51, 1171 (1983)]. It is proved that the model, resulting from the slowly varying envelope approximation and including phase mismatch and detuning from Raman resonance, is integrable by the spectral transform method for arbitrary boundary values. The essential variable in the theory is the phase of the Stokes pulse relative to the pump. For long duration input pump pulses and when pump and Stokes pulses experience a rapid \ensuremath{\pi} phase shift, an anomalous spike of pump radiation is created in the pump depletion zone. It is shown in particular that the decay of Raman spikes is related to the velocity of this \ensuremath{\pi} phase shift. For fast flips, the possibility of observing spike overflow is established and, with multiple phase flips, a multiple-spike phenomenon is produced, suggesting new experiments. Lastly, the number of optical phonons participating to the interaction is explicitly calculated.
A theoretical study on double-resonance optical pumping for the transitions $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{3/2,5/2}$ of 87Rb^{87}\text{R}\text{b}87Rb atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.