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Japanese Journal of Applied Physics

Lineshapes in Three-Level Spectroscopy with an Intense Laser Field

Motowo Tsukakoshi, Kōichi Shimoda

Published Apr 1, 1980• 6 citations
Publisher

Abstract

Effects of an intense saturating radiation on a probe lineshape under Doppler broadening are studied in a three-level system when the frequency of the probe light is higher than that of the saturating light. The problem is analysed in the approximation of weak probe field using an ensemble averaged density matrix. An analytical form of the lineshape is obtained for the resonant saturating field of high intensity at which the Rabi nutation frequency is larger than the Doppler width of the probe transition. The linewidth of probe absorption depends on the Doppler width and the frequency ratio of the probe light to the saturating light. The computer calculation is carried out to find the lineshape in detail at a light intensity where the Rabi nutation frequency is comparable to the Doppler width.

DOI
10.1143/jjap.19.615

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Journal of Experimental and Theoretical Physics•Feb 1, 2005•4 citations
Effects of an intense saturating radiation on a probe lineshape under Doppler broadening are studied in a three-level system when the frequency of the probe light is higher than that of the saturating light. The problem is analysed in the approximation of weak probe field using an ensemble averaged density matrix. An analytical form of the lineshape is obtained for the resonant saturating field of high intensity at which the Rabi nutation frequency is larger than the Doppler width of the probe transition. The linewidth of probe absorption depends on the Doppler width and the frequency ratio of the probe light to the saturating light. The computer calculation is carried out to find the lineshape in detail at a light intensity where the Rabi nutation frequency is comparable to the Doppler width.
We study inhomogeneously broadened three-level atoms ($\ensuremath{\Lambda}$ configuration). Two energy levels are strongly coupled by an intense standing wave. A weak laser field at an adjacent transition is used as a probe. The probe response is calculated by Green's functions involving continued fractions. The general solution is extendable to other three-level configurations as well to other types of multimode saturators. The connection of various approximate solutions to the exact one is discussed. We concentrate on the Doppler-free case where both transitions have nearly equal frequencies. For this we derive a reasonably accurate closed-form solution, the parameter dependencies of which are investigated in detail. In addition to its average changes the dynamics of the saturated transition plays an important role in the steady-state probe response. The spectra show sharp resonances which cannot be explained in terms of traveling wave superposition models. The width of the velocity distribution has a strong effect on the shape of the spectrum---some resonances are smeared away because of incomplete Doppler dephasing. The relaxation processes influence differently the resonances, which facilitates their interpretation.
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.
A previously developed diagrammatic method for calculating the nonlinear response of a dilute gas at near resonance with strong classical radiation fields is extended to include velocity-dependent homogeneous and inhomogeneous broadening phenomena. The method is applied to two-level saturated-absorption (Lamb-dip) spectroscopy. Expressions are obtained for the collision-broadened Lamb dip probed by a weak field in the presence of an arbitrarily strong saturating field and are compared to the usual infinite-Doppler-width, weak-saturation expression. We study the effects of velocity and momentum transfer on the line-shape parameters and discuss the effect of phase-changing and strong inelastic collisions on the intensity.
Previously derived equations describing recoil effects in saturated absorption by a gas of two-level atoms or molecules are solved numerically for the case of standing plane-wave excitation and large Doppler broadening. The numerical techniques and accuracy estimates are discussed briefly. The lineshapes obtained are well approximated by the superposition of two Lorentzian functions whose width, heights, and separation parametrise the lineshape. The dependence of these parameters on saturation, recoil splitting, and relaxation rates is described and compared with corresponding results in the rate equation approximation and in the weak-probe-beam approximation. Saturation broadening depends strongly on these latter approximations, but very little on recoil splitting. When multiphoton processes are retained in the equations, increasing saturation causes a slight decrease in the fitted separation of the peaks. The ratio of the heights of the two Lorentzians is closely related to the ratio of relaxation rates for the level populations.
We describe the influence of the intensity variation of the light in a standing wave on the lineshape of a Doppler-free multi-photon transition. We show that as long as the light shifts and the saturation are small compared to the Doppler width, a motional narrowing effect occurs and the line remains Lorentzian, the centre being shifted by an amount equal to the mean value of the dynamic Stark effect. We consider also the case of transients. We show that at resonance, it is possible to observe different responses according to the light intensity. In particular, it is possible to observe Rabi oscillations only if the Rabi frequency is larger than the natural width and smaller than the Doppler width of the transition.
The spectrum of weak probe field absorption (amplification) by two-level atoms experiencing collisions with buffer gas atoms in a strong resonance laser field is studied theoretically. Analysis is carried out for systems with a weak Doppler broadening under relatively mild constraints on the strong field intensity for the general case of an arbitrary change in the phase of the radiation-induced dipole moment in elastic collisions of gas particles. It is shown that, in spite of uniform broadening of the absorption line, the probe field spectrum exhibits a clearly manifested anisotropy to mutual orientation of the wavevectors of strong and probe radiation. It is found that the width of resonances in the probe field spectrum under definite conditions (that can easily be created in experiments) is proportional to the diffusion coefficient for atoms interacting with radiation. This fact can form the basis of the spectroscopic method for measuring the transport frequencies of collisions between particles absorbing radiation and buffer particles. It is shown that phase memory effects in collisions strongly modify the probe field spectrum both qualitatively and quantitatively. Simple operative formulas proposed for the probe field spectrum are convenient for experimental data processing.