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Molecular population trapping in Y- and Rhomb-type four-level systems

H.-R. Xia, Cen-Yun Ye, Jianwen Xu, Liangen Ding

Published May 8, 1994• 0 citations

Abstract

We report the first observation of molecular population trapping in a pair of coupled upper or coupled intermediate levels in Y-type or rhomb-type four-level systems, respectively. The demonstrations were done by means of equal-frequency two-photon excitations at about 587 and 640 run in sodium dimers. The mentioned coupled levels consist of a pair of wavefunction mixing levels due to spin-orbital perturbation with typical separation of a few GHz. The characteristic of the molecular trapping in a Y- type system was a strong extra UV excitation fluorescence peak against null visible emission in the middle between the two allowed two-photon absorption peaks. On the contrast, a pair of singlet-triplet mixing intermediate levels in a rhomb-type four-level system might provide significant destructive quantum interference for a two- photon transition, depending on their relative offsets. The characteristic of molecular population trapping in a rhomb-type four- level system was only two pieces of residual signals observable al the sides after completely eliminated of the center part of the two-photon lineshape.

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We report the first observation of molecular population trapping in a pair of coupled upper or coupled intermediate levels in Y-type or rhomb-type four-level systems, respectively. The demonstrations were done by means of equal-frequency two-photon excitations at about 587 and 640 run in sodium dimers. The mentioned coupled levels consist of a pair of wavefunction mixing levels due to spin-orbital perturbation with typical separation of a few GHz. The characteristic of the molecular trapping in a Y- type system was a strong extra UV excitation fluorescence peak against null visible emission in the middle between the two allowed two-photon absorption peaks. On the contrast, a pair of singlet-triplet mixing intermediate levels in a rhomb-type four-level system might provide significant destructive quantum interference for a two- photon transition, depending on their relative offsets. The characteristic of molecular population trapping in a rhomb-type four- level system was only two pieces of residual signals observable al the sides after completely eliminated of the center part of the two-photon lineshape.

In this paper we report the first observation of molecular population trapping in four level systems. Constructive and destructive quantum interferences between two sum-frequncy two-photon transitions in Y- and rhomb-type four-level systems, respectively, im sodium molecules have been experimentally achieved by using only one laser source. Their energy level schemes are featured by the extremely near-resonant enhancement of the equal-frequency two-photon transitions, sharing both the initial and the intermediate levels for the Y-type, and sharing both the initial and the final levels for the rhomb-type systems. Their novel spectral effects are to show seriously restrained Doppler-free UV peak at the nominal location of the induced two-photon transition with visible fluorescence in rhomb-type schems, and to show a strong extra UV peak but null visible fluorescence in the middle between the two dipole allowed two-photon transitions.

An unconventional perturbation treatment of the theory of two-photon absorption in a four-level atomic system close to two-photon resonance is developed on the basis of the optical Bloch equations. The results for the longtime populations of the intermediate and upper states are valid in low- and medium-intensity regimes. In both regimes the upper state population shows a lorentzian resonance centred on zero two-photon detuning with a width equal to the natural linewidth of the upper state. The intermediate state population shows a similar behaviour in the intermediate regime only, with no significant dependence on two-photon detuning in the low-intensity regime. However, in both regimes the population of the virtual intermediate state is at least comparable to that of the resonant upper state. The perturbation theory results have been checked by direct numerical calculations based on the Bloch equations. Numerical calculations confirm the presence of a high-intensity regime characterized by power shifts, broadening and saturation effects.

It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. 77, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifest in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory that explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as well as numerically the steady-state fluorescence, and find that the number of peaks depends on the excitation process. If the molecule is driven to the upper levels by a two-photon process, the fluorescent intensity consists of two peaks regardless of the mutual polarization of the transition dipole moments. If the excitation process is composed of both a two-step, one-photon process and a one-step, two-photon process, then there are two peaks on transitions with parallel dipole moments and three peaks on transitions with antiparallel dipole moments. This latter case is in excellent agreement with the experiment.