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Optica Acta International Journal of Optics

Theory of Ultra-high-resolution Optical Raman Ramsey Spectroscopy

Bryan J. Dalton, Tien D. Kieu, P. L. Knight

Published Apr 1, 1986• 12 citations
Publisher

Abstract

A non-perturbative theoretical analysis of Ramsey interference lineshapes in three-level lambda systems excited by laser fields has been developed for the general case of several interaction regions. In conventional Ramsey excitation, two laser fields excite the lambda system each in two separate spatial interaction regions. Here we examine how increasing the number of interaction regions or altering the interaction times change and improve the lineshape characteristics such as fringe visibility. For short interaction times the fringe pattern is strongly dependent on the number of interaction regions, with the n = 2 sinusoidal fringes replaced by sharper fringes of greater visibility. With larger interaction times, the fringe pattern is virtually unchanged on increasing the number of interaction regions. The optimum fringe pattern is obtained with short interaction times and a larger (n a 9) number of regions.

DOI
10.1080/713821945

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Well-resolved Ramsey fringes have been demonstrated using laser Stark spectroscopy of CH3{\mathrm{CH}}_{3}CH3​F in a molecular beam with two interaction regions. Fringe separations as low as 155 kHz were obtained. The interaction regions were produced by masks containing slits placed in the Gaussian-profile beam of a cw CO2{\mathrm{CO}}_{2}CO2​ laser. Population inversion resulting from a frequency sweep associated with the curvature of the slit-diffracted wave fronts has limited the observations at high laser-power values. An imaging system has been shown to eliminate this effect. Experiments with three and five laser-molecular beam crossings were also conducted to demonstrate the feasibility of using multiple interaction regions as a tool for high-resolution spectroscopy. The results have been modeled using the optical Bloch equation for a two-level system. Good agreement with the experiment has been obtained.
It is shown theoretically that Ramsey fringes can be produced when a laser-assisted reaction of the form A2{\mathrm{A}}_{2}A2​+${\mathrm{A}}_{1}^{\ensuremath{'}}$+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}A1{\mathrm{A}}_{1}A1​+${\mathrm{A}}_{2}^{\ensuremath{'}}$ is driven by a pair of ultrafast radiation pulses, each of whose temporal widths is less than the duration ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ of a collision between the A and A\ensuremath{'} atoms. The excitation profile of the laser-assisted collision is calculated as a function of detuning of the laser field frequency from the initial- to final-state transition frequency. For radiation pulses separated by time T, Ramsey fringes appear separated in frequency by ${\mathrm{T}}^{\mathrm{\ensuremath{-}}1}$. The modulation depth and shift of the central Ramsey fringe as a function of (T/${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$) provide information about the collisional interaction. Both the weak- and strong-field regions are considered and comparison with laser-assisted collisions using excitation pulses having temporal widths greater than ${\mathrm{\ensuremath{\tau}}}_{\mathrm{c}}$ is made.
Using two coherent time-delayed short pulses, we have demonstrated that one can obtain, in the profile of Doppler-free two-photon resonances, interference fringes with a splitting 12T\frac{1}{2T}2T1​ (TTT, delay time between the two pulses) much smaller than the spectral width $\frac{1}{\ensuremath{\tau}}$ of each pulse ($\ensuremath{\tau}$ duration of each pulse). This method should lead to a number of important improvements in the presently available techniques of ultrahigh-resolution laser spectroscopy of atoms and molecules.
Raman-Ramsey interference has proved a very effective technique to implement compact and high performing vapor cell frequency standards. In this paper, we theoretically characterize Raman-Ramsey resonances in an optically thick atomic vapor. Specifically, some parameters of interest for frequency standards applications, like contrast and linewidth of the central Raman-Ramsey fringe, are evaluated at different temperatures for 133Cs^{133}\mathrm{Cs}133Cs and 87Rb^{87}\mathrm{Rb}87Rb vapor cells with buffer gas. Density narrowing and broadening effects are described and explained in terms of a three-level theory where laser field propagation through the atomic medium is taken into account. Also, we investigate light shift both in low and high atomic density regimes. Light shift, which potentially degrades the medium- to long-term stability of Raman-Ramsey clocks, is composed of two contributions. The first is a pulling effect exerted by the wide Rabi profile enclosing the interference pattern on the central Raman-Ramsey fringe. The second light-shift term is strictly related to the detection time. Calculations derived from our model well describe already existing experimental results and new behaviors are predicted.