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Physical Review A

Optical Ramsey fringes with traveling waves

Ch. J. Bordé, Ch Salomon, S. Avrillier, A. Van Lerberghe, Ch. Bréant, D. Bassi, G. Scoles

Published Oct 1, 1984• 223 citations
Publisher

Abstract

We present a new interaction geometry for optical Ramsey fringes comprised of four traveling waves instead of the three usual standing waves. First, we demonstrate experimentally that the new method leads to an improved contrast, using the optothermal detection of the vibrational excitation of ${\mathrm{SF}}_{6}$ in a supersonic beam illuminated by a waveguide ${\mathrm{CO}}_{2}$ laser. Second, we give a simple theoretical description of the method, using evolution matrices of spinors and pseudospin-vector representations of these spinors. Finally, we introduce strong-field density-matrix diagrams to discuss the differences between the various interaction geometries as well as between the Ramsey fringes and the usual stimulated photon echoes.

DOI
10.1103/physreva.30.1836

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We present a new interaction geometry for optical Ramsey fringes comprised of four traveling waves instead of the three usual standing waves. First, we demonstrate experimentally that the new method leads to an improved contrast, using the optothermal detection of the vibrational excitation of SF6{\mathrm{SF}}_{6}SF6​ in a supersonic beam illuminated by a waveguide CO2{\mathrm{CO}}_{2}CO2​ laser. Second, we give a simple theoretical description of the method, using evolution matrices of spinors and pseudospin-vector representations of these spinors. Finally, we introduce strong-field density-matrix diagrams to discuss the differences between the various interaction geometries as well as between the Ramsey fringes and the usual stimulated photon echoes.
A general equation for the interaction of atoms with many separated traveling waves is introduced, and the oscillating terms corresponding to the Ramsey fringes are found in the equation. The features of the multizone Ramsey resonance are quite comprehensible with the aid of the diagrammatic representation of the atomic beam and laser fields. The resonance condition and the narrowing effect of the fringe width are discussed. Using the intercombination line of a Ca atom, the multizone Ramsey resonances of up to ten separated fields were demonstrated. With the ten separated fields, the Ramsey fringes with a contrast of 130% to the saturation dip could be obtained at a relatively small excitation power.
The interaction of an atomic beam with four traveling-wave laser beams leads to optically induced Ramsey fringes in the atomic beam. This experimental setup has been used as an optical frequency standard as well as a matter-wave interferometer. We calculate for two-level atoms the shift of the fringes due to the influence of fairly general external forces in lowest order of a perturbation approach. A comparison with the phase shift found in a corresponding WKB treatment of the interaction geometry is made. The consequences of beam reversal and cooling of the atomic beam are studied. As an application, we treat the linear acceleration and rotation of the interferometer and discuss the influence of space-time curvature.
We report the observation of Raman-Ramsey fringes using a double lambda scheme creating coherent population trapping in an atomic ensemble combined with pulsed optical radiations. The observation was made in a Cs vapor mixed with N2 buffer gas in a closed cell. The double lambda scheme is created with lin perpendicular lin polarized laser beams leading to higher contrast than the usual simple lambda scheme. The pulsed trapping technique leads to narrow fringe widths scaling as 1/(2T) with high contrasts which are no longer limited by the saturation effect. This technique operates in a different way from the classical Ramsey sequence: the signal is done by applying a long trapping pulse to prepare the atomic state superposition, and fringe detection is accomplished by optical transmission during a short second trapping pulse without any perturbation of the dark state.
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.
Evidence of coherence effects has been observed in the Zeeman sublevels by means of nonlinear level crossing in a metastable Ca beam with resonance width 3 orders of magnitude less than the radiative linewidth of the investigated transitions. By using two separate traveling waves, Ramsey-like fringes have been observed. The final measured widths are determined by the transit time, are weakly dependent on the magnetic-field inhomogeneities, and are independent of the natural width of the optical transitions and the laser bandwidth.
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.