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Physical Review A

Three-photon resonant atomic excitation in spatially incoherent laser beams

Viktor E. Peet, Sergei Shchemeljov

Published Oct 22, 2003• 4 citations
Publisher

Abstract

Two-color excitation by spatially coherent and incoherent laser beams has been used to study three-photon-resonant excitation and subsequent ionization of xenon in conditions, when internally generated sum-frequency field plays an important role in excitation of atomic resonances through interfering one-photon excitation pathway. We show that the incoherence in one of the pumping fields reduces the efficiency of generated sum-frequency field, and thus suppresses the interference between the three- and the one-photon excitation channels. The degree of suppression is controlled by varying the crossing angle between coherent and incoherent laser beams. We show that ionization profiles can be analyzed on the basis of the well-studied interference of one- and three-photon transition amplitudes, but with pumping field decomposed into multiple small-scale uncorrelated domains where coherent process of four-wave mixing occurs. The gain length for a coherent process in these domains depends on the coherence degree and excitation geometry. It gives a possibility of controlling the contribution of coherent processes to the excitation of multiphoton resonances.

DOI
10.1103/physreva.68.043411

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Two-color excitation by spatially coherent and incoherent laser beams has been used to study three-photon-resonant excitation and subsequent ionization of xenon in conditions, when internally generated sum-frequency field plays an important role in excitation of atomic resonances through interfering one-photon excitation pathway. We show that the incoherence in one of the pumping fields reduces the efficiency of generated sum-frequency field, and thus suppresses the interference between the three- and the one-photon excitation channels. The degree of suppression is controlled by varying the crossing angle between coherent and incoherent laser beams. We show that ionization profiles can be analyzed on the basis of the well-studied interference of one- and three-photon transition amplitudes, but with pumping field decomposed into multiple small-scale uncorrelated domains where coherent process of four-wave mixing occurs. The gain length for a coherent process in these domains depends on the coherence degree and excitation geometry. It gives a possibility of controlling the contribution of coherent processes to the excitation of multiphoton resonances.
We use resonance ionization involving two colors in single-pass and retroreflected geometries to study the suppression of excitation of a four-photon resonance by an interference involving four-wave sum-frequency generation occurring near an intermediate three-photon resonance. The 6p[1/2](J=0) state of xenon is excited by three blue photons plus one infrared photon. One beam, focused to I1{\mathit{I}}_{1}I1​\ensuremath{\simeq}7\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 W/cm2{\mathrm{cm}}^{2}cm2, is nearly three-photon resonant with the 6s[3/2](J=1) resonance; the second, unfocused beam (I2{\mathit{I}}_{2}I2​\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 W/cm2{\mathrm{cm}}^{2}cm2) is tuned to maintain exact four-photon resonance with the 6p[1/2](J=1) state. One additional blue photon ionizes from the four-photon level. Third-harmonic light is generated by the first, nearly three-photon-resonant beam by four-wave sum-frequency mixing. One third-harmonic photon plus one photon from the second laser form a second excitation pathway to the four-photon level; destructive interference between the two pathways results in a reduction in the observed ionization. The degree of reduction depends on the xenon density and the detuning (both positive and negative) from three-photon resonance. This interference may be overcome by retroreflecting the nearly three-photon-resonant beam to provide an additional excitation pathway which generates no third harmonic.The study provides detailed information on the pressure-dependent range from exact resonance over which the familiar three-photon cancellation effect is operative; it shows that the interference occurs in high- and low-energy regions about three-photon resonance; and it establishes that interference is produced for large values of the phase mismatch even if the absorption of the interfering field is low. We compare our measurements of the reduction in ionization with predictions published by us elsewhere [M. G. Payne, J. C. Miller, R. C. Hart, and W. R. Garrett, Phys. Rev. A 44, 7684 (1991)]; excellent agreement is observed. We also report the observation of suppression of pressure-induced wing absorption into the three-photon state observed in a classic ``hybrid'' resonance mode of excitation.
Three-photon excitation and associated wave mixing near the 6s6s6s and $6{s}^{\ensuremath{'}}$ resonances of xenon have been studied utilizing resonance-enhanced multiphoton ionization in angled beams with different polarizations. It has been shown that a complete cancellation of three-photon resonant atomic excitation caused by the well-known destructive wave-mixing interference occurs in sss and ppp polarization of angled beams but distinct resonance ionization enhancement is observed when pump beams have orthogonal polarization planes. Pressure-induced evolution of the resonance ionization peak in cross-polarized beams is identical to that observed with counterpropagating beams. The reason for such resonance ionization enhancement is unknown and cannot be explained within the frame work of existing theory. The effect may result from some peculiarities of wave-mixing interference in a multilevel atomic system, where different degenerate magnetic sublevels of the upper atomic state and multiple interfering excitation processes are involved. Another possibility is that the resonance ionization enhancement results from a process where weak counterpropagating light is generated within the excitation region of cross-polarized angled beams.
We consider effects which occur when four-wave sum frequency generation and multiphoton ionization are induced by lasers tuned near a three-photon resonance and simultaneously near or at a dipole allowed four-photon resonance. In studies with unfocused laser beams, if the phase mismatch of the generated four-wave-mixing field is large and the related two-photon resonance for the absorption of a four-wave-mixing photon and a laser photon results in strong absorption of the four-wave-mixing field, a coherent cancellation occurs between the pumping of the resonance by two- and four-photon processes. This interference effect occurs when the first laser is tuned on either side of the three-photon resonance and \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​L\ensuremath{\Vert}\ensuremath{\gg}1, where \ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​ is the mismatch and L is the length of the path of the laser beams in the gas. With focused laser beams large differences occur between ionization with unidirectional beams and with counterpropagating laser beams when \ensuremath{\Vert}\ensuremath{\Delta}kr{\mathit{k}}_{\mathit{r}}kr​b\ensuremath{\Vert}\ensuremath{\gg}1, where b is the confocal parameter of the focused laser beams. Strong absorption of the four-wave-mixing field is shown not to be necessary for strong destructive interference with focused laser beams when the phase mismatch is large. This work also suggests an explanation for earlier experiments where the presence of a four-photon resonance enabled the generation of third-harmonic light in a positively dispersive wavelength region. We argue that this process can occur when the laser used to achieve the four-photon resonance is focused on the small z (z is the coordinate in the direction of propagation) side of the focal point of the laser responsible for the third-harmonic generation. In this way the absorption of the third-harmonic light on one side of the focal point is made much stronger than on the other side. Correspondingly, contributions to the third-harmonic field from the two sides of the focal point are unequal and cannot undergo complete destructive interference as would otherwise occur in a positively dispersive region.
Three-photon-resonant excitation and subsequent ionization of xenon at high concentrations has been studied utilizing both Bessel and Gaussian beams. Comparisons of analogous results with the two modes of focusing are made. The excitation-ionization profiles can be analyzed on the basis of the well-studied interference effect involving combined contributions of three- and one-photon transition amplitudes in resonant atomic excitation. We show that the principal features of the excitation problem with Bessel beams can be simulated by a simple picture involving crossed plane-wave beams. Using this approach it has been shown that pressure-broadened and shifted lines that result from the interference-based cooperative Lorentzian line shift constitutes the main pressure-dependent peak of off-resonance excitation profiles produced in Bessel beams.
Multiphoton ionization profiles in xenon under three-photon excitation by azimuthally segmented conical laser beams have been studied and analyzed on the basis of the interference-based cooperative shift of the atomic resonance line. Segmentation of the conical wave front with various geometrical slits reduces the possible three-photon azimuthal sub-beam combinations in the third order process and a principal (or ``homogeneous'') Lorentzian component can be selected from the overall excitation profile. This Lorentzian is identical to the pressure-broadened atomic line shifted by the cooperative shift. A possibility of controlling the nonlinear response by spatial selection of interacting waves in conical beams is discussed.
Through multiphoton ionization measurements, the polarization effects in destructive quantum interference under three-photon resonant excitation have been studied. Recent observations [V. Peet, Phys. Rev. A 74, 033406 (2006)] have indicated that contrary to the well-known pattern of a total suppression of resonance excitation, the destructive interference becomes incomplete if three-photon transition is driven by crossed beams with orthogonal polarization planes. These observations have been tested for a more general case of two-color excitation and very similar polarization-dependent anomalies in the interference character have been registered. It has been shown that the destructive interference is modified and the resonance excitation does occur if two crossed laser beams have opposite circular polarizations. The pressure-induced evolution of the uncanceled ionization peaks has the ratio of blue shift to width close to 0.5 exactly as it is known for resonance ionization peaks registered under excitation by counterpropagating laser beams.