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Physical Review Letters

Determination of the Phase Difference between Even and Odd Continuum Wave Functions in Atoms through Quantum Interference Measurements

Zheng-Min Wang, Daniel S. Elliott

Published Oct 4, 2001• 56 citations
Publisher

Abstract

We establish a technique for the determination of the phase difference between even and odd parity continuum wave functions in atoms. This determination is based upon our detailed measurements of a quantum mechanical interference between two photoionization processes using a two-color laser field. We present our measurement of the phase difference between the continuum p and d waves in atomic rubidium, which is in good agreement with the expected value.

DOI
10.1103/physrevlett.87.173001

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We establish a technique for the determination of the phase difference between even and odd parity continuum wave functions in atoms. This determination is based upon our detailed measurements of a quantum mechanical interference between two photoionization processes using a two-color laser field. We present our measurement of the phase difference between the continuum p and d waves in atomic rubidium, which is in good agreement with the expected value.
We present our study on complete measurements of two-photon ionization in atomic rubidium. In this study we developed an effective technique to measure the angular distributions of photoelectrons. Through the measurements with this technique and using elliptically-polarized light we have successfully determined the atomic parameters—the relative cross sections for various ionization channels as well as the phase difference between s- and d-continuum waves. The measured phase differences are in excellent agreement with expected values over the entire range of photoelectron kinetic energy from 0 to 0.5 eV. The measured relative cross sections for ionization into S and D channels are also in good agreement with theoretical data. Both the relative cross sections and phase differences show a slow variation as a function of photoelectron energy. The ratios of cross sections of the two D channels are not in agreement with the expected value, suggesting fine structure effects. We also studied a quantum mechanical interference using two-color laser fields and observed the extremely asymmetric photoelectron angular distribution produced by interfering even- and odd-order photoionization processes in atomic rubidium as the optical phase was varied. We observed these effects with both perpendicularly and parallel-polarized fields components. It is worthy to note that the quantum interference observed with perpendicularly-polarized two-color fields is unique. Based on the analysis of measured angular distributions we derived the phase difference between even and odd continuum waves for the first time. The measured value of the phase difference is in good agreement with the calculated value from quantum defect theory.
We present a complete experimental determination of the atomic parameters necessary to unambiguously characterize two-photon ionization of atomic rubidium, i.e., the relative photoionization cross sections and the continuum wave function phase difference. We obtain these complete results through a single measurement, that of the two-photon photoelectron angular distribution using elliptically polarized light. While measured phase differences are in excellent agreement with expected values, the ratios of photoionization cross sections of the two D channels are not.
In measurements of relative phases in photoionization processes, the contribution of continuum-continuum (CC) couplings to the atomic (Wigner) phases, corresponding to attosecond time delays, is currently accounted for only by theoretical models. Here, we introduce a measurement scheme that is sensitive to phase differences of CC transitions after photoionization in the presence of an optical field. The method allows us to separate CC transitions from the ionization process and can help in testing existing theoretical models. It is based on a multicolor interferometer, similar to the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) method. The key idea involves the comparison of two measurements with different orders of CC transitions. The scheme is illustrated by an ab initio calculation on atomic hydrogen.
We report in detail our complete characterization of atomic photoionization via a single measurement, namely, that of the two-photon photoelectron angular distribution using elliptically polarized light. Through these measurements we are able to determine the atomic parameters necessary to unambiguously describe two-photon ionization of atomic rubidium. These parameters include relative cross sections for photoionization into various outgoing channels as well as the phase difference between the continuum S and D partial waves. We present a derivation of the angular distribution with arbitrarily polarized light in terms of these cross sections and phases, demonstrate the advantages of using elliptically polarized light, discuss details of the experiment, and report the results of our measurements in this paper. While measured phase differences are in excellent agreement with expected values over the entire range of photoelectron kinetic energy of our measurements from 0 to 0.5 eV, ratios of cross sections for photoionization into the two D channels are anomalous, suggesting unexpected fine structure effects in these continua.
We report evidence of an interference process between two bound-free atomic transitions induced by laser fields. Sodium atoms, initially prepared in the 3P1/2{3\mathrm{P}}_{1\mathrm{/}2}3P1/2​ excited state, are ionized by a nonresonant three-photon interaction with 1064-nm laser light and by a one-photon interaction with the third-harmonic field, at 355 nm. Interference between the two transition paths allows the control of the total ionization rate by varying the relative phase of the laser fields. The experiment has provided a fringe visibility as high as 42%.