Circular dichroism in double photoionization

Abstract

One-photon two-electron ionization of an atom by circularly polarized light yields triply differential cross sections different for left and right circular polarization. Necessary kinematical conditions for a finite dichroism are worked out. A numerical calculation for helium which employs correlated wave functions shows the angular correlations of the escaping electron pair to be very different for left and right circular polarization such that the effect should be observable in a coincidence experiment.PACS numbers: 32.80.Rm, 33.55.AdIt is well known that for single photoionization of an atom the polarization of the incident light enters only kinematically into the differential cross section; see, e.g., [1]. For circular polarization the angular distribution of photoelectrons is given bywhere do is the total cross section, ft is the asymmetry parameter, k is the direction of incident light, p is the momentum of the photoelectron, and Pi is the second Legendre polynomial. Equation (1) holds for right and left circularly polarized light, and also for unpolarized light. For linearly polarized light one has simply to replace p by -2/3 and k by the direction of the electric field strength in Eq. (l). In other words, switching from one polarization to another yields no new physical information. This, however, is not true for double photoionization. It is the purpose of this Letter to show that the light polarization, in particular the helicity of circular polarization, enters dynamically in a nontrivial way into the angular correlation pattern of the photoelectron pair. Our following analysis for double photoionization is based on first-order perturbation theory and on the dipole approximation for the radiation field. As usual we assume randomly oriented initial target atoms, no observation of the photoions, and no spin analysis of the photoelectrons. Only under these circumstances does Eq. (l) hold for single photoionization. For double photoionization the triply differential cross section (TDCS) for the pair of photoelectrons detected in coincidence including energy analysis is then given by [2][3][4] d'a da a da b dEa =cX 1 -XK^PTPJ^-DIO,)! 2 (2) Mf 2Jj + 1 M { with the constant C ^A^aaoEyPaPb-Here, energies E and momenta p of the photoelectrons are labeled by indices a and b, a is the fine-structure constant, ao is the Bohr radius, E r is the incident radiation energy, D ~Zn r« is the dipole operator in length form, and e is the polarization vector. Equation (2) averages over the initial magnetic sublevels A//, and sums over the magnetic sublevels Mf of the photoion.We focus now on circular polarization where e is a complex unit vector and employ a tensorial calculus which formally resembles that used by Fano and Macek [5] in their polarization analysis of dipole light emitted from oriented and aligned targets. To this end we write in Eq.(2) for convenience

Circular dichroism at equal energy sharing in photo-double-ionization of He

“…Up to now, all theoretical treatments of CD have employed the EDA (Refs. [1,3,4,[6][7][8][9][10][11][12][13]) and their predictions are generally in agreement with experiments [12][13][14][15][16]. Measurement of CD provides a sensitive means for probing two-electron dynamics in PDI, since the photon-helicity-dependent CD term in the TDCS originates from an interference between real and imaginary parts of particular components of the (generally non-Hermitian) PDI amplitude [4,7].…”

“…(5), the parameter ⌬ CD in Eq. (6) (where Im c 3 =Im͕f 1 f 2 ‫ء‬ ͖) reduces to the known result for the dipole CD [4,7], whereas the nonzero imaginary parts of other terms in Eq. (5) determine the contribution of retardation effects to ⌬ CD .…”

“…A most interesting feature of PDI is the circular dichroism (CD) effect, i.e., the dependence of the TDCS upon the handedness of an elliptically polarized photon (i.e., upon the sign of the degree of circular polarization, , where −1 ഛ ഛ +1). The CD effect for PDI of He was first predicted theoretically [4] and then observed experimentally [5]. Up to now, all theoretical treatments of CD have employed the EDA (Refs.…”

“…[1,3,4,[6][7][8][9][10][11][12][13]) and their predictions are generally in agreement with experiments [12][13][14][15][16]. Measurement of CD provides a sensitive means for probing two-electron dynamics in PDI, since the photon-helicity-dependent CD term in the TDCS originates from an interference between real and imaginary parts of particular components of the (generally non-Hermitian) PDI amplitude [4,7]. Dichroic effects thus permit direct experimental measurements of this otherwise elusive "cross-interference" caused by the pseudoscalar origin of the parameter [17].…”

Nondipole Effects in Double Photoionization of He

“…The results in Eqs. (3), (4), (6) and (7) are general and do not depend upon the dynamical model used for calculation of the reduced matrix elements dla (p, p') and qll, (p, p') .…”