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Generalized Sturmian approach to extracting transition amplitudes for two-photon ionization of atoms by electromagnetic pulses
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Conf. Ser. 635 092123 (http://iopscience.iop.org/1742-6596/635/9/092123) View the table of contents for this issue, or go to the journal homepage for more
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XXIX International Conference on Photonic, Electronic, and Atomic Collisions (ICPEAC2015) IOP Publishing Journal of Physics: Conference Series 635 (2015) 092123 doi:10.1088/1742-6596/635/9/092123
Generalized Sturmian approach to extracting transition amplitudes for two-photon ionization of atoms by electromagnetic pulses A.I. G´ omez† 1 , G. Gasaneo† and D.M. Mitnik‡ †
Departamento de F´ısica, Universidad Nacional del Sur - IFISUR, Bah´ıa Blanca, C.P. 8000, Buenos Aires, Argentina ‡ Instituto de Astronom´ıa y F´ısica del Espacio, CONICET-UBA, C.C. 67, Suc. 28 (C1428ZAA), Ciudad Aut´ onoma de Buenos Aires, Buenos Aires, Argentina Synopsis In this work we present the application of the Generalized Sturmian basis to the process of photonionization by an electromagnetic pulse in the framework of a perturbation theory. The Generalized Sturmian basis have the proper asymptotic behavior allowing us to extract the transition amplitudes directly from the coefficients of expansion.
∂ i − Ha − λW Ψ(t, r) = 0 ∂t
(1)
where Ha is the non-relativistic atomic Hamiltonian, W is the perturbation that contains the interaction with the electromagnetic field and λ defines the field intensity. In the perturbative scheme λ is a small parameter. We propose an expansion in powers of the field intensity λ, P Ψ(t, r) = n λn ψ (n) (t, r), which yields a coupled system of differential equations for successive orders ψ (n) (t, r). To represent the time evolution of the system we use Fourier representation for both wave function and the electromagnetic field. We make use of Generalized Sturmian Functions (GSF) [3, 4] to solve the time-independent equations obtained. The ionization amplitude is extracted from the asymptotic limit of the scat(n) tering functions ψesc to the order solved , simply, as the sum of expansion coefficients. For the case in which the system is a hydrogen atom interacting with a laser pulse, the firstorder equation has an analytic solution. This
allowed us to test the method and verify its efficiency (see figure 1). In this work we extend this methodology concerning the interaction of atoms with up to two photons. 100
Cross Section (MB)
In the last years there have been impressive progress in attosecond physics [1, 2] mainly because of the fast experimental development of ultrafast lasers, which enabled the temporal study of dynamic processes at the natural atomic time scale. In turn, this led to the development of theoretical and computational methods to study ultrafast phenomena with high resolution in the time domain. Our aim is to describe the interaction of atoms with trains of laser pulses. For that reason we start analyzing the details on the structure corresponding to atoms. In particular we will consider the case where up to two photons are absorbed. Our starting point is the time-dependent Schr¨ odinger equation
TISE: Perturvative Sturmian Method TISE: Analytical
10
TISE: Rescigno-McCoy (1975) TDSE, Sanz-Vicario et.al.(2007)
10
1
1
0,1 0,1
0
0,5
1
1,5
0,01 0
1
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Photoelectron Energy (a.u.) Figure 1. Cross section of H atom in mega-barns versus photoelectron energy in atomic units. Our results after solving the perturbative TISE with Sturmian method (red, solid line), are compared with the exact analytical result (blue, dashed line) and with the from [5](black, dotted line), and with the calculated one after solving the TDSE (green, star points) by Sanz-Vicario [6].
References [1] F. Krausz y M. Ivanov 2009 Rev. Mod. Phys 81 163 [2] M. Drescher et al. 2002 Nature 419 803 [3] G. Gasaneo et al. 2013 Adv. Quantum Chem. 67 153. [4] D.M. Mitnik et al. 2011 Comp. Phys. Comm. 45 1145 [5] T.N. Rescigno and V. Mckoy 1975 Phys. Rev. A 12 522 [6] J.L. Sanz-Vicario et al. 2007 J. Electron Spectrosc. Relat. Phenom. 161 182 1
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