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Journal of the Optical Society of America B

Multilevel light-induced continuum structure: limitations of adapted Fano theory

R. Parzyński, J. Schmidt, Antoni Wójcik

Published Apr 1, 1994• 4 citations
Publisher

Abstract

An analytical, time-dependent, fully nonperturbative solution of a general model of a light-induced continuum structure, in which a dense Rydberg-like quasi-continuum is laser-embedded into a previously structureless atomic continuum, is reported. On the basis of this solution we point to the limitations of Fano theory, which was originally formulated for an analogous problem of a number of discrete states and one continuum with configuration interaction, when this theory is adapted to the problem of multilevel light-induced continuum structures.

DOI
10.1364/josab.11.000644

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Gao‐xiang Li, Huang Guang-ming, PENG JIN-SHENG

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Acta Physica Sinica (Overseas Edition)•Jun 1, 1998•3 citations
An analytical, time-dependent, fully nonperturbative solution of a general model of a light-induced continuum structure, in which a dense Rydberg-like quasi-continuum is laser-embedded into a previously structureless atomic continuum, is reported. On the basis of this solution we point to the limitations of Fano theory, which was originally formulated for an analogous problem of a number of discrete states and one continuum with configuration interaction, when this theory is adapted to the problem of multilevel light-induced continuum structures.
We present an analytical solution to a multilevel model of light-induced continuum structure, in which, instead of a single level, a quasicontinuum of excited levels is laser embedded into a previously structureless atomic continuum. The found solution is fully time dependent and is valid for probing strengths of the structured continuum from the ground level by another laser, which can vary from being much weaker than the embedding one to being as strong as the embedding one. For three different embeddings (weak, moderate, and strong), each one determined by a different relation between the ionization rate \ensuremath{\gamma} and the spacing \ensuremath{\Delta} of the quasicontinuum levels (\ensuremath{\Elzxh}\ensuremath{\gamma}/\ensuremath{\Delta}\ensuremath{\ll}1, \ensuremath{\Elzxh}\ensuremath{\gamma}/\ensuremath{\Delta}\ensuremath{\simeq}1, and \ensuremath{\Elzxh}\ensuremath{\gamma}/\ensuremath{\Delta}\ensuremath{\gg}1), we study the evolution of the ionization spectrum with increasing probing strength. We observe and interpret such strong-field effects in the spectra as (i) conversion of a Fano-like train of peaks into a train of dips; (ii) peak moving, narrowing, and lowering; and (iii) saturation, population trapping, and stabilization against ionization.
Laser-induced continuum structures (LICS) can be produced by a strong laser embedding a low-lying atomic state into a flat atomic continuum, which leads to a tunable asymmetric Fano resonance of adjustable width that can be probed by a second weak laser. In this paper the effects on LICS of transitions caused by the embedding laser between the original atomic continuum and a second atomic continuum are studied in the Markoff approximation by means of Laplace transform methods. Formal results correct to all orders are presented in terms of a T-matrix approach. Numerical calculations are presented which include continuum-continuum coupling correct to the lowest power of the embedding laser intensity. The time evolution of the pure LICS Fano profile is also shown.
Laser induced continuum structures (LICS) can be produced by a strong laser embedding an excited atomic bound state into a flat atomic continuum, leading to a tunable resonance of adjustable width that can be probed by a second laser. If this second laser is of similar intensity to the embedding laser then the distinction between the two becomes artificial and saturation effects become important. In this paper the effect on LICS of transitions caused by both lasers between the original atomic continuum and a second atomic continuum are studied in the Markoff approximation by means of Laplace transform methods and allowing for the ionization of each atomic state by both laser fields. Formal results correct to all orders are also given in terms of a T-matrix approach. Numerical calculations are presented showing the effects on the LICS resonant structures of continuum-continuum coupling processes. Significant changes to the Fano profiles (second laser weak) and to coherence holes (second laser strong) occur. Analytical results are also given.
We obtain an explicit solution for the stationary state populations of a dissipative Fano model, where a discrete excited state is coupled to a continumm set of states; both excited set of states are reachable by photo-excitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values. We show that the continuum states population as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 × 4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic induced-transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter. The original Fano model was introduced by U. Fano in 1961 [1] to explain the asymmetric profile that was obtained when monitoring the photo-current as a function of the laser frequency used to ionize a gaz of Helium-like atoms. In parallel, Friederichs [2] developed the mathematical formalism to describe the essential feature of the Fano model: a discrete state coupled to a continuum set of states; both sets of states being reachable by photo-excitation from the ground state. The resulting photo-current, which is proportional to the population of the continuum set of states, as a function of the excitation laser frequency ω L is known as the Beutler-Fano or Fano profile: f (q) = (q + 2 /(2 + 1), where q is the ratio of the transition dipole moment of the ground-discrete and ground-continuum transitions, and = (ω L − ω e)/γ where e is the energy of the discrete state relative to the ground state, ω L is te radiation field frequency, and = nπV 2 is the linewidth of the excited state, induced by its coupling (per unit of energy) nV 2 to the continuum set of states, n being the density of states. Two extensions of the original model have been considered: inclusion of incoherent relaxation and dephasing processes and high field intensities. The motivation to include incoherent processes was first to describe the pressure broadening [3] due to elastic collisions, laser phase fluctuations [4] and spontaneous emission [5, 6]. Nowadays , Fano profiles in nanoscale structures are standard [7, 8], for example in plasmonic nanostructures [9–11], quantum dots, decorated nanoparticles [12] and spin filters [13]. The coherent coupling with the incident light induces large Rabi frequencies which in turn compete with the relaxation rates in order to modify the stationary state. The ability to predict the lineshape, and in general to investigate non linear optical phenomena in
We have investigated the atomic coherent population trapping in a multilevel laser-induced continuum structure system including cascade two-photon processes, in which two sets of quasicontinua of excited levels to be modeled as the Bixon-Jortner quasicontinuum are laser-embedded into a previously structureless atomic continuum. The condition leading to the atomic coherent population trapping and the coherent population trapping state are given explicitly. And the effects of the Fano factors, the laser intensities and the detunings on the amount of population trapped in the atomic bound states and the populations distributed in the two sets of quasicontinua are also examined.