Laser-Induced Degeneracies Involving Autoionizing States in Complex Atoms

Latinne, Olivier; Kylstra, N. J.; Dörr, Martin; Purvis, J; Terao-Dunseath, Mariko; Joachain, Charles; Burke, P. G.; Noble, C. J.

doi:10.1103/physrevlett.74.46

Cited by 154 publications

(138 citation statements)

References 25 publications

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“…Many interesting and important phenomena associated with qualitative changes in the dynamics of mechanical systems [20,29,30,36], stability optimization [6,21,25], and bifurcations of eigenvalues under matrix perturbations [32,35,34,38] are related to multiple eigenvalues. Recently, multiple eigenvalues with one Jordan block became of great interest in physics, including quantum mechanics and nuclear physics [2,17,24], optics [5], and electrical engineering [8]. In most applications, multiple eigenvalues appear through the introduction of parameters.…”

Section: Introductionmentioning

confidence: 99%

Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

Mailybaev

2006

Numer. Linear Algebra Appl.

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The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix having a multiple eigenvalue of given multiplicity. The method also works in the whole matrix space (in the absence of parameters). The approach is based on the versal deformation theory for matrices. Numerical examples are given.

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Section: Introductionmentioning

confidence: 99%

Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

Mailybaev

2006

Numer. Linear Algebra Appl.

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“…Introduction -Lately the interference effects of resonances and in particular the occurrence of a double pole of the S-matrix has been examined frequently [1][2][3][4][5]. Several, widely different systems where double poles can occur have been identified, such as: atomic states in intense laser fields, general two channel systems, and other systems.…”

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confidence: 99%

Double pole of theSmatrix in a double-well system

Vanroose

2001

Phys. Rev. A

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We discuss the interaction between two resonant states in a quantum double-well structure. The behaviour of the resonant states depends on the coupling between the wells, i.e. the height and width of the barrier that separates them. We distinguish a region with resonant tunneling and a region where the two resonances repel each other. The transition between the two regions is marked by a double pole of the S-matrix. 03.65Nk, 73.23, 11.55 Introduction -Lately the interference effects of resonances and in particular the occurrence of a double pole of the S-matrix has been examined frequently [1][2][3][4][5]. Several, widely different systems where double poles can occur have been identified, such as: atomic states in intense laser fields, general two channel systems, and other systems. Recently Hernandez et al [6] have investigated a model with two spherical cavities bounded by δ-function barriers and shown that a double pole of the S-matrix can be induced by tuning the parameters of the model. In this letter, we study the interference effects between two resonances in a one-dimensional quantum system with a double square well. In our opinion it is, besides being more general than a model with singular potentials, more suitable for a physical discussion about the genesis of the double pole and its relation to the internal structure of the system, as it can be related to concepts like coupling and tunneling. Such a double well structure is similar to the structure of two vertically coupled quantum dots or an "artificial molecule" [7]. To our knowledge (and surprise), these aspects of the double well system have not been described in the literature.As model problem we take the motion of a particle in a one-dimensional potential V (x) governed by the Schrödinger equation

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“…Clearly, for λ n = λ y M (the largest eigenvalue of the subset), the matrix (λ n − lω − H 0 ) is never singular for any l = 1, 2, 3, .... Henceλ y M is a quasienergy and the corresponding Floquet eigenstate is again defined by Eqs. (11) and (13). Conversely, for any other eigenvalue λ n = λ yα of the subset (α = 1, 2, ..., M − 1), the matrix (λ yα − lω − H 0 ) becomes singular for some positive integer l. In particular, let G be the positive integer such that λ y M − λ yα = −Gω, so that (λ yα − lω − H 0 ) is not singular for any l ≥ G + 1 while it is singular at l = G (and possibly also at some smaller indices l).…”

Section: Quasi-energy Spectrum Floquet Eigenstates and Floquet Epsmentioning

confidence: 99%

“…Such a solution is of the form (11) with λ = λ n and with vectors a (l) formally given by Eq. (13). If λ n is not any of the eigenvalue λ yα of the subset, the matrix (λ n − lω − H 0 ) entering on the right hand side of Eq.…”

Section: Quasi-energy Spectrum Floquet Eigenstates and Floquet Epsmentioning

confidence: 99%

“…EPs are at the heart of many intriguing physical phenomena appearing in several systems that experience gain or loss. They have been predicted and observed in a wide variety of physical systems, including atomic and molecular systems [13,14,15], microwave cavities and waveguides [16,17,18], electronic circuits [19], optical structures [20,21], Bose-Einstein condensates [22,23], acoustic cavities [24], non-Hermitian Bose-Hubbard models [25], exciton-polariton billiards [26], opto-mechanical systems [27] and many others. Besides of their theoretical interest, EPs can find important applications, for example in the design and realization of unidirectionally invisible media [28,29,30,31,32], for asymmetric mode switching [18,33] and topological energy transport [27], for the design of novel laser devices [34,35,36,37,38], for optical sensing [39] and polarization mode conversion [40].…”

Section: Introductionmentioning

confidence: 99%

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Floquet exceptional points and chirality in non-Hermitian Hamiltonians

Longhi¹

2017

J. Phys. A: Math. Theor.

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Abstract. Floquet exceptional points correspond to the coalescence of two (or more) quasi-energies and corresponding Floquet eigenstates of a time-periodic non-Hermitian Hamiltonian. They generally arise when the oscillation frequency satisfies a multiphoton resonance condition. Here we discuss the interplay between Floquet exceptional points and the chiral dynamics observed, over several oscillation cycles, in a wide class of non-Hermitian systems when they are slowly cycled in opposite directions of parameter space.

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Laser-Induced Degeneracies Involving Autoionizing States in Complex Atoms

Cited by 154 publications

References 25 publications

Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters

Double pole of theSmatrix in a double-well system

Floquet exceptional points and chirality in non-Hermitian Hamiltonians

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