A truncated shift-operator technique for the calculation of resonances in Stark systems

Glück, Markus; Kolovsky, Andrey R.; Korsch, Hans Jürgen

doi:10.1088/0305-4470/32/4/002

Cited by 10 publications

(3 citation statements)

References 9 publications

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“…In this work we describe a novel approach to the Wannier-Stark problem which has been developed by the authors during the last few years [149][150][151][152][153][154][155][156][157][158][159][160][161][162][163][164]. By using this approach, one finds the complex spectrum (1.3) as the poles of a rigorously constructed scattering matrix.…”

Section: This Workmentioning

confidence: 99%

Wannier–Stark resonances in optical and semiconductor superlattices

2002

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In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.

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Section: This Workmentioning

confidence: 99%

Wannier–Stark resonances in optical and semiconductor superlattices

2002

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“…Equivalent ways of avoiding reflection at x → −∞ include the use of complex absorbing potentials (see [15,19] and section 4) or complex scaling of the coordinate x [15,22]. Here, we use an efficient calculation method introduced in [22,23] based on a finite basis expansion in momentum space. The Wannier-Stark ladder (2) can be understood by considering the commutator…”

Section: Wannier-stark Resonancesmentioning

confidence: 99%

Exceptional points in bichromatic Wannier–Stark systems

Elsen¹,

Rapedius²,

Witthaut³

et al. 2011

J. Phys. B: At. Mol. Opt. Phys.

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The resonance spectrum of a tilted periodic quantum system for a bichromatic periodic potential is investigated. For such a bichromatic Wannier-Stark system exceptional points, degeneracies of the spectrum, can be localized in parameter space by means of an efficient method for computing resonances. Berry phases and Petermann factors are analyzed. Finally the influence of a nonlinearity of the Gross-Pitaevskii type on the resonance crossing scenario is briefly discussed.Submitted to: J. Phys. B: At. Mol. Phys.

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“…. .. An efficient method to calculate the resonance eigenstates was introduced in [30], a recent review can be found in [31].…”

Section: Wannier-stark Resonances In Double-periodic Latticesmentioning

confidence: 99%

Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and crossing of resonances

et al. 2007

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We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schrödinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.

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A truncated shift-operator technique for the calculation of resonances in Stark systems

Cited by 10 publications

References 9 publications

Wannier–Stark resonances in optical and semiconductor superlattices

Wannier–Stark resonances in optical and semiconductor superlattices

Exceptional points in bichromatic Wannier–Stark systems

Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and crossing of resonances

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