Analytical solutions for laser excitation of multilevel systems in the rotating-wave approximation

Einwohner, T. H.; Wong, J.; Garrison, J. C.

doi:10.1103/physreva.14.1452

Cited by 50 publications

(13 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As (10) where the upper and lower signs correspond to d8/dt =+ tr/2T, meaning intuitive and counterintuitive pulse order. Here the functions C and 5, which depend on x, denote C =e 'cosh&, 5 =e "sinhp/p, where p=(x -tr /4)'t .…”

mentioning

confidence: 99%

Coherent population transfer via the continuum

1992

View full text Add to dashboard Cite

mentioning

confidence: 99%

Coherent population transfer via the continuum

1992

View full text Add to dashboard Cite

“…Following [3], the multilevel rotating wave approximation is done by neglecting all non-resonant termsĤ…”

Section: The Modelmentioning

confidence: 99%

“…This approximation has been introduced for two level quantum systems, and then generalized for N -level systems [3]. The deviations from this approximation for big intensities are well known and commonly described as Bloch-Siegert shifts, breaking the harmonicity of the system dynamics [4].…”

mentioning

confidence: 99%

“…The Rotating Wave Approximation (RWA) plays a major role in simplifying the quantum mechanical description of laser driven systems in the low intensity regime: it takes into account only the co-rotating field with the system and it neglects the counter-rotating part [1,2]. This approximation has been introduced for two level quantum systems, and then generalized for N -level systems [3]. The deviations from this approximation for big intensities are well known and commonly described as Bloch-Siegert shifts, breaking the harmonicity of the system dynamics [4].…”

mentioning

confidence: 99%

“…The paper is structured as follow: In Section I we present the model studied and for the sake of completeness we review the work of Einwohner et al on the generalized N -level RWA [3] and in Section II we review the algorithm based on graph theory to recast systems in a time-independent form. Section III presents the analytic solutions of the state-to-state transfer in the two-level system and a special case of the N -level system while numerical results are presented in Section IV.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Quantum optimal control within the rotating-wave approximation

et al. 2015

View full text Add to dashboard Cite

We study the interplay between rotating wave approximation and optimal control. In particular, we show that for a wide class of optimal control problems one can choose the control field such that the Hamiltonian becomes time-independent under the rotating wave approximation. Thus, we show how to recast the functional minimization defined by the optimal control problem into a simpler multi-variable function minimization. We provide the analytic solution to the state-to-state transfer of the paradigmatic two-level system and to the more general star configuration of an N -level system. We demonstrate numerically the usefulness of this approach in the more general class of connected acyclic N -level systems with random spectra. Finally, we use it to design a protocol to entangle Rydberg via constant laser pulses atoms in an experimentally relevant range of parameters.The Rotating Wave Approximation (RWA) plays a major role in simplifying the quantum mechanical description of laser driven systems in the low intensity regime: it takes into account only the co-rotating field with the system and it neglects the counter-rotating part [1,2]. This approximation has been introduced for two level quantum systems, and then generalized for N -level systems [3]. The deviations from this approximation for big intensities are well known and commonly described as Bloch-Siegert shifts, breaking the harmonicity of the system dynamics [4]. Finally, a more general description is given by Floquet theory that allows to treat periodically driven systems [5].Developing error-free protocols for the manipulation of quantum systems -also along the development of quantum technologies but not restricted to them -is one of the major challenges in contemporary research in atom and molecular physics [6]. During the last decades, an increasing contribution in such effort has come from the exploitation of Quantum Optimal Control (QOC), the search for an optimal control pulse to perform a given system manipulation [7]. Methods to solve QOC problems have been developed [8][9][10] and experiments have shown the great benefit from them, see e.g. [11][12][13][14][15]. We have now deep theoretical understanding of QOC, in particular about the possibilities and hurdles to control quantum systems [16][17][18], and we even start to understand the complexity of QOC problems [19,20]. Graph theory concepts have been exploited to attack a question that lies at the heart of controllability studies: given a Hamiltonian depending on some time dependent tunable control field, is it possible to dynamically connect every pair of arbitrary initial and final state, i.e. it is possible to realize every possible state-to-state transfer? A widely used criterion to answer to this question is via dynamical Lie-Algebras [18], while here we make use of a different criterion based on graph theory: Turinici and Rabitz showed that if the graph corresponding to the control Hamiltonian is connected and the spacings of the eigenvalues of the uncontrolled part of the Hamiltonian ar...

show abstract

States in a Weak—Near-Resonant Laser

Mittleman

1982

Introduction to the Theory of Laser-Atom Interactions

View full text Add to dashboard Cite

Analytical solutions for laser excitation of multilevel systems in the rotating-wave approximation

Cited by 50 publications

References 6 publications

Coherent population transfer via the continuum

Coherent population transfer via the continuum

Quantum optimal control within the rotating-wave approximation

States in a Weak—Near-Resonant Laser

Contact Info

Product

Resources

About