Controllability of the discrete-spectrum Schrödinger equation driven by an external field

Chambrion, Thomas; Mason, Paolo; Sigalotti, Mario; Boscain, Ugo

doi:10.1016/j.anihpc.2008.05.001

Cited by 142 publications

(216 citation statements)

References 33 publications

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“…[107]. Moreover, it appears to be promising for two reasons -it does not rely on a priori assumptions on the reduced dynamics, and most likely it will benefit from recent progress in the controllability of infinite-dimensional systems [108][109][110][111].…”

Section: A Controllability Of Open Quantum Systemsmentioning

confidence: 99%

Controlling open quantum systems: tools, achievements, and limitations

Koch

2016

J. Phys.: Condens. Matter

250

222

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The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to preserve the relevant nonclassical features at the level of device operation. A major obstacle is decoherence which is caused by interaction with the environment. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. We review here recent advances in optimal control methodology that allow for tackling typical tasks in device operation for open quantum systems and discuss examples of relaxation-optimized dynamics. Optimal control theory is also a useful tool to exploit the environment for control. We discuss examples and point out possible future extensions.

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Section: A Controllability Of Open Quantum Systemsmentioning

confidence: 99%

Controlling open quantum systems: tools, achievements, and limitations

Koch

2016

J. Phys.: Condens. Matter

250

222

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“…A second strategy consists in deducing approximate controllability in regular spaces (containing H 3 ) from exact controllability results in infinite time by Nersesyan and Nersisyan [32] A third strategy, due to Chambrion, Mason, Sigalotti, and Boscain [16], relies on geometric techniques for the controllability of the Galerkin approximations. It proves (under appropriate assumptions on V and µ) the approximate controllability of (7) in L 2 , with piece-wise constant controls.…”

Section: Local Exact Results In 1dmentioning

confidence: 99%

Local exact controllability of the 2D-Schrödinger-Poisson system

Beauchard¹,

Laurent²

2017

Journal De L’École Polytechnique — Mathématiques

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International audienceIn this article, we investigate the exact controllability of the 2D-Schrödinger-Poisson system, which couples a Schrödinger equation on a bounded domain of R 2 with a Poisson equation for the electrical potential. The control acts on the system through a Neumann boundary condition on the potential, locally distributed on the boundary of the space domain. We prove several results, with or without nonlinearity and with dierent boundary conditions on the wave function, of Dirichlet type or of Neumann type

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“…For approximate controllability results via Lyapunov methods, see [20], [19]. Notice that except for the results given in [10], most of the controllability results are obtained for systems in the form…”

Section: Introductionmentioning

confidence: 99%

“…For exact controllability results for a one-dimensional well of potential see [5]. For approximate controllability results for discrete spectrum, via Galerkin approximations, see [10]. For approximate controllability results via Lyapunov methods, see [20], [19].…”

Section: Introductionmentioning

confidence: 99%

Motion planning in quantum control via intersection of eigenvalues

Boscain

Chittaro

Mason

et al. 2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper we consider the problem of inducing a transition in a controlled quantum mechanical system whose spectrum loses simplicity for some values of the control. We study the situation in which the Hamiltonian of the system is real, and we are in presence of two controls. In this case, eigenvalue crossings are generically conical. Adiabatic approximation is used to decouple a finite dimensional subsystem from the original one (usually infinite dimensional).The main advantage of this method is that as a byproduct of the controllability result it permits to get an explicit expression of the controls. Moreover it may be used in the case in which the dependence of the Hamiltonian from the controls is non-linear, for which at the moment, no other method works.In this paper we study the basic block of this controllability method, that is a two by two system whose spectrum presents a conical intersection. We show how to control exactly this system with a control strategy that can be slowed down. The possibility of slowing down the control law is essential to obtain an adiabatic decoupling from the rest of the system with an arbitrary precision.

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Controllability of the discrete-spectrum Schrödinger equation driven by an external field

Cited by 142 publications

References 33 publications

Controlling open quantum systems: tools, achievements, and limitations

Controlling open quantum systems: tools, achievements, and limitations

Local exact controllability of the 2D-Schrödinger-Poisson system

Motion planning in quantum control via intersection of eigenvalues

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