Related papers: Single-input perturbative control of a quantum sym…
We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schr\"odinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability,…
We show the approximate rotational controllability of a polar linear molecule by means of three nonresonant linear polarized laser fields. The result is based on a general approximate controllability result for the bilinear Schr\"odinger…
We study both the classical and quantum rotational dynamics of an asymmetric top molecule, controlled through three orthogonal electric fields that interact with its dipole moment. The main difficulties in studying the controllability of…
In this paper we prove an approximate controllability result for the bilinear Schr\"odinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schr\"odinger operator than those…
We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schr\"odinger equation. The first part is a quick presentation of some of the…
We prove approximate controllability of the bilinear Schr\"odinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and…
In this paper we study the controllability problem for a symmetric-top molecule, both for its classical and quantum rotational dynamics. The molecule is controlled through three orthogonal electric fields interacting with its electric…
We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with…
In this paper we study the error in the approximate simultaneous controllability of the bilinear Schrodinger equation. We provide estimates based on a tracking algorithm for general bilinear quantum systems and on the study of the finite…
We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric field (the control). We prove the controllability of this system, in any positive time, locally…
We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…
Quantum tracking control aims to identify applied fields to steer the expectation values of particular observables along desired paths in time. The associated temporal fields can be identified by inverting the underlying dynamical equations…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
The bilinear control problem of the Schr\"odinger equation $i\frac{\partial}{\partial t}\psi(t)$ $=(A+u(t) B)\psi(t)$, where $u(t)$ is the control function, is investigated through topological irreducibility of the set…
In [14] Duca and Nersesyan proved a small-time controllability property of nonlinear Schr\"odinger equations on a d-dimensional torus $\mathbb{T}^d$. In this paper we study a similar property, in the linear setting, starting from a closed…
We consider the problem of steering control for the systems of one spin 1/2 particle and two interacting homonuclear spin 1/2 particles in an electro-magnetic field. The describing models are bilinear systems whose state varies on the Lie…
We systematically derive a linear quantum collision operator for the spinorial Wigner transport equation from the dynamics of a composite quantum system. For suitable two particle interaction potentials, the particular matrix form of the…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…