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

Abstract

We prove approximate controllability of the bilinear Schrödinger 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 to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials.

References in corpus (2)

• Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field
• On finite-dimensional projections of distributions for solutions of randomly forced PDE's

Cited by in corpus (57)

• Training Schrödinger's cat: quantum optimal control
• Quantum control of molecular rotation
• Controlling open quantum systems: Tools, achievements, and limitations
• Controllability issues for continuous-spectrum systems and ensemble controllability of Bloch Equations
• Lyapunov control of a quantum particle in a decaying potential
• A weak spectral condition for the controllability of the bilinear Schrödinger equation with application to the control of a rotating planar molecule
• Finite Controllability of Infinite-Dimensional Quantum Systems
• Periodic excitations of bilinear quantum systems
• Approximate controllability, exact controllability, and conical eigenvalue intersections for quantum mechanical systems
• Introduction to Theoretical and Experimental aspects of Quantum Optimal Control
• Complete Controllability Despite Degeneracy: Quantum Control of Enantiomer-Specific State Transfer in Chiral Molecules
• Controlling Several Atoms in a Cavity
• Simultaneous local exact controllability of 1D bilinear Schrödinger equations
• Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications
• Explicit approximate controllability of the Schrödinger equation with a polarizability term
• Lie algebra for rotational subsystems of a driven asymmetric top
• Regular propagators of bilinear quantum systems
• Quantum Control of Infinite Dimensional Many-Body Systems
• Quantum Control and Representation Theory
• Models and Feedback Stabilization of Open Quantum Systems
• Quantum control of ro-vibrational dynamics and application to light-induced molecular chirality
• Computing solutions of Schrödinger equations on unbounded domains- On the brink of numerical algorithms
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Semi-global weak stabilization of bilinear Schrödinger equations
• Quantum Control at the Boundary
• Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls
• On the problem of quantum control in infinite dimensions
• Local controllability of 1D Schrödinger equations with bilinear control and minimal time
• Local controllability of the bilinear 1D Schr{ö}dinger equation with simultaneous estimates
• A remark on the attainable set of the Schrödinger equation
• Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
• Optimal bilinear control of Gross-Pitaevskii equations
• On global approximate controllability of a quantum particle in a box by moving walls
• Controllability of the Jaynes-Cummings-Hubbard model
• Quantum control of "quantum triple collisions" in a maximally symmetric three-body Coulomb problem
• Small-Time Local Controllability of the multi-input bilinear Schrödinger equation thanks to a quadratic term
• Superexponential stabilizability of evolution equations of parabolic type via bilinear control
• Local exact controllability of a 1D Bose-Einstein condensate in a time-varying box
• Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity
• Reachability, Coolability, and Stabilizability of Open Markovian Quantum Systems with Fast Unitary Control
• Rapid Stabilization of a Linearized Bilinear $1-D$ Schrödinger Equation
• On the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space
• Controllability of the bilinear Schrödinger equation with several controls and application to a 3D molecule
• Quantum control in infinite dimensions and Banach-Lie algebras: Pure point spectrum
• Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations
• On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control
• Approximate controllability of the Schrödinger Equation with a polarizability term in higher Sobolev norms
• Energy Estimates for Low Regularity Bilinear Schrödinger Equations
• Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues
• Generic controllability properties for the bilinear Schrödinger equation
• An obstruction to small-time controllability of the bilinear Schr{ö}dinger equation
• Global approximate controllability of quantum systems by form perturbations and applications
• Global exact controllability of a 1D Schrödinger equations with a polarizability term
• Quantum Control at the Boundary: an application to quantum circuits
• Small-time local controllability of the bilinear Schrödinger equation, despite a quadratic obstruction, thanks to a cubic term
• Controllability of bilinear quantum systems in explicit times via explicit control fields
• Bilinear control of discrete spectrum Schrödinger operators