Analytic Controllability of Time-Dependent Quantum Control Systems

Details Analytic Controllability of Time-Dependent Quantum Control Systems Analytic Controllability of Time-Dependent Quantum Control Systems

2004-09-22

arxiv.org/abs/quant-ph/0409147v1

Physics

Quantum Physics

13 pages

Scientific paper

10.1063/1.1867979

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.

Affiliated with

Also associated with

No associations

Rating

Analytic Controllability of Time-Dependent Quantum Control Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analytic Controllability of Time-Dependent Quantum Control Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytic Controllability of Time-Dependent Quantum Control Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-442808