6533b832fe1ef96bd129a3ef
RESEARCH PRODUCT
Newton algorithm for Hamiltonian characterization in quantum control
Julien SalomonMamadou NdongDominique Sugnysubject
Statistics and Probability[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC][ PHYS.QPHY ] Physics [physics]/Quantum Physics [quant-ph]Non uniquenessFOS: Physical sciencesGeneral Physics and AstronomyQuantum controlsymbols.namesake[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]Fixed time[ CHIM.OTHE ] Chemical Sciences/OtherQuantum systemNumerical testsMathematical PhysicsMathematicsQuantum PhysicsPropagatorStatistical and Nonlinear PhysicsNMRContinuation methodModeling and Simulationsymbolsinverse problemidentification02.30.Yy Control theory02.30.Tb Operator theory42.50.Ct Quantum description of interaction of light and matter; related experiments02.60.Cb Numerical simulation; solution of equations03.65.Ge Solutions of wave equations: bound states02.30.Mv Approximations and expansions[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Quantum Physics (quant-ph)Hamiltonian (quantum mechanics)[CHIM.OTHE]Chemical Sciences/OtherAlgorithmcontroldescription
We propose a Newton algorithm to characterize the Hamiltonian of a quantum system interacting with a given laser field. The algorithm is based on the assumption that the evolution operator of the system is perfectly known at a fixed time. The computational scheme uses the Crank-Nicholson approximation to explicitly determine the derivatives of the propagator with respect to the Hamiltonians of the system. In order to globalize this algorithm, we use a continuation method that improves its convergence properties. This technique is applied to a two-level quantum system and to a molecular one with a double-well potential. The numerical tests show that accurate estimates of the unknown parameters are obtained in some cases. We discuss the numerical limits of the algorithm in terms of basin of convergence and non uniqueness of the solution.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-06-12 |