A greedy algorithm for the identification of quantum systems

The control of quantum phenomena is a topic that has carried out many challenging problems. Among others, the Hamiltonian identification, i.e, the inverse problem associated with the unknown features of a quantum system is still an open issue. In this work, we present an algorithm that enables to design a set of selective laser fields that can be used, in a second stage, to identify unknown parameters of quantum systems.

[1]  David J. Tannor,et al.  Control of Photochemical Branching: Novel Procedures for Finding Optimal Pulses and Global Upper Bounds , 1992 .

[2]  Yvon Maday,et al.  Monotonic time-discretized schemes in quantum control , 2006, Numerische Mathematik.

[3]  H. Rabitz,et al.  HAMILTONIAN IDENTIFICATION FOR QUANTUM SYSTEMS: WELL-POSEDNESS AND NUMERICAL APPROACHES ¤ , 2007 .

[4]  Karine Beauchard,et al.  Local controllability of a 1-D Schrödinger equation , 2005 .

[5]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[6]  Herschel Rabitz,et al.  Optimal identification of Hamiltonian information by closed-loop laser control of quantum systems. , 2002, Physical review letters.

[7]  P. Bucksbaum,et al.  Controlling the shape of a quantum wavefunction , 1999, Nature.

[8]  A. Haraux,et al.  An Introduction to Semilinear Evolution Equations , 1999 .

[9]  H Rabitz,et al.  Selective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses , 2001, Science.

[10]  Julien Salomon,et al.  Convergence of the time-discretized monotonic schemes , 2007 .

[11]  Herschel Rabitz,et al.  Optimal Hamiltonian identification: The synthesis of quantum optimal control and quantum inversion , 2003 .

[12]  Julien Salomon,et al.  A monotonic method for solving nonlinear optimal control problems , 2008, 0906.3361.

[13]  H. Rabitz,et al.  Explicit Method for Parameter Identification , 1997 .

[14]  Mario Sigalotti,et al.  Controllability of the discrete-spectrum Schrödinger equation driven by an external field , 2008, 0801.4893.

[15]  Yvon Maday,et al.  Towards efficient numerical approaches for quantum control , 2002, CRM Workshop.

[16]  Neil Shenvi,et al.  Nonlinear Kinetic Parameter Identification through Map Inversion , 2002 .