Degrees of controllability for quantum systems and application to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions for each type of controllability are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.

[1]  Ramakrishna,et al.  Controllability of molecular systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[2]  S. Glaser,et al.  Unitary bounds and controllability of quantum evolution in NMR spectroscopy , 1999 .

[3]  Herschel Rabitz,et al.  A RAPID MONOTONICALLY CONVERGENT ITERATION ALGORITHM FOR QUANTUM OPTIMAL CONTROL OVER THE EXPECTATION VALUE OF A POSITIVE DEFINITE OPERATOR , 1998 .

[4]  A. I. Solomon,et al.  Complete controllability of quantum systems , 2000, quant-ph/0010031.

[5]  A. I. Solomon,et al.  Complete controllability of finite-level quantum systems , 2001 .

[6]  J. F. Poyatos,et al.  Quantum Reservoir Engineering with Laser Cooled Trapped Ions. , 1996, Physical review letters.

[7]  H. Rabitz.  Ramifications of Feedback for Control of Quantum Dynamics Feedback for Control of Quantum Dynamics , 1997 .

[8]  Seth Lloyd,et al.  Quantum feedback with weak measurements , 1999, quant-ph/9905064.

[9]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

[10]  K. Jacobs,et al.  FEEDBACK CONTROL OF QUANTUM SYSTEMS USING CONTINUOUS STATE ESTIMATION , 1999 .

[11]  H. Sussmann,et al.  Control systems on Lie groups , 1972 .

[12]  Sophie Schirmer,et al.  KINEMATICAL BOUNDS ON OPTIMIZATION OF OBSERVABLES FOR QUANTUM SYSTEMS , 1998 .

[13]  Navin Khaneja,et al.  Cartan decomposition of SU(2n) and control of spin systems , 2001 .

[14]  S. Schirmer.  Laser cooling of internal molecular degrees of freedom for vibrationally hot molecules , 2000 .

[15]  Kompa,et al.  Whither the future of controlling quantum phenomena? , 2000, Science.

[16]  Ramakrishna,et al.  Relation between quantum computing and quantum controllability. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[17]  Gabriel Turinici,et al.  Contrôlabilité exacte de la population des états propres dans les systèmes quantiques bilinéaires , 2000 .

[18]  Herschel Rabitz,et al.  Quantum wavefunction controllability , 2001 .

[19]  Faraday Discuss , 1985 .

[20]  S. G. Schirmer,et al.  Limits of control for quantum systems: Kinematical bounds on the optimization of observables and the question of dynamical realizability , 2001 .

[21]  H. Rabitz,et al.  Explicit generation of unitary transformations in a single atom or molecule , 2000 .

[22]  Herschel Rabitz,et al.  Monotonically convergent algorithm for quantum optimal control with dissipation , 1999 .

[23]  S. G. Schirmer,et al.  Efficient Algorithm for Optimal Control of Mixed-State Quantum Systems , 1999 .

[24]  Herschel Rabitz,et al.  Quantum control by decompositions of SU(2) , 2000 .

[25]  Hideo Mabuchi,et al.  Quantum feedback control and classical control theory , 1999, quant-ph/9912107.

[26]  V. Ramakrishna.  Control of molecular systems with very few phases , 2001 .

[27]  David J. Tannor,et al.  Laser cooling of internal degrees of freedom. II , 1997 .

[28]  David J. Tannor,et al.  Laser cooling of internal degrees of freedom of molecules by dynamically trapped states , 1999 .

[29]  D. Montgomery,et al.  Transformation Groups of Spheres , 1943 .

[30]  Optimal control of quantum dynamics: a new theoretical approach , 2000, physics/0306170.

[31]  Yukiyoshi Ohtsuki,et al.  QUANTUM CONTROL OF NUCLEAR WAVE PACKETS BY LOCALLY DESIGNED OPTIMAL PULSES , 1998 .

[32]  Herschel Rabitz,et al.  Noniterative algorithms for finding quantum optimal controls , 1999 .