Sonia G Schirmer's Research

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Control of Quantum Systems

Motivation
The main focus of my research in recent years has been in the area of control of quantum-mechanical systems. The primary motivation for the systematic study of control of quantum systems is the realization that the ability to control quantum systems is an essential prerequisite for many exciting applications ranging from control of chemical reactions to quantum computing to laser cooling of internal molecular degrees of freedom. In addition, mastery of the challenging problem of controlling quantum systems, despite their often counter-intuitive behaviour, is likely to advance our knowledge and understanding of quantum systems.

Collaborators
I have collaborated with quite a few people over the years. Recent collaborators include (NB: If I forgot to mention you and you would like to be added to this list, please forgive me and let me know.):

Daniel Oi, Tom Stace, Andrey Bychkov from CQC Cambridge,
Andrew Greentree, Jared Cole, Simon Devitt, Gaj Kandasamy and Lloyd Hollenberg from the Centre for Quantum Computer Technology and the Microanalytical Research Centre at the University of Melbourne
Allan Solomon from The Open University and the University of Paris
John Leahy from the University of Oregon
Marvin Girardeau from the University of Arizona
Herschel Rabitz from Princeton University
There are also ongoing collaborations with several departments at the MIT, as well as Oxford University, especially the Department of Materials.

Selected Publications
Monotonically convergent algorithms for optimal control field design, S. G. Schirmer, I. C. H. Pullen, in preparation
Subspace Confinement: How good is your qubit?, Simon J. Devitt, Sonia G. Schirmer, Daniel K. L. Oi, Jared H. Cole, Lloyd Hollenberg, to appear in Proceedings of Annual Conference of the Australian Physical Society (2006)
Quantum Choreography: Making Molecules Dance to Technology's Tune?, Sonia G Schirmer, to appear in Triennial Issue of Phil. Trans. R. Soc. A. (2006)
Hamiltonian engineering for quantum systems, Sonia G Schirmer, in Proceedings of the 3rd IFAC Workshop on Lagragian and Hamiltonian Methods in Nonlinear Control (Nagoya, Japan, July 2006)
Identifying a two-state Hamiltonian in the presence of decoherence, J. H. Cole, A. D. Greentree, D. K. L. Oi, S. G. Schirmer, C. J. Wellard, L. C. L. Hollenberg, Phys. Rev. A 73>, 062333 (2006); Virtual Journal of Quantum Information (July 2006).

Bohm-Aharanov type effects in dissipative atomic systems, Allan I Solomon, Sonia G Schirmer, preprint quant-ph/0512198, to appear in Proceedings of 23rd Int'l Conference on Differential Geometric Methods in Theoretical Physics (Nankai, China, Aug 20-26, 2005)
Controllability of multi-partite quantum systems and selective excitation of quantum dots, S. G. Schirmer, I. C. H. Pullen, A. I. Solomon, J. Opt. B 7, S293-S299 (2005); Special Issue on Quantum Control.
Identifying an experimental two-state Hamiltonian to arbitary accuracy, J. H. Cole, S. G. Schirmer, A. D. Greentree, C. J. Wellard, D. K. L. Oi, L. C. L. Hollenberg, Phys. Rev. A 71, 062312 (2005); Virtual Journal of Quantum Information (June 2005).
Robust charge-based qubit encoding, D. K. L. Oi, S. G. Schirmer, A. D. Greentree, T. M. Stace, Phys. Rev. B, 72, 075348 (2005); Virtual Journal of Nanoscale Science & Technology (Sep 5, 2005)
Controlled phase gate for solid-state charge-qubit architectures, S. G. Schirmer, D. K. L. Oi, A. D. Greentree, Phys. Rev. A 71, 012325 (2005); Virtual Journal of Quantum Information (Feb 2005); Virtual Journal of Nanoscale Science and Technology (Jan 31, 2005)

Experimental Hamiltonian identification for qubits subject to multiple independent control mechanisms, S. G. Schirmer, A. Kolli, D. K. L. Oi, J. H. Cole, in Proceedings of the QCMC04, American Institute of Physics. 2004.
Constraints on relaxation rates for N-level quantum systems, S. G. Schirmer, A. I. Solomon, Phys. Rev. A 70, 022107 (2004)
Experimental Hamiltonian identification for controlled two-level systems, S. G. Schirmer, A. Kolli and D. K. L. Oi, Phys. Rev. A 69, 050306 (2004); Virtual Journal of Quantum Information (June 2004)
Implementation of controlled multi-qudit operations for a solid-state quantum computer based on charge qudits , S. G. Schirmer, A. D. Greentree and D. K. L. Oi, preprint quant-ph/0305052
Maximizing the Hilbert space for a finite number of distinguishable quantum states , A. D. Greentree, S. G. Schirmer, F. Green, L. C. L. Hollenberg, A. R. Hamilton and R. C. Clark, Phys. Rev. Lett., 92, 097901 (2004); also published in Virtual Journal of Quantum Information (March 2004) and Virtual Journal of Nanoscale Science and Technology (March 15, 2004)
Orbits of quantum states and geometry of Bloch vectors for N-level systems S. G. Schirmer, T. Zhang and J V. Leahy, J. Phys. A 37, 1389 (2004)

Controllability of Quantum Systems , S. G. Schirmer, I. C. H. Pullen and A. I. Solomon, in Hamiltonian and Lagrangian Methods in Nonlinear Control (ISBN 0-08-044278-1) 2003
Dissipative Groups and the Bloch Ball A. I. Solomon and S. G. Schirmer, in Group 24: Physical and Mathematical Aspects of Symmetries (ISBN 0-75-030933-4) 2003

Criteria for reachability of states for quantum systems , S. G. Schirmer, J. V. Leahy and A. I. Solomon, J. Phys. A 35, 8551-8562 (2002)
Quantum control using sequences of simple control pulses , S. G. Schirmer, A. D. Greentree, V. Ramakrishna and H. Rabitz, J. Phys. A 35, 8315-8339 (2002)
Limitations on quantum control , A. I. Solomon and S. G. Schirmer, Int. J. Mod. Phys. B 16, 2107-2112 (2002)
Degrees of controllability for quantum systems and application to atomic systems , S. G. Schirmer, J. V. Leahy and A. I. Solomon, J. Phys. A 35, 4125-4141 (2002)
Geometric control for atomic systems , S. G. Schirmer, in Proceedings SIAM Conference on Mathematical Theory of Systems and Networks (South Bend, IN, 2002), see also www.nd.edu/~mtns/papers/20270_3.pdf.
Quantum control of dissipative systems , S. G. Schirmer, in Proceedings SIAM Conference on Mathematical Theory of Systems and Networks (South Bend, IN, 2002), see also www.nd.edu/~mtns/papers/2178_4.pdf.

Complete controllability of finite-level quantum systems , H. Fu, S. G. Schirmer and A. I. Solomon, J. Phys. A 34, 1679-1693 (2001)
Complete controllability of quantum systems , S. G. Schirmer, H. Fu and A. I. Solomon, Phys. Rev. A 63, 063410 (2001)
Laser cooling of internal molecular degrees of freedom for vibrationally hot molecules , S. G. Schirmer, Phys. Rev. A 63, 013407 (2001)
Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability , S. G. Schirmer and J. V. Leahy, Phys. Rev. A 63, 025403 (2001)
Non-reachable target states for pure-state controllable and non-controllable quantum systems , S. G. Schirmer and A. I. Solomon, in 40th IEEE CDC Proceedings (ISBN 0-7803-7063-5), 2605-2606 (2001)
Quantum control using Lie group decompositions, S. G. Schirmer, 40th IEEE CDC Proceedings (ISBN 0-7803-7063-5), 298-303 (2001)
Group-theoretical aspects of control of quantum systems , S. G. Schirmer and A. I. Solomon, in Proceedings 2nd Int'l Symposium on Quantum Theory and Symmetries (Cracow, Poland, July 2001)
Control of population inversion in presence of spontaneous emission , S. G. Schirmer, A. D. Greentree and A. V. Durrant, in Proceedings 8th Rochester Conference on Quantum Coherence (Rochester, NY, 2001)
Robust quantum memory using quantum control , A. D. Greentree, S. G. Schirmer and A. I. Solomon, Proceedings 1st Int'l Conference on Quantum Information (Rochester, NY, 2001)

Efficient algorithm for optimal control of mixed-state quantum systems , S. G. Schirmer, M. D. Girardeau and J. V. Leahy, Phys. Rev. A 61, 012101 (2000)
Laser cooling of internal molecular degrees of freedom , S. G. Schirmer, in 39th IEEE CDC Proceedings (ISBN 0-7803-6641-7), 1376-1381 (2000)
Dynamical realizability of kinematical bounds on the optimization of observables for quantum systems , J. V. Leahy and S. G. Schirmer, in 39th IEEE CDC Proceedings (ISBN 0-7803-6641-7), 1358-1363 (2000)
Kinematical bounds on the optimization of observables for quantum systems, the question of their dynamical realizability and Lie groups , S. G. Schirmer, H. Fu and A. I. Solomon, in Proceedings 23rd Colloquium on Group Theoretical Methods in Physics (Dubna, Russia, 2000)

Kinematical bounds on optimization of observables for quantum systems , M. D. Girardeau, S. G. Schirmer, J. V. Leahy and R. M. Koch, Phys. Rev. A 58, 2684-2689 (1998)

Kinematical bounds on evolution and optimization of mixed quantum states , M. D. Girardeau, M. Ina, S. G. Schirmer and T. Gulsrud, Phys. Rev. A 55, R1565-R1568 (1997)

Selected Conference Presentations
System Identification for Controlled Two-level Systems, Quantum Communication, Measurement & Computing (Glasgow, UK, July 2004)

Quantum Dot Charge Qubit with Controllable Coulomb Interaction, Quantum Communication, Measurement & Computing (Glasgow, UK, July 2004)

Controllability of Quantum Systems, 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control (Seville, Spain, April 2003)

Quantum control of dissipative systems, SIAM Conference on Mathematical Theory of Networks and Systems (South Bend, IN, Aug 2002)
Geometric control for atomic systems, SIAM Conference on Mathematical Theory of Networks and Systems (South Bend, IN, Aug 2002)

Quantum control using Lie group decompositions, 40th IEEE Conference on Decision and Control (Orlando, Florida, Dec 2001)
Non-reachable target states for pure-state controllable and non-controllable quantum systems, 40th IEEE Conference on Decision and Control (Orlando, Florida, Dec 2001)
Laser-cooling of vibrational degrees of freedom for molecules using coherent control, Euroconference on Cold Molecules and Coherent Control (Gif-sur-Yvette, France, Oct 2001)
Group theoretical aspects of control of quantum systems, International Symposium on Symmetries in Science (Bregenz, Austria, Aug 2001)
Robust quantum memory via quantum control, International Conference on Quantum Information (Rochester, NY, June 2001)

Laser cooling of internal molecular degrees of freedom, 39th IEEE Conference on Decision and Control (Sydney, Australia, Dec 2000)
Dynamical realizability of kinematical bounds, 39th IEEE Conference on Decision and Control (Sydney, Australia, Dec 2000)
Kinematical bounds on the optimization of observables, the question of their dynamical realizability and Lie groups XXIII Colloquium on Group Theoretical Methods in Physics (Dubna, Russia, Aug 2000)

Controlling the Dynamics of Quantum Systems 5th SIAM Conference on Dynamical Systems (Snowbird, Utah, May 1999)
Optimization of Observables for Quantum Systems 4th SIAM Conference on Control (Jacksonville, Florida, May 1998)

Selected Talks
Control of Quantum Systems: Theory and Applications, Applied Maths Seminar, The Open University (Milton Keynes, UK, 2001)
Control of Quantum Systems: An Overview, Physics Seminar, University of Hertfordshire (Hatfield, UK, 2001)
Group-theoretical aspects of control of quantum systems Theoretical Physics Seminar, University of Paris VI (Paris, France, 2001)
Control of quantum systems, Mathematics Colloquium, Murray State University (Murray, KY, 2001)
Laser cooling of internal molecular degrees of freedom, BEC for molecules and coherent control, Physics Seminar, The Open University (Milton-Keynes, UK, 2000)

Movies (gif)
Here are some movies for our favourite toy problems. The field movies show how the optimal pulse shape for the control field develops from the initial guess (usually random noise) as the iteration proceeds. The population movies illustrate how the evolution of the energy level populations changes as the control field is adjusted/optimized. The observable movies show how the evolution of the observable changes as the control field is adjusted in each step. Note the drastic changes in the first iteration step and the rapid convergence.
(1) Energy maximization for 4-level Morse oscillator model of hydrogen fluoride.

Pure state case: system initially in the ground state
Control field, population, observable.
Mixed state case: system initially in thermal equilibrium
Control field, population, observable.
(2) Energy maximization for a decoupled 4-level system initally in thermal equilibrium

Only transitions 1->2, 2->1 and 3->4, 4->3 permitted
Control field, population, observable.
Only transitions 1->4, 4->1 and 2->3, 3->2 permitted
Control field, population, observable.
(3) Maximization of the top level population for a 3-level system initially in the ground state

without dissipation
Control field, population, observable.
with dissipation
Control field, population, observable.

Motivation	The main focus of my research in recent years has been in the area of control of quantum-mechanical systems. The primary motivation for the systematic study of control of quantum systems is the realization that the ability to control quantum systems is an essential prerequisite for many exciting applications ranging from control of chemical reactions to quantum computing to laser cooling of internal molecular degrees of freedom. In addition, mastery of the challenging problem of controlling quantum systems, despite their often counter-intuitive behaviour, is likely to advance our knowledge and understanding of quantum systems.
Collaborators	I have collaborated with quite a few people over the years. Recent collaborators include (NB: If I forgot to mention you and you would like to be added to this list, please forgive me and let me know.): Daniel Oi, Tom Stace, Andrey Bychkov from CQC Cambridge, Andrew Greentree, Jared Cole, Simon Devitt, Gaj Kandasamy and Lloyd Hollenberg from the Centre for Quantum Computer Technology and the Microanalytical Research Centre at the University of Melbourne Allan Solomon from The Open University and the University of Paris John Leahy from the University of Oregon Marvin Girardeau from the University of Arizona Herschel Rabitz from Princeton University There are also ongoing collaborations with several departments at the MIT, as well as Oxford University, especially the Department of Materials.
Selected Publications	Monotonically convergent algorithms for optimal control field design, S. G. Schirmer, I. C. H. Pullen, in preparation Subspace Confinement: How good is your qubit?, Simon J. Devitt, Sonia G. Schirmer, Daniel K. L. Oi, Jared H. Cole, Lloyd Hollenberg, to appear in Proceedings of Annual Conference of the Australian Physical Society (2006) Quantum Choreography: Making Molecules Dance to Technology's Tune?, Sonia G Schirmer, to appear in Triennial Issue of Phil. Trans. R. Soc. A. (2006) Hamiltonian engineering for quantum systems, Sonia G Schirmer, in Proceedings of the 3rd IFAC Workshop on Lagragian and Hamiltonian Methods in Nonlinear Control (Nagoya, Japan, July 2006) Identifying a two-state Hamiltonian in the presence of decoherence, J. H. Cole, A. D. Greentree, D. K. L. Oi, S. G. Schirmer, C. J. Wellard, L. C. L. Hollenberg, Phys. Rev. A 73>, 062333 (2006); Virtual Journal of Quantum Information (July 2006). Bohm-Aharanov type effects in dissipative atomic systems, Allan I Solomon, Sonia G Schirmer, preprint quant-ph/0512198, to appear in Proceedings of 23rd Int'l Conference on Differential Geometric Methods in Theoretical Physics (Nankai, China, Aug 20-26, 2005) Controllability of multi-partite quantum systems and selective excitation of quantum dots, S. G. Schirmer, I. C. H. Pullen, A. I. Solomon, J. Opt. B 7, S293-S299 (2005); Special Issue on Quantum Control. Identifying an experimental two-state Hamiltonian to arbitary accuracy, J. H. Cole, S. G. Schirmer, A. D. Greentree, C. J. Wellard, D. K. L. Oi, L. C. L. Hollenberg, Phys. Rev. A 71, 062312 (2005); Virtual Journal of Quantum Information (June 2005). Robust charge-based qubit encoding, D. K. L. Oi, S. G. Schirmer, A. D. Greentree, T. M. Stace, Phys. Rev. B, 72, 075348 (2005); Virtual Journal of Nanoscale Science & Technology (Sep 5, 2005) Controlled phase gate for solid-state charge-qubit architectures, S. G. Schirmer, D. K. L. Oi, A. D. Greentree, Phys. Rev. A 71, 012325 (2005); Virtual Journal of Quantum Information (Feb 2005); Virtual Journal of Nanoscale Science and Technology (Jan 31, 2005) Experimental Hamiltonian identification for qubits subject to multiple independent control mechanisms, S. G. Schirmer, A. Kolli, D. K. L. Oi, J. H. Cole, in Proceedings of the QCMC04, American Institute of Physics. 2004. Constraints on relaxation rates for N-level quantum systems, S. G. Schirmer, A. I. Solomon, Phys. Rev. A 70, 022107 (2004) Experimental Hamiltonian identification for controlled two-level systems, S. G. Schirmer, A. Kolli and D. K. L. Oi, Phys. Rev. A 69, 050306 (2004); Virtual Journal of Quantum Information (June 2004) Implementation of controlled multi-qudit operations for a solid-state quantum computer based on charge qudits , S. G. Schirmer, A. D. Greentree and D. K. L. Oi, preprint quant-ph/0305052 Maximizing the Hilbert space for a finite number of distinguishable quantum states , A. D. Greentree, S. G. Schirmer, F. Green, L. C. L. Hollenberg, A. R. Hamilton and R. C. Clark, Phys. Rev. Lett., 92, 097901 (2004); also published in Virtual Journal of Quantum Information (March 2004) and Virtual Journal of Nanoscale Science and Technology (March 15, 2004) Orbits of quantum states and geometry of Bloch vectors for N-level systems S. G. Schirmer, T. Zhang and J V. Leahy, J. Phys. A 37, 1389 (2004) Controllability of Quantum Systems , S. G. Schirmer, I. C. H. Pullen and A. I. Solomon, in Hamiltonian and Lagrangian Methods in Nonlinear Control (ISBN 0-08-044278-1) 2003 Dissipative Groups and the Bloch Ball A. I. Solomon and S. G. Schirmer, in Group 24: Physical and Mathematical Aspects of Symmetries (ISBN 0-75-030933-4) 2003 Criteria for reachability of states for quantum systems , S. G. Schirmer, J. V. Leahy and A. I. Solomon, J. Phys. A 35, 8551-8562 (2002) Quantum control using sequences of simple control pulses , S. G. Schirmer, A. D. Greentree, V. Ramakrishna and H. Rabitz, J. Phys. A 35, 8315-8339 (2002) Limitations on quantum control , A. I. Solomon and S. G. Schirmer, Int. J. Mod. Phys. B 16, 2107-2112 (2002) Degrees of controllability for quantum systems and application to atomic systems , S. G. Schirmer, J. V. Leahy and A. I. Solomon, J. Phys. A 35, 4125-4141 (2002) Geometric control for atomic systems , S. G. Schirmer, in Proceedings SIAM Conference on Mathematical Theory of Systems and Networks (South Bend, IN, 2002), see also `www.nd.edu/~mtns/papers/20270_3.pdf`. Quantum control of dissipative systems , S. G. Schirmer, in Proceedings SIAM Conference on Mathematical Theory of Systems and Networks (South Bend, IN, 2002), see also `www.nd.edu/~mtns/papers/2178_4.pdf`. Complete controllability of finite-level quantum systems , H. Fu, S. G. Schirmer and A. I. Solomon, J. Phys. A 34, 1679-1693 (2001) Complete controllability of quantum systems , S. G. Schirmer, H. Fu and A. I. Solomon, Phys. Rev. A 63, 063410 (2001) Laser cooling of internal molecular degrees of freedom for vibrationally hot molecules , S. G. Schirmer, Phys. Rev. A 63, 013407 (2001) Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability , S. G. Schirmer and J. V. Leahy, Phys. Rev. A 63, 025403 (2001) Non-reachable target states for pure-state controllable and non-controllable quantum systems , S. G. Schirmer and A. I. Solomon, in 40th IEEE CDC Proceedings (ISBN 0-7803-7063-5), 2605-2606 (2001) Quantum control using Lie group decompositions, S. G. Schirmer, 40th IEEE CDC Proceedings (ISBN 0-7803-7063-5), 298-303 (2001) Group-theoretical aspects of control of quantum systems , S. G. Schirmer and A. I. Solomon, in Proceedings 2nd Int'l Symposium on Quantum Theory and Symmetries (Cracow, Poland, July 2001) Control of population inversion in presence of spontaneous emission , S. G. Schirmer, A. D. Greentree and A. V. Durrant, in Proceedings 8th Rochester Conference on Quantum Coherence (Rochester, NY, 2001) Robust quantum memory using quantum control , A. D. Greentree, S. G. Schirmer and A. I. Solomon, Proceedings 1st Int'l Conference on Quantum Information (Rochester, NY, 2001) Efficient algorithm for optimal control of mixed-state quantum systems , S. G. Schirmer, M. D. Girardeau and J. V. Leahy, Phys. Rev. A 61, 012101 (2000) Laser cooling of internal molecular degrees of freedom , S. G. Schirmer, in 39th IEEE CDC Proceedings (ISBN 0-7803-6641-7), 1376-1381 (2000) Dynamical realizability of kinematical bounds on the optimization of observables for quantum systems , J. V. Leahy and S. G. Schirmer, in 39th IEEE CDC Proceedings (ISBN 0-7803-6641-7), 1358-1363 (2000) Kinematical bounds on the optimization of observables for quantum systems, the question of their dynamical realizability and Lie groups , S. G. Schirmer, H. Fu and A. I. Solomon, in Proceedings 23rd Colloquium on Group Theoretical Methods in Physics (Dubna, Russia, 2000) Kinematical bounds on optimization of observables for quantum systems , M. D. Girardeau, S. G. Schirmer, J. V. Leahy and R. M. Koch, Phys. Rev. A 58, 2684-2689 (1998) Kinematical bounds on evolution and optimization of mixed quantum states , M. D. Girardeau, M. Ina, S. G. Schirmer and T. Gulsrud, Phys. Rev. A 55, R1565-R1568 (1997)
Selected Conference Presentations	System Identification for Controlled Two-level Systems, Quantum Communication, Measurement & Computing (Glasgow, UK, July 2004) Quantum Dot Charge Qubit with Controllable Coulomb Interaction, Quantum Communication, Measurement & Computing (Glasgow, UK, July 2004) Controllability of Quantum Systems, 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods in Nonlinear Control (Seville, Spain, April 2003) Quantum control of dissipative systems, SIAM Conference on Mathematical Theory of Networks and Systems (South Bend, IN, Aug 2002) Geometric control for atomic systems, SIAM Conference on Mathematical Theory of Networks and Systems (South Bend, IN, Aug 2002) Quantum control using Lie group decompositions, 40th IEEE Conference on Decision and Control (Orlando, Florida, Dec 2001) Non-reachable target states for pure-state controllable and non-controllable quantum systems, 40th IEEE Conference on Decision and Control (Orlando, Florida, Dec 2001) Laser-cooling of vibrational degrees of freedom for molecules using coherent control, Euroconference on Cold Molecules and Coherent Control (Gif-sur-Yvette, France, Oct 2001) Group theoretical aspects of control of quantum systems, International Symposium on Symmetries in Science (Bregenz, Austria, Aug 2001) Robust quantum memory via quantum control, International Conference on Quantum Information (Rochester, NY, June 2001) Laser cooling of internal molecular degrees of freedom, 39th IEEE Conference on Decision and Control (Sydney, Australia, Dec 2000) Dynamical realizability of kinematical bounds, 39th IEEE Conference on Decision and Control (Sydney, Australia, Dec 2000) Kinematical bounds on the optimization of observables, the question of their dynamical realizability and Lie groups XXIII Colloquium on Group Theoretical Methods in Physics (Dubna, Russia, Aug 2000) Controlling the Dynamics of Quantum Systems 5th SIAM Conference on Dynamical Systems (Snowbird, Utah, May 1999) Optimization of Observables for Quantum Systems 4th SIAM Conference on Control (Jacksonville, Florida, May 1998)
Selected Talks	Control of Quantum Systems: Theory and Applications, Applied Maths Seminar, The Open University (Milton Keynes, UK, 2001) Control of Quantum Systems: An Overview, Physics Seminar, University of Hertfordshire (Hatfield, UK, 2001) Group-theoretical aspects of control of quantum systems Theoretical Physics Seminar, University of Paris VI (Paris, France, 2001) Control of quantum systems, Mathematics Colloquium, Murray State University (Murray, KY, 2001) Laser cooling of internal molecular degrees of freedom, BEC for molecules and coherent control, Physics Seminar, The Open University (Milton-Keynes, UK, 2000)
Movies (gif)	Here are some movies for our favourite toy problems. The field movies show how the optimal pulse shape for the control field develops from the initial guess (usually random noise) as the iteration proceeds. The population movies illustrate how the evolution of the energy level populations changes as the control field is adjusted/optimized. The observable movies show how the evolution of the observable changes as the control field is adjusted in each step. Note the drastic changes in the first iteration step and the rapid convergence. (1) Energy maximization for 4-level Morse oscillator model of hydrogen fluoride. Pure state case: system initially in the ground state Control field, population, observable. Mixed state case: system initially in thermal equilibrium Control field, population, observable. (2) Energy maximization for a decoupled 4-level system initally in thermal equilibrium Only transitions 1->2, 2->1 and 3->4, 4->3 permitted Control field, population, observable. Only transitions 1->4, 4->1 and 2->3, 3->2 permitted Control field, population, observable. (3) Maximization of the top level population for a 3-level system initially in the ground state without dissipation Control field, population, observable. with dissipation Control field, population, observable.