On the diversity of multiple optimal controls for quantum systems

This study presents simulations of optimal field-free molecular alignment and rotational population transfer (starting from the J = 0 rotational ground state of a diatomic molecule), optimized by means of laser pulse shaping guided by evolutionary algorithms. Qualitatively different solutions are obtained that optimize the alignment and population transfer efficiency to the maximum extent that is possible given the existing constraints on the optimization due to the finite bandwidth and energy of the laser pulse, the finite degrees of freedom in the laser pulse shaping and the evolutionary algorithm employed. The effect of these constraints on the optimization process is discussed at several levels, subject to theoretical as well as experimental considerations. We show that optimized alignment yields can reach extremely high values, even with severe constraints being present. The breadth of optimal controls is assessed, and a correlation is found between the diversity of solutions and the difficulty of the problem. In the pulse shapes that optimize dynamic alignment we observe a transition between pulse sequences that maximize the initial population transfer from J = 0 to J = 2 and pulse sequences that optimize the transfer to higher rotational levels.

[1]  Herschel A Rabitz,et al.  Quantum Optimally Controlled Transition Landscapes , 2004, Science.

[2]  Yongwei Zhang,et al.  Controlling rotational state distributions using two-pulse stimulated Raman excitation , 2007 .

[3]  H. Rabitz,et al.  Photonic reagent control of dynamically homologous quantum systems. , 2007, The Journal of chemical physics.

[4]  Ofer M. Shir,et al.  Gaining Insights into Laser Pulse Shaping by Evolution Strategies , 2007, IWINAC.

[5]  A. Weiner.  Femtosecond pulse shaping using spatial light modulators , 2000 .

[6]  H. Stapelfeldt,et al.  Alignment enhancement of a symmetric top molecule by two short laser pulses , 2006 .

[7]  M. Shapiro,et al.  Coherent Control of Atomic, Molecular, and Electronic Processes , 2000 .

[8]  Herschel Rabitz,et al.  Laboratory observation of quantum control level sets , 2006 .

[9]  Ofer M. Shir,et al.  Learning the Complete-Basis-Functions Parameterization for the Optimization of Dynamic Molecular Alignment by ES , 2006, IDEAL.

[10]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[11]  Marcus Motzkus,et al.  Quantum control of energy flow in light harvesting , 2002, Nature.

[12]  H. Stapelfeldt,et al.  Aligning molecules with intense nonresonant laser fields , 1999 .

[13]  H. Rabitz,et al.  Molecular alignment by trains of short laser pulses. , 2003, Physical review letters.

[14]  H. Rabitz,et al.  Enhanced molecular alignment by short laser pulses , 2004 .

[15]  Joshua Vaughan,et al.  Analysis of replica pulses in femtosecond pulse shaping with pixelated devices. , 2006, Optics express.

[16]  Ofer M. Shir,et al.  Niche Radius Adaptation in the CMA-ES Niching Algorithm , 2006, PPSN.

[17]  Gerber,et al.  Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses , 1998, Science.

[18]  Emilio Corchado,et al.  Intelligent Data Engineering and Automated Learning - IDEAL 2006, 7th International Conference, Burgos, Spain, September 20-23, 2006, Proceedings , 2006, IDEAL.

[19]  Gustav Gerber,et al.  Femtosecond pump-shaped-dump quantum control of retinal isomerization in bacteriorhodopsin , 2006 .

[20]  M. Vrakking,et al.  Experimental observation of revival structures in picosecond laser-induced alignment of I2. , 2001, Physical review letters.

[21]  N. Vitanov,et al.  Laser-induced population transfer by adiabatic passage techniques. , 2001, Annual review of physical chemistry.

[22]  G. Gerber,et al.  Photoselective adaptive femtosecond quantum control in the liquid phase , 2001, Nature.

[23]  J. Levesque,et al.  Tomographic imaging of molecular orbitals , 2004, Nature.

[24]  A. Rothman,et al.  Exploring the level sets of quantum control landscapes (9 pages) , 2006 .

[25]  I. Christov,et al.  Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays , 2000, Nature.

[26]  Ofer M. Shir,et al.  Evolutionary algorithms in the optimization of dynamic molecular alignment , 2006 .

[27]  P. Johnsson,et al.  Direct determination of the sign of the NO dipole moment. , 2007, Physical review letters.

[28]  Bruno Lavorel,et al.  Optimization of field-free molecular alignment by phase-shaped laser pulses , 2007 .

[29]  D. Pinkham,et al.  Optimizing dynamic alignment in room temperature CO , 2007 .

[30]  M. Vrakking,et al.  Revival structures in picosecond laser-induced alignment of I2 molecules. II. Numerical modeling , 2002 .

[31]  M. Vrakking,et al.  Control of the production of highly charged ions in femtosecond-laser cluster fragmentation , 2004 .

[32]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

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

[34]  Nikolaus Hansen,et al.  Step-Size Adaption Based on Non-Local Use of Selection Information , 1994, PPSN.

[35]  J. Mauritsson,et al.  Attosecond pulse trains generated using two color laser fields , 2006 .

[36]  Ofer M. Shir,et al.  Niching in Evolution Strategies and Its Application to Laser Pulse Shaping , 2005, Artificial Evolution.

[37]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[38]  Stuart A. Rice,et al.  Coherent Pulse Sequence Control of Product Formation in Chemical Reactions , 2007 .

[39]  Henrik Stapelfeldt,et al.  Colloquium: Aligning molecules with strong laser pulses , 2003 .

[40]  Friedrich,et al.  Alignment and trapping of molecules in intense laser fields. , 1995, Physical review letters.

[41]  T. Kanai,et al.  Quantum interference during high-order harmonic generation from aligned molecules , 2005, Nature.

[42]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[43]  Herschel Rabitz,et al.  Mechanistic analysis of optimal dynamic discrimination of similar quantum systems , 2004 .