Adaptive coherent control using the von Neumann basis.

Recently we introduced the von Neumann representation as a joint time-frequency description for femtosecond laser pulses. Here we show that the von Neumann basis can be implemented into an evolutionary algorithm for adaptive optimization in coherent control. We perform simulations that demonstrate the efficiency compared to other parametrizations in the frequency domain. We also illustrate pulse-shape simplification by basis-function reduction. Essential structures using the von Neumann basis are retained without losing control performance significantly. In an optical demonstration experiment we show the practicality by producing double pulses with a given time separation. Adaptive control in time-frequency space will be especially valuable for quantum systems requiring specific transition frequencies at definite times.

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

[2]  T. Baumert,et al.  Femtosecond strong-field quantum control with sinusoidally phase-modulated pulses , 2006 .

[3]  D Yelin,et al.  Adaptive femtosecond pulse compression. , 1997, Optics letters.

[4]  Herschel Rabitz,et al.  Incorporating physical implementation concerns into closed loop quantum control experiments , 2000 .

[5]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

[6]  Analysis of femtosecond quantum control mechanisms with colored double pulses , 2006 .

[7]  B. Lavorel,et al.  Pulse trains produced by phase-modulation of ultrashort optical pulses: tailoring and characterization. , 2004, Optics express.

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

[9]  B. Shore,et al.  Coherent population transfer among quantum states of atoms and molecules , 1998 .

[10]  Rick Trebino,et al.  Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating , 1997 .

[11]  L. González,et al.  Deciphering the Reaction Dynamics Underlying Optimal Control Laser Fields , 2003, Science.

[12]  Jianshu Cao,et al.  MOLECULAR PI PULSE FOR TOTAL INVERSION OF ELECTRONIC STATE POPULATION , 1998 .

[13]  T. Brixner,et al.  Experimental implementation of ultrashort laser pulses in the von Neumann picture , 2008 .

[14]  Stuart A. Rice,et al.  Control of selectivity of chemical reaction via control of wave packet evolution , 1985 .

[15]  U. Gaubatz,et al.  Population switching between vibrational levels in molecular beams , 1988 .

[16]  Gerber,et al.  Femtosecond time-resolved molecular multiphoton ionization: The Na2 system. , 1991, Physical review letters.

[17]  T. Brixner,et al.  Accurate and efficient implementation of the von Neumann representation for laser pulses with discrete and finite spectra , 2009 .

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

[19]  Vladislav V. Yakovlev,et al.  Feedback quantum control of molecular electronic population transfer , 1997 .

[20]  R. de Vivie-Riedle,et al.  Modified ant-colony-optimization algorithm as an alternative to genetic algorithms , 2009 .

[21]  A. Perelomov.  On the completeness of a system of coherent states , 1971, math-ph/0210005.

[22]  J. Neumann.  Die Eindeutigkeit der Schrödingerschen Operatoren , 1931 .

[23]  Yakovlev,et al.  Quantum Control of Wave Packet Evolution with Tailored Femtosecond Pulses. , 1995, Physical review letters.

[24]  Paul Brumer,et al.  Control of unimolecular reactions using coherent light , 1986 .

[25]  Herschel Rabitz,et al.  Revealing spectral field features and mechanistic insights by control pulse cleaning , 2005 .

[26]  H. Rabitz,et al.  Coherent learning control of vibrational motion in room temperature molecular gases , 2001 .

[27]  Florian Langhojer,et al.  Gaining mechanistic insight from closed loop learning control: the importance of basis in searching the phase space. , 2005, The Journal of chemical physics.

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

[29]  G. Gerber,et al.  Quantum control of gas-phase and liquid-phase femtochemistry. , 2003, Chemphyschem : a European journal of chemical physics and physical chemistry.

[30]  T. Brixner,et al.  Molecular quantum control landscapes in von Neumann time-frequency phase space. , 2010, The Journal of chemical physics.

[31]  T. Feurer,et al.  Understanding optimal control results by reducing the complexity , 2005 .

[32]  G. Gerber,et al.  The von Neumann picture: a new representation for ultrashort laser pulses. , 2007, Optics express.

[33]  Yaron Silberberg,et al.  Coherent quantum control of two-photon transitions by a femtosecond laser pulse , 1998, Nature.

[34]  J. Paye,et al.  The chronocyclic representation of ultrashort light pulses , 1992 .

[35]  T. Hornung,et al.  Optimal control of molecular states in a learning loop with a parameterization in frequency and time domain , 2000 .

[36]  Yin,et al.  Interference between optical transitions. , 1990, Physical review letters.

[37]  Vladislav V. Yakovlev,et al.  Quantum Control of Population Transfer in Green Fluorescent Protein by Using Chirped Femtosecond Pulses , 1998 .

[38]  A. H. Zewail,et al.  Femtosecond laser control of a chemical reaction , 1992, Nature.

[39]  D. Zeidler,et al.  Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback , 2000 .

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

[41]  N. Damrauer,et al.  General method for the dimension reduction of adaptive control experiments. , 2006, The journal of physical chemistry. A.

[42]  Š. Vajda,et al.  One parameter fs-pulse form control on NaK and Na2K , 2003 .

[43]  H. Rabitz,et al.  Transformations to diagonal bases in closed-loop quantum learning control experiments. , 2005, The Journal of chemical physics.

[44]  R. de Vivie-Riedle,et al.  Multi-objective genetic algorithm optimization of 2D- and 3D-Pareto fronts for vibrational quantum processes , 2009 .

[45]  Stefan M. Weber,et al.  Application of parametric time and frequency domain shaping , 2005 .

[46]  T. Baumert,et al.  Photoelectron angular distributions from strong-field coherent electronic excitation , 2009 .

[47]  Gustav Gerber,et al.  Femtosecond quantum control of molecular dynamics in the condensed phase. , 2007, Physical chemistry chemical physics : PCCP.

[48]  T. Baumert,et al.  Femtosecond pulse shaping by an evolutionary algorithm with feedback , 1997 .

[49]  C. Shank,et al.  Selective excitation of vibrational wave packet motion using chirped pulses. , 1995, Physical review letters.