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.
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.
ENGLISH ABSTRACT: We present here a new generalized Time-Frequency-Represenation (TFR) for use in describing ultra-fast laser pulses. The TFR is developed in terms of Fourier- Hermite-Gauss (FHG) polynomials on a von Neumann TFR lattice, by expanding the lattice in a third dimension, thus forming a lattice cube. The temporal and spectral coefficients of the Hermite-Gauss (HG) clearly are inherently functionally Fourier transform invariant. The enhanced numerical complexity of the FHG TFR is greatly reduced by exploiting the translation property of Hermite polynomials by means of Pascal matrices. Although the new FHG TFR represents an over complete basis set, it can be reduced by a subset selection to a complete basis. This method and the accompanying overlap integral is then developed and the complex orthogonality and similarity of the temporal and spectral overlap integral matrices is then analytically proved. Numerically the Pascal matrices are unstable. The new two correlation FHG TFR lattice cubes present an improvement on the traditional TFRs in that they have the advantage that it is unnecessary to compute the undesirable inverse overlap matrix to reconstruct the signal, temporally and spectrally, i.e. they contain all the information necessary to reconstruct the signal. It is then proven that it is a digital requirement to double the original proposed bandwidths of the signal inputs, here and also for the von Neumann TFR. The Hermite-Gauss polynomials correspond to the number states {nk} of the Glauber-Sudarshan coherent states in Fock space. A classical correspondence analogy between Glauber-Sudarshan coherent states in Fock space and the temporal FHG TFR is then considered under certain conditions and thus allows for a comparison of the amplitudes between the two decompositions for each kkk = !k/c, culminating in an optimization procedure to determine a “classical” coherent state correlation TFR. Application simulation results of quantum coherent control of IR ultra-short laser pulse interaction with octahedral molecules utilizing an optimal genetic algorithm are presented. A representative shaped laser pulse is used throughout to compare various TFRs.
Coherent control of quantum phenomena can be achieved by using phase- and amplitude modulated laser pulses. With a self-learning loop, which combines a femtosecond pulse shaper, an optimization algorithm and an experimental feedback signal, it is possible to automatically steer the interaction between system and electric field. This approach allows control even without any knowledge of the Hamiltonian. We have successfully implement this learning loop for the coherent control of the nonresonant two-photon excitation in sodium. New solutions for 'bright' and 'dark' pulses could be designed for this two-photon resonance without previous knowledge of the resonances. In a further experiment we combined the self-learning loop with degenerate four-wave-mixing spectroscopy in order to study the influence of phase and amplitude modulated pulses on the molecular FWM response of the prototype system K2. The obtained control pulses typically show a complex structure which hides the responsible physical mechanism. In order to extract the applied mechanism the concept of parameterization has been introduced which allows the learning algorithm to optimize already known control processes. Therefore the control of vibrational wavepacket motion in the electronic ground and excited state could be attributed to chirped pulse excitation, impulsive Raman excitation by pulse trains and phase-related double pulses representing the well-known Tannor-Rice-Kosloff control scheme.
Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. Among numerous theoretical insights and technological improvements that produced the present state-of-the-art in quantum control, there have been several breakthroughs of foremost importance. On the technology side, the current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. On the theory side, the two most critical insights were (i) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (ii) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control (AFC), which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in AFC experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. AFC of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control designs in experimental realizations and real-time quantum feedback control. The paper concludes with a perspective of open research directions that are likely to attract significant attention in the future.
Control of quantum phenomena has grown from a dream to a burgeoning field encompassing wide-ranging experimental and theoretical activities. Theoretical research in this area primarily concerns identification of the principles for controlling quantum phenomena, the exploration of new experimental applications and the development of associated operational algorithms to guide such experiments. Recent experiments with adaptive feedback control span many applications including selective excitation, wave packet engineering and control in the presence of complex environments. Practical procedures are also being developed to execute real-time feedback control considering the resultant back action on the quantum system. This focus issue includes papers covering many of the latest advances in the field. Focus on Quantum Control Contents Control of quantum phenomena: past, present and future Constantin Brif, Raj Chakrabarti and Herschel Rabitz Biologically inspired molecular machines driven by light. Optimal control of a unidirectional rotor Guillermo Pérez-Hernández, Adam Pelzer, Leticia González and Tamar Seideman Simulating quantum search algorithm using vibronic states of I2 manipulated by optimally designed gate pulses Yukiyoshi Ohtsuki Efficient coherent control by sequences of pulses of finite duration Götz S Uhrig and Stefano Pasini Control by decoherence: weak field control of an excited state objective Gil Katz, Mark A Ratner and Ronnie Kosloff Multi-qubit compensation sequences Y Tomita, J T Merrill and K R Brown Environment-invariant measure of distance between evolutions of an open quantum system Matthew D Grace, Jason Dominy, Robert L Kosut, Constantin Brif and Herschel Rabitz Simplified quantum process tomography M P A Branderhorst, J Nunn, I A Walmsley and R L Kosut Achieving 'perfect' molecular discrimination via coherent control and stimulated emission Stephen D Clow, Uvo C Holscher and Thomas C Weinacht A convenient method to simulate and visually represent two-photon power spectra of arbitrarily and adaptively shaped broadband laser pulses M A Montgomery and N H Damrauer Accurate and efficient implementation of the von Neumann representation for laser pulses with discrete and finite spectra Frank Dimler, Susanne Fechner, Alexander Rodenberg, Tobias Brixner and David J Tannor Coherent strong-field control of multiple states by a single chirped femtosecond laser pulse M Krug, T Bayer, M Wollenhaupt, C Sarpe-Tudoran, T Baumert, S S Ivanov and N V Vitanov Quantum-state measurement of ionic Rydberg wavepackets X Zhang and R R Jones On the paradigm of coherent control: the phase-dependent light-matter interaction in the shaping window Tiago Buckup, Jurgen Hauer and Marcus Motzkus Use of the spatial phase of a focused laser beam to yield mechanistic information about photo-induced chemical reactions V J Barge, Z Hu and R J Gordon Coherent control of multiple vibrational excitations for optimal detection S D McGrane, R J Scharff, M Greenfield and D S Moore Mode selectivity with polarization shaping in the mid-IR David B Strasfeld, Chris T Middleton and Martin T Zanni Laser-guided relativistic quantum dynamics Chengpu Liu, Markus C Kohler, Karen Z Hatsagortsyan, Carsten Muller and Christoph H Keitel Continuous quantum error correction as classical hybrid control Hideo Mabuchi Quantum filter reduction for measurement-feedback control via unsupervised manifold learning Anne E B Nielsen, Asa S Hopkins and Hideo Mabuchi Control of the temporal profile of the local electromagnetic field near metallic nanostructures Ilya Grigorenko and Anatoly Efimov Laser-assisted molecular orientation in gaseous media: new possibilities and applications Dmitry V Zhdanov and Victor N Zadkov Optimization of laser field-free orientation of a state-selected NO molecular sample Arnaud Rouzee, Arjan Gijsbertsen, Omair Ghafur, Ofer M Shir, Thomas Back, Steven Stolte and Marc J J Vrakking Controlling the sense of molecular rotation Sharly Fleischer, Yuri Khodorkovsky, Yehiam Prior and Ilya Sh Averbukh Optimal control of interacting particles: a multi-configuration time-dependent Hartree-Fock approach Michael Mundt and David J Tannor Exact quantum dissipative dynamics under external time-dependent driving fields Jian Xu, Rui-Xue Xu and Yi Jing Yan Pulse trains in molecular dynamics and coherent spectroscopy: a theoretical study J Voll and R de Vivie-Riedle Quantum control of electron localization in molecules driven by trains of half-cycle pulses Emil Persson, Joachim Burgdorfer and Stefanie Grafe Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling Jean-Michel Coron, Andreea Grigoriu, Catalin Lefter and Gabriel Turinici Sliding mode control of quantum systems Daoyi Dong and Ian R Petersen Implementation of fault-tolerant quantum logic gates via optimal control R Nigmatullin and S G Schirmer Generalized filtering of laser fields in optimal control theory: application to symmetry filtering of quantum gate operations Markus Schroder and Alex Brown
Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. Among numerous theoretical insights and technological improvements that produced the present state-of-the-art in quantum control, there have been several breakthroughs of foremost importance. On the technology side, the current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. On the theory side, the two most critical insights were (i) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (ii) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control (AFC), which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in AFC experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. AFC of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control designs in experimental realizations and real-time quantum feedback control. The paper concludes with a perspective of open research directions that are likely to attract significant attention in the future.