Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1208.5564 · Physical Review A

Optimal-control theory of harmonic generation

Ido Schaefer, Ronnie Kosloff

Published Dec 26, 2012• 11 citations
arXivHTMLPDF

Abstract

Coherent control of harmonic generation was studied theoretically. A specific harmonic order was targeted. An optimal control theory was employed to find the driving field where restrictions were imposed on the frequency band. Additional restrictions were added to suppress undesired outcomes, such as ionization and dissociation. The method was formulated in the frequency domain. An update procedure for the field based on relaxation was employed. The method was tested on several examples demonstrating the generation of high frequencies from a driving field with a restricted frequency band.

DOI
10.1103/physreva.86.063417

Related papers

Quantum Optimal Control Theory of Harmonic Generation

Ido Schaefer

A new method for controlling harmonic generation, in the framework of quantum optimal control theory (QOCT), is developed. The problem is formulated in the frequency domain using a new maximization functional. The relaxation method is used as the optimization procedure. The new formulation is generalized to other control problems with requirements in the frequency domain. The method is applied to several simple problems. The results are analysed and discussed. General conclusions on harmonic generation mechanisms are obtained.

arXiv:1202.6520•Feb 29, 2012•3 citations

Quantum-optical analysis of high-order harmonic generation

Javier Rivera Deán

High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.

•Sep 9, 2019•1 citation

Frequency domain quantum optimal control under multiple constraints

Chuan‐Cun Shu, Tak‐San Ho, Xing Xi +1 more

Optimal control of quantum systems with complex constrained external fields is one of the longstanding theoretical and numerical challenges at the frontier of quantum control research. Here, we present a theoretical method that can be utilized to optimize the control fields subject to multiple constraints while guaranteeing monotonic convergence towards desired physical objectives. This optimization method is formulated in the frequency domain in line with the current ultrafast pulse shaping technique, providing the possibility for performing quantum optimal control simulations and experiments in a unified fashion. For illustrations, this method is successfully employed to perform multiple constraint spectral-phase-only optimization for maximizing resonant multiphoton transitions with desired pulses.

Physical Review A•Mar 23, 2016•47 citations

Optimal quantum control: Designing lasers for controlling quantum systems

Renuka Rai

In this article, we present an overview of theory and technique for optimal control of molecular dynamics using tailored light fields. The goal of this research is to design an optical field, which can drive a system to a desired target state with a fairly high probability and low power expenditure. For the laboratory implementation of the designed field, it is desirable that it has simple frequency structure and that the control outcome is robust in the presence of noise which will always accompany the field. The ability of the control field to cooperate with noise in the manipulation of quantum dynamics is also discussed.

International Conference on Recent Advances in Engineering & Computational Sciences•Mar 1, 2014•1 citation

A Simple Theory of Optimal Coherent Control

Rui‐Xue Xu, Ji‐Xin Cheng, Yan

By combining the theories of optimal control and coherent control, we derive an analytical formulation to evaluate the optimal 1-photon and n -photon fields together with their relative phase and intensity in the optimal “1 + n ”-coherent control scheme. The optimal coherent control exploits tailored light pulses to produce the best overlap with a predefined nuclear target in an electronically degenerate region. It also exploits explicitly the quantum interference between two optimal excitation pathways to achieve the product electronic selectivity. Numerical demonstrations are carried out to selectively control a minimum-uncertainty outgoing wave packet target in a molecular system. The electronically degenerate byproduct is shown to be completely discriminated against via the destructive interference between two optimal excitation pathways. The target considered in this paper would neither be achievable via the conventional continuous-wave coherent control nor via a single optimal control pathway in the weak response regime. Proposed is also a time-dependent excitation frequency degeneracy condition that incorporates the evolution of carrier frequencies in the optimal coherent control with tailored light fields.

The Journal of Physical Chemistry A•Nov 18, 1999•10 citations

Optimal control under spectral constraints: enforcing multi-photon absorption pathways

Daniel M. Reich, José P. Palao, Christiane P. Koch

Shaped pulses obtained by optimal control theory often possess unphysically broad spectra. In principle, the spectral width of a pulse can be restricted by an additional constraint in the optimization functional. However, it has so far been impossible to impose spectral constraints while strictly guaranteeing monotonic convergence. Here, we show that Krotov’s method allows for simultaneously imposing temporal and spectral constraints without perturbing monotonic convergence, provided the constraints can be expressed as positive semi-definite quadratic forms. The optimized field is given by an integral equation which can be solved efficiently using the method of degenerate kernels. We demonstrate that Gaussian filters suppress undesired frequency components in the control of non-resonant two-photon absorption.

arXiv:1307.3568•Journal of Modern Optics•Nov 8, 2013•28 citations
Coherent control of harmonic generation was studied theoretically. A specific harmonic order was targeted. An optimal control theory was employed to find the driving field where restrictions were imposed on the frequency band. Additional restrictions were added to suppress undesired outcomes, such as ionization and dissociation. The method was formulated in the frequency domain. An update procedure for the field based on relaxation was employed. The method was tested on several examples demonstrating the generation of high frequencies from a driving field with a restricted frequency band.
A new method for controlling harmonic generation, in the framework of quantum optimal control theory (QOCT), is developed. The problem is formulated in the frequency domain using a new maximization functional. The relaxation method is used as the optimization procedure. The new formulation is generalized to other control problems with requirements in the frequency domain. The method is applied to several simple problems. The results are analysed and discussed. General conclusions on harmonic generation mechanisms are obtained.
High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.
Optimal control of quantum systems with complex constrained external fields is one of the longstanding theoretical and numerical challenges at the frontier of quantum control research. Here, we present a theoretical method that can be utilized to optimize the control fields subject to multiple constraints while guaranteeing monotonic convergence towards desired physical objectives. This optimization method is formulated in the frequency domain in line with the current ultrafast pulse shaping technique, providing the possibility for performing quantum optimal control simulations and experiments in a unified fashion. For illustrations, this method is successfully employed to perform multiple constraint spectral-phase-only optimization for maximizing resonant multiphoton transitions with desired pulses.
In this article, we present an overview of theory and technique for optimal control of molecular dynamics using tailored light fields. The goal of this research is to design an optical field, which can drive a system to a desired target state with a fairly high probability and low power expenditure. For the laboratory implementation of the designed field, it is desirable that it has simple frequency structure and that the control outcome is robust in the presence of noise which will always accompany the field. The ability of the control field to cooperate with noise in the manipulation of quantum dynamics is also discussed.
By combining the theories of optimal control and coherent control, we derive an analytical formulation to evaluate the optimal 1-photon and n -photon fields together with their relative phase and intensity in the optimal “1 + n ”-coherent control scheme. The optimal coherent control exploits tailored light pulses to produce the best overlap with a predefined nuclear target in an electronically degenerate region. It also exploits explicitly the quantum interference between two optimal excitation pathways to achieve the product electronic selectivity. Numerical demonstrations are carried out to selectively control a minimum-uncertainty outgoing wave packet target in a molecular system. The electronically degenerate byproduct is shown to be completely discriminated against via the destructive interference between two optimal excitation pathways. The target considered in this paper would neither be achievable via the conventional continuous-wave coherent control nor via a single optimal control pathway in the weak response regime. Proposed is also a time-dependent excitation frequency degeneracy condition that incorporates the evolution of carrier frequencies in the optimal coherent control with tailored light fields.
Shaped pulses obtained by optimal control theory often possess unphysically broad spectra. In principle, the spectral width of a pulse can be restricted by an additional constraint in the optimization functional. However, it has so far been impossible to impose spectral constraints while strictly guaranteeing monotonic convergence. Here, we show that Krotov’s method allows for simultaneously imposing temporal and spectral constraints without perturbing monotonic convergence, provided the constraints can be expressed as positive semi-definite quadratic forms. The optimized field is given by an integral equation which can be solved efficiently using the method of degenerate kernels. We demonstrate that Gaussian filters suppress undesired frequency components in the control of non-resonant two-photon absorption.