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:1809.06349 · Physical Review A

Singularity-free quantum tracking control of molecular rotor orientation

Alicia B Magann, Tak‐San Ho, HERSCHEL A. RABITZ

Published Oct 24, 2018• 26 citations
arXivHTMLPDF

Abstract

Quantum tracking control aims to identify applied fields to steer the expectation values of particular observables along desired paths in time. The associated temporal fields can be identified by inverting the underlying dynamical equations for the observables. However, fields found in this manner are often plagued by undesirable singularities. In this paper we consider a planar molecular rotor and derive singularity-free tracking expressions for the fields that steer the expectation of the orientation of the rotor along the desired trajectories in time. Simulations are presented that utilize two orthogonal control electric fields to drive the orientation of the rotor along a series of designated tracks.

DOI
10.1103/physreva.98.043429

Related papers

Quantum tracking control of the orientation of symmetric-top molecules

Alicia B Magann, Tak‐San Ho, Christian Arenz +1 more

The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables. In this paper, we generalize the ideas in [Phys. Rev. A 98, 043429 (2018)] to the task of orienting symmetric top molecules in three dimensions. To this end, we derive equations for the control fields capable of directly tracking the expected value of the three-dimensional dipole orientation vector along a desired path in time. We show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric-top tracking control problems.

arXiv:2301.04255•Physical Review A•Sep 18, 2023•6 citations

Inverse control of quantum-mechanical systems: some application studies

G. Huang, P. Gross, H. Singh +2 more

Applies the invertibility of a quantum mechanical systems concept to design open loop controls of molecular systems. The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Applications to diatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.>

IEEE Conference on Decision and Control (CDC)•Dec 30, 2002•1 citation

Quantum observable homotopy tracking control

Adam E. Rothman, Tak‐San Ho, HERSCHEL A. RABITZ

This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.

The Journal of Chemical Physics•Sep 29, 2005•59 citations

Inverse quantum-mechanical control: A means for design and a test of intuition

Peter Groß, Harjinder Singh, HERSCHEL A. RABITZ +2 more

The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method, a requisite external field is obtained to track exactly a prescribed molecular objective expectation value as a function of time. Applications to diatomic and polyatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for position and energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.

Physical Review A•Jun 1, 1993•115 citations

Managing singular behavior in the tracking control of quantum dynamical observables

Wusheng Zhu, Martina Smit, HERSCHEL A. RABITZ

Singularities can arise in the external field obtained by tracking control of quantum mechanical systems. Whether or not the trajectory is disturbed by the presence of a singular point is shown to mainly depend on the average momentum along the trajectory at the moment of passing the singular point. If the singularity occurs on a turning point, the tracking will be quite unstable since the direction taken by the trajectory is very sensitive to field errors. The theoretical analysis of these situations yields detailed conclusions about the impact of field singularities in quantum tracking control. A rank index is defined to characterize nontrivial singularities, and the rank is shown to play an important role in determining the tracking quality while passing over a singular turning point where the field has a unique solution. A special class of nontrivial singularities is identified by the ability to remove the singularity under a proper limiting process. These insights into the nature and influence of singularities in tracking control of quantum systems are beneficial for developing numerical schemes and for designing controls.

The Journal of Chemical Physics•Jan 22, 1999•45 citations

Machine Learning for Quantum Rotor Dynamics: A Surrogate Model Approach to Rotational Excitation in External Electric Fields

Vinod Prasad, Ashish Tyagi, Urvashi Arya +1 more

The quantum rotor in external fields such as static electric, magnetic, and time-dependent fields is one of the most studied research problems due to its applicability in chemical physics, molecular dynamics, and many other related areas. The problem finds applications in quantum chaos and nonlinear dynamics as well. In this work, we present a Machine learning (ML) approach to model a one-dimensional quantum rotor in an external electric field. Our approach is to develop a surrogate model, keeping in mind the inherent smoothness of the eigenenergies of the dressed rotor and the directional parameters such as orientation, i.e., expectation value of cosϕ , and the alignment parameter ( 〈 cos 2 ϕ 〉 ) with the applied static field. The model we developed is very efficient, achieving microsecond-scale predictions with high accuracy. The model we developed is as follows: first, we train it on the basis of data generated from numerical calculations taking rotor-static field interaction into account and expanding the wavefunction as a finite basis. The model gives an excellent performance with R2 values exceeding 0.9999 for all predicted quantities. We further explore the physics of the system and the data generation, the details of the ML model, and its uses in designing an inverse model. The work shows that ML can be used to speed up computational time in related areas such as molecular physics and may be used to optimize the experimental parameters. This approach is directly extensible to three-dimensional rotors, time-dependent fields, and multi-parameter optimization, with potential applications in quantum control, molecular alignment, and spectroscopic fitting.

Journal of Modern Physics•Jan 1, 2026•0 citations
Quantum tracking control aims to identify applied fields to steer the expectation values of particular observables along desired paths in time. The associated temporal fields can be identified by inverting the underlying dynamical equations for the observables. However, fields found in this manner are often plagued by undesirable singularities. In this paper we consider a planar molecular rotor and derive singularity-free tracking expressions for the fields that steer the expectation of the orientation of the rotor along the desired trajectories in time. Simulations are presented that utilize two orthogonal control electric fields to drive the orientation of the rotor along a series of designated tracks.
The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables. In this paper, we generalize the ideas in [Phys. Rev. A 98, 043429 (2018)] to the task of orienting symmetric top molecules in three dimensions. To this end, we derive equations for the control fields capable of directly tracking the expected value of the three-dimensional dipole orientation vector along a desired path in time. We show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric-top tracking control problems.
Applies the invertibility of a quantum mechanical systems concept to design open loop controls of molecular systems. The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Applications to diatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.>
This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.
The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method, a requisite external field is obtained to track exactly a prescribed molecular objective expectation value as a function of time. Applications to diatomic and polyatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for position and energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.
Singularities can arise in the external field obtained by tracking control of quantum mechanical systems. Whether or not the trajectory is disturbed by the presence of a singular point is shown to mainly depend on the average momentum along the trajectory at the moment of passing the singular point. If the singularity occurs on a turning point, the tracking will be quite unstable since the direction taken by the trajectory is very sensitive to field errors. The theoretical analysis of these situations yields detailed conclusions about the impact of field singularities in quantum tracking control. A rank index is defined to characterize nontrivial singularities, and the rank is shown to play an important role in determining the tracking quality while passing over a singular turning point where the field has a unique solution. A special class of nontrivial singularities is identified by the ability to remove the singularity under a proper limiting process. These insights into the nature and influence of singularities in tracking control of quantum systems are beneficial for developing numerical schemes and for designing controls.
The quantum rotor in external fields such as static electric, magnetic, and time-dependent fields is one of the most studied research problems due to its applicability in chemical physics, molecular dynamics, and many other related areas. The problem finds applications in quantum chaos and nonlinear dynamics as well. In this work, we present a Machine learning (ML) approach to model a one-dimensional quantum rotor in an external electric field. Our approach is to develop a surrogate model, keeping in mind the inherent smoothness of the eigenenergies of the dressed rotor and the directional parameters such as orientation, i.e., expectation value of cosϕ , and the alignment parameter ( 〈 cos 2 ϕ 〉 ) with the applied static field. The model we developed is very efficient, achieving microsecond-scale predictions with high accuracy. The model we developed is as follows: first, we train it on the basis of data generated from numerical calculations taking rotor-static field interaction into account and expanding the wavefunction as a finite basis. The model gives an excellent performance with R2 values exceeding 0.9999 for all predicted quantities. We further explore the physics of the system and the data generation, the details of the ML model, and its uses in designing an inverse model. The work shows that ML can be used to speed up computational time in related areas such as molecular physics and may be used to optimize the experimental parameters. This approach is directly extensible to three-dimensional rotors, time-dependent fields, and multi-parameter optimization, with potential applications in quantum control, molecular alignment, and spectroscopic fitting.