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Related Experiment Video

Updated: Jun 11, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Higher order Magnus expansion for driven two-level quantum dynamics.

Chen Wei1, Frank Großmann1

  • 1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany.

The Journal of Chemical Physics
|June 10, 2026
PubMed
Summary
This summary is machine-generated.

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The Magnus expansion accurately approximates two-level systems, offering near-exact results for Landau-Zener-Stückelberg-Majorana and Rabi models with third-order approximations. Even second-order approximations show strong agreement.

Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Mathematical physics

Background:

  • Time-dependent two-level systems are fundamental in quantum mechanics.
  • The Magnus expansion provides a perturbative approach to solve such systems.
  • Understanding non-adiabatic transitions and quasienergies is crucial for quantum control.

Purpose of the Study:

  • To investigate the Magnus expansion for time-dependent two-level systems.
  • To simplify the expansion using Lie algebra and apply it to specific models.
  • To assess the accuracy of the expansion for non-adiabatic transitions and quasienergy calculations.

Main Methods:

  • Decomposition of the Magnus expansion into a commutator-free form using su(2) Lie algebra.
  • Application to the Landau-Zener-Stückelberg-Majorana model.

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  • Systematic treatment of the semiclassical Rabi model by determining Floquet quasienergy.
  • Utilizing picture transformations and enforcing model symmetry for convergence.

    • Main Results:

    • A third-order Magnus expansion approximation yields highly accurate results for both models.
    • The commutator-free form simplifies the expansion.
    • Second-order Magnus approximation in the adiabatic picture provides near-exact results for the Rabi model over a wide parameter range.

    Conclusions:

    • The Magnus expansion, particularly at third order, is a powerful tool for analyzing time-dependent two-level systems.
    • The simplified commutator-free form enhances applicability.
    • The study highlights the efficiency of the Magnus expansion for quantum dynamics, even in non-adiabatic regimes.