Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian

Hiromichi Nakazato, Alessandro Sergi, Agostino Migliore, Antonino Messina*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator (Formula presented.) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of (Formula presented.) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any (Formula presented.) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.

Original languageEnglish
Article number96
Issue number1
Publication statusPublished - 2023 Jan


  • control field
  • geometric methods
  • quantum dynamical invariants
  • qubit
  • time-dependent SU(2) Hamiltonian models

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering


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