Ensemble propagators for quantum systems
Phys. Rev. A 113, 022623 – Published 24 February, 2026
DOI: https://doi.org/10.1103/mzsl-s793
Abstract
We develop a framework for constructing unitary propagators for ensemble states of a quantum system characterized by a continuous distribution of resonance frequencies. The evolution of quantum states is realized through time-dependent electromagnetic control fields. The ensemble members evolve under distinct Hamiltonians, and their evolution is uniquely dependent on their resonance frequencies. The aim of this article is to develop the theory and technique for designing control pulse sequences that generate identical rotations of angular momentum or equivalently the magnetic moments for all members of the quantum ensemble about an arbitrarily chosen axis, regardless of their individual resonance frequencies, while simultaneously preserving the angular momentum component along that axis for every ensemble member. In this way, the control pulse sequence enforces an engineered symmetry in the ensemble dynamics. The control pulse sequence as a whole thereby functions as a universal operator, an engineered ensemble propagator that implements uniform evolutions of the ensemble states while preserving the angular momentum component along a specified axis, for all members across the continuous spectrum of resonance frequencies.
