Design of broadband propagators in two-level systems

Abstract

We describe a method suitable for the design of broadband propagators in two-level or pseudo-two-level systems via amplitude-modulated irradiation. Irradiation sequences are described in terms of a Fourier expansion. The Fourier coefficients of the expansion are used to calculate the time-independent Floquet Hamiltonian which represents the time-dependent Hamiltonian. This transformation removes the difficulty of integrating the time-dependent equations of motion. The infinite Floquet matrix is approximately diagonalized by an application of perturbation theory. A set of infinite matrix operators is introduced which assists in the diagonalization. The perturbation-theory expressions are used to derive approximate expressions for the propagator. Successive terms in the perturbation expansion can be nulled by considering additional Fourier coefficients. Broadband-irradiation sequences with low mean power or low peak power are described corresponding to coherent excitation in two-level systems through the flip angles 45°, 90°, 135°, and 180°.