An electron spin in a static field precesses at per tesla

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin

The Structure of Quantum Mechanics, Ch Spin one-half, SU(2) and two-level dynamics

Problem

An electron spin in a static field precesses at

28.0\,\mathrm{GHz}

per tesla, so the magnitude of its gyromagnetic ratio is

|\gamma_e| = 2\pi\times28.0\,\mathrm{GHz\,T^{-1}}

. In an electron spin resonance experiment the spin is driven on resonance by a field of amplitude

B_1 = 0.50\,\mathrm{mT}

rotating in the plane perpendicular to the static field, in the same sense as the free precession, giving the Rabi frequency

\omega_1 = |\gamma_e| B_1

. ((a)) Estimate

\omega_1

in rad s

^{-1}

. ((b)) Estimate the duration of a

\pi

pulse, the time on resonance needed to invert the population fully from

|\uparrow\rangle

|\downarrow\rangle