Modern experimental techniques can generate magnetic fields of the form H(t) = H0 z-hat + H1 [x-hat cos(ωt) + y-hat sin(ωt)], at frequencies within an order of magnitude of the nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) frequencies, ωn0 and ωe0, respectively, when acting on atoms or molecules. We derive simple closed-form expressions for the exact nuclear- and electronic-spin wave functions that enable controlled transitions between entangled states, allowing an atom or molecule to function as a quantum computer. These solutions also enable precise NMR or EPR measurements of nuclear moments in atoms and molecules. We present examples relevant to measurements of the nuclear moments of 14N, 7Li, and 133Cs. Because existing hyperfine measurements of the lowest three nuclear moments of 133Cs are mutually inconsistent, the proposed NMR/EPR experiments provide a route to measuring all seven of its nuclear moments with high precision.
Maser action due to a mixing between unperturbed spin states, which is produced by a strong coherent pumping field at an angular frequency ω, is investigated by using rate equations of a spin density matrix referred to a rotating coordinate system. The relaxation of each state, which was introduced usually by phenomenological considerations, is obtained from an interaction Hamiltonian of the spin moments with local fields. The induced oscillating fields at 2ω±ω s and ω s , which are proportional to a small signal field at a frequency ω s , have the possibility of power emission (or absorption) by choosing suitably the pumping field. The components at 2ω±ω s are responsible for a frequency mixing between ω and ω±ω s occuring in the rotating coordinates. The emitted (or absorbed) line shape is not a simple Lorentzian in the case of the spin moment
1×ℏ and considered to be a quantum affect in the three level scheme. The frequencies of the emitted (or absorbed) fields are expected to be shifted by varying the magnitude, or the frequency of the pumping field, or the static magnetic field.