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.
The analytic solutions of equations, which describe the time behavior of density-matrix elements of a two-level medium driven by weak-probe tunable and strong fields, namely, scrE(t)=E(t)cos[\ensuremath{\omega}t+\ensuremath{\varphi}(t)]+\ensuremath{\varepsilon} cos[(\ensuremath{\omega}+\ensuremath{\delta})t], the amplitude E(t) and phase \ensuremath{\varphi}(t) of which are any arbitrary functions of time, are obtained. We obtain explicit expressions of the medium polarizability in two cases of the strong-field parameters modulation: first, E(t)=
E0cos(\ensuremath{\xi} cos\ensuremath{\Omega}t), where
E0, \ensuremath{\Omega}, and \ensuremath{\xi} are constants, and \ensuremath{\varphi}=0; and second, both the amplitude E(t) and the phase \ensuremath{\varphi}(t) are periodic functions of time, and E(t)=C\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, where C is an arbitrary constant. These cases of modulation are generalizations of cases that were considered earlier. The first case of modulation causes a shift of the well-known Rabi resonances in the weak-probe absorption and dispersion spectra by the factor
J0(\ensuremath{\xi}) (
J0 is the zero-order Bessel function of the first kind) in comparison with a nonmodulated exciting field. In the second case of the modulation, the Rabi resonances are present but the effect of such a modulation results in an attenuation of the amplitude-modulation effect. The values of the parameters
E0, \ensuremath{\Omega}, C, and \ensuremath{\xi} and the frequency ranges in which the weak-probe gain, caused by resonant Rayleigh scattering and by three-photon scattering, takes place are determined for these two cases of the modulation.