Coherent Cross-Polarization Theory for a Spin-½ Coupled to a General Object

Zero-order average-Hamiltonian theory is used to extend the product-operator description of coherent spin–spin cross-polarization to the case of a spin-½ coupled to a general object, like a molecular rotor or a quantum oscillator. The object, which is not necessarily in a Boltzmann equilibrium state, is assumed to have no interaction with the lattice and no internal relaxation capacity. The Bloch–Wangsness–Redfield (BWR) theory for incoherent processes like spin–lattice relaxation does not apply for such an isolated spin– object pair. Nevertheless spectral density at the Larmor frequency, of key importance in BWR theory, also plays a central role in object-induced spin polarization. Spectral density in our theory is represented by quantum operators J2 and J1. If J2 and J1 do not commute, the spin– object coupling may cause spin polarization in an initially saturated spin system. This represents a coherent mechanism for spin cooling, which in specific cases may lead to enhanced spin polarization above the thermal equilibrium value. A master equation is derived for general spin– object crosspolarization, and applied to the case of a spin pair inside a uniaxial rotor, and a spin coupled to a microelectronic LC circuit.