Nuclear-spin noise and spontaneous emission

The spontaneous emission from nuclear spins has been observed at liquid${\mathrm{-}}^4$He temperatures. The spins, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ nuclei, are placed in the inductor of a tuned LCR circuit coupled to a dc superconducting quantum interference device used as a radio-frequency amplifier. When the spins are saturated and have zero polarization, the emission is observed at the nuclear quadrupole Larmor frequency as a bump in the spectral density of the Nyquist noise current in the tuned circuit. This bump arises from the temperature-independent fluctuations in the transverse component of the nuclear magnetization. When the spins are in thermal equilibrium, on the other hand, a dip in the spectral density of the current noise is observed, arising from an induced absorption of noise power from the circuit at the Larmor frequency. The standard circuit-coupled Bloch’s equation, modified to take into account radiation damping and transverse spin fluctuations, is consistent with the predictions of the Nyquist theorem and the Einstein equation for spontaneous emission. A spin-pendulum model for spin noise is described. The signal-to-noise ratio obtainable in a spin-noise measurement is discussed.