All-Order Theory of Continuous Quantum Noise Measurements: Application to Spin Noise Spectroscopy

The stochastic detector output $z(t)$ of a general continuously measured quantum system is calculated using a stochastic master equation approach. The resulting continuous quantum noise formula (CQNF) is valid in all orders of the measurement strength. The CQNF provides a rigorous route to the calculation of higher order noise spectra of quantum systems with applications in spin noise spectroscopy and quantum measurement theory in general.