Characterizing spin-bath parameters using conventional and time-Asymmetric Hahn-echo sequences

Spin-bath noise characterization, which is typically performed by multipulse control sequences, is essential for understanding most spin dynamics in the solid state. Here, we theoretically propose a method for extracting the characteristic parameters of a noise source with a known spectrum, using modified Hahn-echo pulses. By varying the application time of the pulse, measuring the coherence curves of an addressable spin, and fitting these curves to a theoretical function derived by us, we extract parameters characterizing the physical nature of the noise. Assuming a Lorentzian noise spectrum, we illustrate this method for extracting the correlation time of a bath of nitrogen paramagnetic impurities in diamond, and its coupling strength to the addressable spin of a nitrogen-vacancy center. First, we demonstrate that fitting conventional Hahn-echo measurements to the explicit coherence function is essential for extracting the correct parameters in the general physical regime, for which common methods relying on the assumption of a slow bath are inaccurate. Second, considering a realistic experimental scenario with a 5% noise floor, we simulate the extraction of these parameters utilizing the asymmetric Hahn-echo scheme. The scheme is effective for samples having a natural homogeneous coherence time (T2) up to two orders of magnitude greater than the inhomogeneous coherence time (T2∗). In the presence of realistic technical drifts for which averaging capabilities are limited, we simulate more than a factor of 3 improvement of the extracted parameter uncertainties over conventional Hahn-echo measurements. Beyond its potential for reducing experiment times by an order of magnitude, such single-pulse noise characterization could minimize the effects of long timescale drifts and accumulating pulse imperfections and numerical errors.