Direct access to the initial polarization of ${}^{13}C$ nuclei by measuring coherence evolution of an nitrogen-vacancy center spin qubit

TL;DR

This paper presents a simple, minimally invasive method to estimate the initial polarization of ${}^{13}C$ nuclei in diamond by analyzing the coherence evolution of an NV center spin qubit, avoiding direct environment access.

Contribution

The authors introduce a novel technique that infers nuclear polarization from qubit coherence measurements, which is easier to implement than existing direct measurement methods.

Findings

Method effectively estimates nuclear polarization in simulated environments.

Minimal dependence on magnetic field strength for polarization inference.

Applicable to environments with up to fifteen nuclear spins.

Abstract

We introduce a method for the measurement of the lower bound on the initial polarization of spinful nuclei in a diamond by following the coherence evolution of an NV center spin qubit after a simple scheme is operated on the qubit to facilitate the transfer of information from the environment into the qubit state. Current polarization measurement techniques are challenging to implement due to the need for direct access to the environment. In our method, information is obtained by measuring the difference of the evolution of the qubit coherence resulting from preparation phase when the environment evolution is conditional on the qubit pointer state. We find that the method does not depend strongly on the applied magnetic field, but rather on the number of spinfull nuclei that lead to decoherence, and gives a reasonable estimate if the environment is polarized. The key advantage of this approach is its simplicity and minimal experimental requirements, allowing the inference of initial nuclear polarizations without direct access to the environment. We demonstrate the efficacy of this method using a simulated environment of up to fifteen randomly placed nuclear spins.