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arXiv:2602.19701

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

Mateusz Kuniej, Katarzyna Roszak

quant-phSubmitted Feb 23, 2026• Announced Feb 24, 2026• 0 citations
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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.

Comments
9 pages, 6 figures

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Direct access to the initial polarization of 13C{}^{13}C13C nuclei by measuring coherence evolution of an nitrogen-vacancy center spin qubit
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.
We propose a method for the estimation of the initial polarization of spinful nuclei of the 13C^{13}\mathrm{C}13C isotope in diamond via a measurement of the evolution of the coherence of a nitrogen-vacancy-center spin qubit. Existing polarization measurement methods are difficult to implement experimentally because they require direct interference in the environment of the qubit. Here, in order to obtain the information, it is necessary to measure the qubit coherence at certain points of time, which are unambiguously determined by the applied magnetic field. For sufficiently high magnetic fields, the minimum value of the measured coherence constitutes an upper bound on the product of the initial polarizations of each environmental spin. The most significant advantage of the method, which allows to infer initial values of nuclear polarizations without any direct access to the environment, lies in its simplicity and the small amount of experimental resources that it requires. We exemplify the operation of the scheme on a realistic, randomly generated environment of eight nuclear spins, obtaining a reasonably accurate estimation of the initial polarization.
We study the evolution of qubit-environment entanglement, quantified using negativity, for nitrogen-vacancy-center spin qubits interacting with an environment of partially polarized nuclear spins in the diamond lattice. We compare it with the evolution of the fidelity of environmental states conditional on the pointer states of the qubit, which can serve as a tool to distinguish between entangling and nonentangling decoherence in the pure-dephasing scenario considered here. The two quantities show remarkable agreement during the evolution in a wide range of system parameters, leading to the conclusion that the amount of entanglement generated between the qubit and the environment is likely to be proportional to the trace that the joint evolution leaves on the environment.
Precision measurements based on optically detected nuclear magnetic resonance offer exquisite sensitivity to absolute shifts in spin transition frequencies, with potential applications in fundamental physics experiments and inertial sensing. We investigate 13C nuclear spins in diamond as a candidate system for solid-state implementations, which hold the promise for high-fidelity readout of large numbers of coherent nuclear spins in millitesla or lower magnetic fields. We demonstrate a technique that allows for both optical polarization and readout of large ensembles of ~10^{16} polarized nuclear spins. Our method takes advantage of state-selective Landau-Zener transitions under microwave frequency sweeping, which bidirectionally transfer spin polarization between Nitrogen-Vacancy (NV) electron spins and remote 13C nuclear spins. Using natural isotopic abundance diamonds with nitrogen densities of ~0.5-10 ppm, we perform optically-detected 13C Ramsey spectroscopy and realize a nuclear-spin-dependent fluorescence contrast exceeding 0.5% peak-to-peak. We observe nuclear spin dephasing times T2*~2 ms that only modestly improve with homonuclear dipolar decoupling, indicating that they are limited by the longitudinal spin relaxation of nearby NV electron spins. We study the magnetic field dependence of the optical readout and find comparable contrast and dephasing times for magnetic fields in the range 8-20 mT. Our method can be interpreted as a type of repetitive readout, where each NV center optically reads out the spin state of ~10^2 nuclei before nuclear spins depolarize.
The nuclear spin in the vicinity of a nitrogen-vacancy (NV) center possesses long coherence time and convenient manipulation assisted by the strong hyperfine interaction with the NV center. It is suggested for the subsequent quantum information storage and processing after appropriate initialization. However, current experimental schemes are either sensitive to the inclination and magnitude of the magnetic field or require thousands of repetitions to achieve successful realization. Here, we propose a method to polarize a 13C^{13}\mathrm{C}13C nuclear spin in the vicinity of an NV center via a dark state. We demonstrate theoretically and numerically that it is robust to polarize various nuclear spins with different hyperfine couplings and noise strengths.
The nitrogen vacancy (NV) center in diamond is promising as an electron spin qubit due to its long-lived coherence and optical addressability. The ground state is a spin triplet with two levels $({m}_{s}=\ifmmode\pm\else\textpm\fi{}1)$ degenerate at zero magnetic field. Polarization-selective microwave excitation is an attractive method to address the spin transitions independently since this allows operation down to zero magnetic field. Using a resonator designed to produce circularly polarized microwaves, we have investigated the polarization selection rules of the NV center. We first apply this technique to NV ensembles in [100]- and [111]-oriented samples. Next, we demonstrate an imaging technique, based on optical polarization dependence, which allows rapid identification of the orientations of many single NV centers. Finally, we test the microwave polarization selection rules of individual NV centers of known orientation.
We propose efficient schemes of direct concurrence measurement for two-qubit spin and photon-polarization entangled states via the interaction between single-photon pulses and nitrogen-vacancy (NV) centers in diamond embedded in optical microcavities. For different entangled-state types, diversified quantum devices and operations are designed accordingly. The initial unknown entangled states are possessed by two spatially separated participants, and nonlocal spin (polarization) entanglement can be measured with the aid of detection probabilities of photon (NV center) states. This non-demolition entanglement measurement manner makes initial entangled particle-pair avoid complete annihilation but evolve into corresponding maximally entangled states. Moreover, joint inter-qubit operation or global qubit readout is not required for the presented schemes and the final analyses inform favorable performance under the current parameters conditions in laboratory. The unique advantages of spin qubits assure our schemes wide potential applications in spin-based solid quantum information and computation.