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EPJ Quantum Technology

Full qubit control of the double quantum transition in NV centers for low-field or high-frequency sensing

Alberto López-García, Javier Cerrillo

Published May 15, 2025• 1 citation
Publisher

Abstract

Abstract We present a scheme for the implementation of fast arbitrary qubit gates in the ground state of the negatively charged nitrogen-vacancy (NV) defect in diamond. The protocol is especially useful for sensing in two regimes: on the one hand, in the low-field limit where the Zeeman splitting of the NV-center is smaller than the MW Rabi frequency; on the other hand, for the detection of high-frequency signals, comparable to the Zeeman splitting of the NV center. It constitutes an extension to the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. Here we derive a full theoretical framework of the scheme, identifying the complete unitary associated to the approach, and more specifically the relevant basis transformation for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast single qubit gates in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We finally demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields and numerically test its effectiveness in a Hahn echo sequence in the high-frequency or low-field regime.

DOI
10.1140/epjqt/s40507-025-00358-x

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Abstract We present a scheme for the implementation of fast arbitrary qubit gates in the ground state of the negatively charged nitrogen-vacancy (NV) defect in diamond. The protocol is especially useful for sensing in two regimes: on the one hand, in the low-field limit where the Zeeman splitting of the NV-center is smaller than the MW Rabi frequency; on the other hand, for the detection of high-frequency signals, comparable to the Zeeman splitting of the NV center. It constitutes an extension to the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. Here we derive a full theoretical framework of the scheme, identifying the complete unitary associated to the approach, and more specifically the relevant basis transformation for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast single qubit gates in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We finally demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields and numerically test its effectiveness in a Hahn echo sequence in the high-frequency or low-field regime.
We present a scheme for the implementation of fast arbitrary qubit gates in the ground state of the negatively charged nitrogen-vacancy (NV) defect in diamond [1]. The protocol is especially useful for sensing in two regimes: on the one hand, in the low-field limit where the Zeeman splitting of the NV-center is smaller than the MW Rabi frequency; on the other hand, for the detection of high-frequecy signals, comparable to the Zeeman splitting of the NV-center. It constitutes an extension to the NV-ERC technique [2, 3], which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. Here we derive a full theoretical framework of the scheme, identifying the complete unitary associated to the approach, and more specifically the relevant basis transformation for each of two characteristic pulse durations. Based on this insight, we propose a scheme to perform fast single qubit gates in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We finally demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields and numerically test its effectiveness in a Hahn echo sequence in the high-frequency or low-field regime.
Microwave control of the negatively charged nitrogen-vacancy (NV) defect in diamond is usually based on a two-level approximation of its ground state that is only valid in the regime of high bias magnetic fields or low microwave power. We present the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level, thanks to an effective Raman coupling. The protocol may be used in the low-field regime and for high-frequency sensing. Furthermore, we propose a scheme to perform fast single-qubit gates in the double quantum transition, consisting of pulse trains of constant frequency and intensity. We analyze its robustness with respect to pulse-timing errors resulting from inaccurate identification of system parameters or phase-control limitations. We also demonstrate that the technique can be implemented in the presence of unknown electric or strain fields.
The negatively charged nitrogen-vacancy (NV) defect in diamond has established itself as a promising quantum sensing platform with applications in nuclear magnetic resonance at the nanoscale. Still, control protocols are not yet optimized to work in all imaginable regimes. We present the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level thanks to an effective Raman coupling. The protocol is especially useful in the low-field regime and for high-frequency sensing applications. Based on this insight, we propose a scheme to perform fast single qubit gates in the double quantum transition. We study its robustness with respect to pulse-timing errors resulting from faulty identification of system parameters or phase-control limitations. We demonstrate that the technique can also be implemented in the presence of unknown electric or strain fields.
The ground state of the negatively charged NV center forms a spin-1 manifold providing a versatile platform for sensing and information processing. Here we present a scheme for implementing fast arbitrary qutrit gates in the low-field regime using monochromatic microwave pulses of constant intensity tuned to the zero-field transition. By concatenating pulses with appropriate phases and durations, the NV-ERC scheme is extended from SU(2) operations in the double-quantum subspace to the full three-level structure. We show that arbitrary SU(3) operations can be decomposed into rotations in the double-quantum subspace together with effective implementations of the generators related to λ^5\hatλ_5λ^5​ and λ^8\hatλ_8λ^8​. We illustrate this decomposition with a use case: performing quantum state tomography of the complete three-level density matrix.
The NV-ERC technique for control of the NV ground state exploits the spin-1 nature of the system to best initialize the double-quantum transition. It has been proven to be a crucial control strategy for low field or high frequency sensing. Beyond initialization and readout, the scheme to perform 𝜋 rotations in the transition was inefficient for low intensity pulses. We present a complete theoretical picture of the strategy and demonstrate a mechanism for fast arbitrary unitaries in the double quantum transition. We show it is a robust approach with respect to pulse strength inaccuracies even in the presence of unexpected electric or strain fields.
We propose and experimentally demonstrate a method to strongly increase the sensitivity of spin measurements on nitrogen-vacancy (NV) centers in diamond, which can be readily implemented in existing quantum sensing experiments. While charge state transitions of this defect are generally considered a parasitic effect to be avoided, we show here that these can be used to significantly increase the NV center's spin contrast, a key quantity for high sensitivity magnetometry and high fidelity state readout. The protocol consists of a two-step procedure, in which the charge state of the defect is first purified by a strong laser pulse, followed by weak illumination to obtain high spin polarization. We observe a relative improvement of the readout contrast by 17 %, and infer a reduction of the initialization error of more than 50 %. The contrast enhancement is accompanied by a beneficial increase of the readout signal. For long sequence durations, typically encountered in high-resolution magnetometry, a measurement speedup by a factor of >1.5 is extracted, and we find that the technique is beneficial for sequences of any duration. Additionally, our findings give detailed insight into the charge and spin polarization dynamics of the NV center, and provide actionable insights for direct optical, spin-to-charge, and electrical readout of solid-state spin centres.