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arXiv:2501.18244

Entanglement Generation on the Double Quantum Transition of NV Ground State Via Globally Addressing Microwave Pulse

Marcel Morillas-Rozas, Alberto López-García, Javier Cerrillo

Published Jan 30, 2025• 0 citations
arXivHTMLPDF

Abstract

Entanglement is a key quantum feature that enables quantum sensors to improve their sensitivity up to the Heisenberg limit. In the NV center platform, the Heisenberg limit can only be achieved when the axes of the NV centers are parallel. Nevertheless, parallel NV centers are spectrally indistinguishable and no mechanisms to directly prepare Heisenberg--limit--grade entanglement in such configurations are known to date. In this work we propose for the first time a viable mechanism to prepare entangled states in the double quantum transition of two dipolarly coupled NV centers whose axes are parallel without populating intermediate states, so as to reach the Heisenberg limit in sensing. Our approach is based on the NV effective Raman coupling (NV-ERC) protocol and makes use of global addressing of both NV centers with a single monochromatic microwave pulse. Supported by an adiabatic elimination analysis, several mechanisms for the preparation of different entangled states are identified, all of which avoid the involvement of intermediate states. This not only minimizes the impact of additional noise sources, but also enables the state generation process itself to serve as effective sensing time--an advantage over conventional approaches where such preparation typically constitutes a separate, non--contributory stage. We consider the generation of different entangled states belonging to the double quantum transition, sensitive to either transverse electric fields or longitudinal magnetic fields, all with a fourfold improved sensitivity compared to conventional single NV settings.

DOI
10.48550/arxiv.2501.18244

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Entanglement is a key quantum feature that enables quantum sensors to improve their sensitivity up to the Heisenberg limit. In the NV center platform, the Heisenberg limit can only be achieved when the axes of the NV centers are parallel. Nevertheless, parallel NV centers are spectrally indistinguishable and no mechanisms to directly prepare Heisenberg--limit--grade entanglement in such configurations are known to date. In this work we propose for the first time a viable mechanism to prepare entangled states in the double quantum transition of two dipolarly coupled NV centers whose axes are parallel without populating intermediate states, so as to reach the Heisenberg limit in sensing. Our approach is based on the NV effective Raman coupling (NV-ERC) protocol and makes use of global addressing of both NV centers with a single monochromatic microwave pulse. Supported by an adiabatic elimination analysis, several mechanisms for the preparation of different entangled states are identified, all of which avoid the involvement of intermediate states. This not only minimizes the impact of additional noise sources, but also enables the state generation process itself to serve as effective sensing time--an advantage over conventional approaches where such preparation typically constitutes a separate, non--contributory stage. We consider the generation of different entangled states belonging to the double quantum transition, sensitive to either transverse electric fields or longitudinal magnetic fields, all with a fourfold improved sensitivity compared to conventional single NV settings.
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.
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.
The precision measurements provided by quantum sensing plays a significant role in fields of science. However, the sensitivity is limited by the standard quantum limit (SQL). Quantum entangled state have a potential to beat the SQL and to approach the Heisenberg limit (HL). In particular, entanglement sensors based on Nitrogen-Vacancy (NV) centers provide high spatial resolution at room temperature. In 2021, it was reported that the multi-spin sensor constituted by the NV electron spin (S=1), the 14N nuclear spin (I=1), and proximate 13C nuclear spin (I=1/2) beat the SQL1 . However, since the nuclear gyromagnetic ratio is ~MHz/T, it does not lead to a dramatic improvement of sensitivity. For enhancement of quantum sensing, it is required to utilize the entangled state among dipole coupled NV centers.
The Nitrogen-Vacancy (NV) center in diamond is applied as quantum sensor for magnetic fields, temperature, electric field, etc. Quantum sensing based on an entangled state between dipole coupled NV center pair can overcome standard quantum limit to reach Heisenberg limit. It is expected to be more sensitive measurement than quantum sensing based on single NV center. Even though the generation of entangled state has been demonstrated by Double Electron-Electron Resonance (DEER)1,2, the utilization of entanglement state for enhancement of quantum sensing has not yet been studied. To realize the quantum sensing based on entangled state, we have developed organic compound ion implantation3,4 method to efficiently create dipole coupled NV centers. We reported the creation of NV center pair with dipole-dipole interaction strengths of about 100 kHz by using C5N4Hn ion implantation and pointed out the potential of entangled state with high fidelity (~0.9) at 5th IFQMS. In this study, we will report the generation of quantum entangled states between NV center pair and discuss the magnetic field sensing by using entangled state.
Nitrogen vacancy (NV) centers in diamond are widely deployed as local magnetic sensors, using coherent, single qubit control to measure both time-averaged fields and noise with nanoscale spatial resolution. Moving beyond single qubits to multi-qubit control enables new sensing modalities such as measuring nonlocal spatiotemporal correlators, or using entangled states to improve measurement sensitivity. Here, we describe protocols to use optically unresolved NV center pairs and nuclear spins as multi-qubit sensors for measuring correlated noise, enabling covariance magnetometry at nanometer length scales. For NV centers that are optically unresolved but have spectrally resolved spin transitions, we implement a phase-cycling protocol that disambiguates magnetic correlations from variance fluctuations by alternating the relative spin orientations of the two NV centers. For NV centers that are both optically and spectrally unresolved, we leverage the presence of a third qubit, a 13C nucleus that is strongly coupled to one of the NV centers, to effect coherent single-NV spin flips and enable a similar phase-cycling protocol. For length scales around 10 nm, we create maximally entangled Bell states through dipole-dipole coupling between two NV centers, and use these entangled states to directly read out the magnetic field correlation, rather than reconstructing it from independent measurements of unentangled NV centers. Importantly, this changes the scaling of sensitivity with readout noise from quadratic to linear. For conventional off-resonant readout of the NV center spin state (for which the readout noise is roughly 30 times the quantum projection limit), this results in a dramatic sensitivity improvement. Finally, we demonstrate methods for the detection of high spatial- and temporal-resolution correlators with pairs of strongly interacting NV centers.
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.