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 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.
Quantum sensing has witnessed rapid development and transition from laboratories to practical applications in the past decade. Applications of quantum sensors, ranging from nanotechnologies to biosensing, are expected to benefit from quantum sensors' unprecedented spatial resolution and sensitivity. Solid-state spin systems are particularly attractive platforms for quantum sensing technologies because room temperature operation is viable while reaching the quantum limits of sensitivity. Among various solid-state spin systems, nitrogen-vacancy (NV) centers in diamond demonstrated high-fidelity initialization, coherent control, and high contrast readout of the electron spin state. However, electron spin coherence due to noise from the surrounding spin bath and this environment effect limits the sensitivity of NV centers. Thus, a critical task in NV center-based quantum sensing is sensitivity enhancement through coherence protection. Several strategies, such as dynamical decoupling techniques, feedback control, and nuclear spin-assisted sensing protocols, have been developed and realized for this task. Among these strategies, nuclear spin-assisted protocols have demonstrated greater enhancement of electron spin coherence. In addition, the electron and nuclear spin pair of an NV center in diamond naturally allows the application of the nuclear spin-assisted sensitivity enhancement protocol. Owing to long nuclear coherence times, further enhancement of sensitivity can be achieved by exploiting active nuclear spins (e.g., 14N, 13C) in the proximity of an NV center as memory ancillas when coupled with the NV center. Here, we review the spin properties of NV centers, mechanisms of the nuclear spin-assisted protocol and its gate variation, and the status of quantum sensing applications in high-resolution nuclear spin spectroscopy, atomic imaging, and magnetic field sensing. We discuss the potential for commercialization, current challenges in sensitivity enhancement, and conclude with future research directions for promoting the development of nuclear spin-assisted protocol and its integration into industrial applications.
In the field of quantum sensing, quantum entangled states have the potential to beat the standard quantum limit (SQL) and to approach the Heisenberg limit (HL)1. Since the nitrogen-vacancy (NV) center is a qubit at room temperature, the entangled state among an NV array will offer new possibilities for quantum sensing and computing. However, considering decoherence, it is not clear whether entangled sensing can achieve sensitivity beyond the SQL under ambient conditions2,3. We have previously evaluated the decoherence of a shallow NV-NV pair. At Quantum Innovation (QI) 2024, we characterized the decoherence using noise spectroscopy and observed two types of noise with autocorrelation times on the ~μs and ~ns scales. Our results are consistent with previous studies, which attributed these noise sources to the surface electron spin bath and the surface-modified phonons4. As demonstrated by Y. Matsuzaki et al.3, the autocorrelation time is required to be comparable to the evolution time (~μs) for the entangled state. Therefore, we showed that the ratio of the coupling constants to the two types of noise determines whether the entangled state between NV-NV pair beats the SQL. Compared to the temperature-dependent phonon effects, the electron spin density is more readily controlled by surfacetermination techniques. Surface electron spins are a promising target for designing the decoherence environment surrounding NV-NV entangled sensors. In this study, to determine the optimal surface electron spin density for NV-NV entangled sensing, we calculated the flip-flop rate among surface electron spins, as well as the coupling constant to the NV center.
Quantum entangled states have a potential to beat the standard quantum limit (SQL) and approach the Heisenberg limit (HL). We previously demonstrated that phase shifts induced by magnetic fields are coherently accumulated in a Ramsey protocol using an entangled Nitrogen-Vacancy (NV) pair. However, the sensitivity is limited to the order of ~µT/√Hz due to the various sources of error and noise, including classical readout noise, spin manipulation and initialization errors, and decoherence error. One of the most critical problems is that decoherence of entangled sensing proceeds more rapidly than ensemble-based sensing. When decoherence follows a Markovian process (i.e., when the environment noises behave as white noise without autocorrelation), the sensitivity of entangled sensing is limited to SQL3,4. Therefore, enhancement from entanglement cannot be achieved under the white noise conditions. To realize entanglement-enhanced sensing to beat SQL, it is essential to characterize the environment noise and prepare a suitable condition. In this study, we conducted noise spectroscopy to evaluate the environmental noise and demonstrated that diamond NV centers have the potential to beat SQL.
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.
The use of entangled sensors improves the precision limit from the standard quantum limit (SQL) to the Heisenberg limit. Most previous experiments beating the SQL are performed on the sensors that are well isolated under extreme conditions. Here, we demonstrate a sub-SQL interferometer at ambient conditions by using a multispin system, namely, the nitrogen-vacancy (NV) defect in diamond. We achieve two-spin interference with a phase sensitivity of 1.79 ± 0.06 dB beyond the SQL and three-spin interference with a phase sensitivity of 2.77 ± 0.10 dB. Besides, a magnetic sensitivity of 0.87 ± 0.09 dB beyond the SQL is achieved by two-spin interference for detecting a real magnetic field. Particularly, the deterministic and joint initialization of NV negative state, NV electron spin, and two nuclear spins is realized at room temperature. The techniques used here are of fundamental importance for quantum sensing and computing, and naturally applicable to other solid-state spin systems.
Quantum sensing affects many fields of science, both fundamental and applied, since a high spatial resolution in combination with high sensitivities enables closeup investigation of interesting phenomena via for example spin-wave measurements [1]. One example quantum sensor that offers a high resolution due to its atomic size and works under ambient conditions is the nitrogen-vacancy (NV) centre. Two quantum resources separate quantum sensing from classical sensing: coherence and entanglement. The former is already basic in many known detection protocols. However, the latter has so far not been used efficiently with any quantum sensor. This is an indication of the major challenge ahead, but the potential result is a significant enhancement of the sensitivity, further increasing the possibilities with quantum sensors.