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.
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.
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.
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 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.
Controlling the dynamics of targeted quantum correlations is a central goal across many disciplines of quantum science. For applications in nanoscale quantum sensing, nitrogen-vacancy (NV) centers in diamond have recently emerged as a leading platform due to their atom-like nature, exquisite magnetic sensitivity and well-developed coherent control techniques under ambient conditions. However, harnessing the entanglement structure required to improve this sensitivity beyond the standard quantum limit (SQL) from the native dipolar interactions between NV centers is challenging due to their strong positional disorder, three-dimensional geometry and low-fidelity readout. Coupled tightly to proof of principle experimental demonstrations, this thesis provides a theoretical blueprint to realize practical, entanglement-enhanced quantum sensing in the solid-state via far-from-equilibrium dynamics of dense ensembles of NV centers in diamond. Our most fundamental contribution is to identify a universal mechanism exploiting the thermalization of long-wavelength spin textures to generate scalable spin squeezing in the absence of finite temperature symmetry breaking. We further develop a novel sensing protocol based on asymmetric time-reversal capable of rapidly breaking the SQL without high-fidelity readout. Challenging long-standing beliefs in the field, these results open the door to a new era of entanglement-enhanced sensing under ambient conditions, with applications ranging from nanoscale imaging of biological structures to covariance magnetometry of exotic quantum materials.
The performance of solid-state quantum sensors based on electronic spin defects is often limited by the presence of environmental spin impurities that cause decoherence. A promising approach to improve these quantum sensors is to convert environment spins into useful resources for sensing, in particular, entangled states. However, the sensitivity enhancement that can be achieved from entangled states is limited by experimental constraints, such as control errors, decoherence, and time overheads. Here we experimentally demonstrate the efficient use of an unknown electronic spin defect in the proximity of a nitrogen-vacancy center in diamond to achieve both an entangled quantum sensor and a quantum memory for readout. We show that, whereas entanglement alone does not provide an enhancement in sensitivity, combining both entanglement and repetitive readout achieves an enhancement in performance over the use of a single-spin sensor, and more broadly we discuss regimes where sensitivity could be enhanced. Our results critically highlight the challenges in improving quantum sensors using entangled states of electronic spins, while providing an important benchmark in the quest for entanglement-assisted metrology.
We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ∼10^{9} two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. This work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.