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Optics Express

Highly sensitive gyroscope based on a levitated nanodiamond

Huaijin Zhang, Zhang‐qi Yin

Published Feb 3, 2023• 6 citations
Publisher

Abstract

A gyroscope is one of the core components of an inertial navigation system. Both the high sensitivity and miniaturization are important for the applications of the gyroscope. We consider a nitrogen-vacancy (NV) center in a nanodiamond, which is levitated either by an optical tweezer or an ion trap. Based on the Sagnac effect, we propose a scheme to measure the angular velocity with ultra-high sensitivity through the matter-wave interferometry of the nanodiamond. Both the decay of the motion of the center of mass of the nanodiamond and the dephasing of the NV centers are included when we estimate the sensitivity of the proposed gyroscope. We also calculate the visibility of the Ramsey fringes, which can be used for estimating the limitation of gyroscope sensitivity. It is found that the sensitivity ∼ 6.86 × 10 − 7 r a d / s / H z can be achieved in an ion trap. As the working area of the gyroscope is extremely small (∼0.01~μm 2 ), it could be made on-chip in the future.

DOI
10.1364/oe.482436

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A gyroscope is one of the core components of an inertial navigation system. Both the high sensitivity and miniaturization are important for the applications of the gyroscope. We consider a nitrogen-vacancy (NV) center in a nanodiamond, which is levitated either by an optical tweezer or an ion trap. Based on the Sagnac effect, we propose a scheme to measure the angular velocity with ultra-high sensitivity through the matter-wave interferometry of the nanodiamond. Both the decay of the motion of the center of mass of the nanodiamond and the dephasing of the NV centers are included when we estimate the sensitivity of the proposed gyroscope. We also calculate the visibility of the Ramsey fringes, which can be used for estimating the limitation of gyroscope sensitivity. It is found that the sensitivity ∼ 6.86 × 10 − 7 r a d / s / H z can be achieved in an ion trap. As the working area of the gyroscope is extremely small (∼0.01~μm 2 ), it could be made on-chip in the future.
Abstract The nanodiamond, which hosts nitrogen‐vacancy (NV) centers, has been levitated in vacuum either through optical tweezers or through an ion trap. It combines the advantages of the large mass and long coherent discrete internal energy levels, which makes it an ideal platform for quantum information processing and precision measurement. In this review, the quantum information processing and the precision measurement based on the levitated nanodiamond are briefly summarized. The basic physics of the levitated nanodiamond and the NV centers is first introduced. Then the methods of manipulating motional states of the nanodiamond with the NV centers are discussed. The magnetic coupling mechanisms between the NV centers and the translational mode or the torsional mode are discussed, and the method of cooling the mechanical modes with the NV centers is discussed. Several applications are discussed, such as the mass spectrometry, the gravitational acceleration measurement, etc. The levitated nanodiamond can also be used for realizing universal quantum logic gates and quantum simulation. Finally, the conclusion and perspective are given.
The ground-state cooling and quantum control of levitated nanoparticles have become attainable, which makes the enhanced quantum sensing based on the large mass advantage of mesoscopic quantum systems accessible. Here, we propose an enhanced gravity-sensing protocol for a nanodiamond levitated in a linear ion trap, which improves the sensing sensitivity and further reduces device size. By introducing gravitational acceleration into the vibrational state through transient free fall, we achieve a square-accelerated relative phase accumulation, yielding higher sensitivity than the linear accumulation process. The sensitivity reaches the standard quantum limit for a nanodiamond containing multiple nitrogen-vacancy (N-V) centers. Besides, by using phonon-mediated one-axis twisting dynamics induced by magnetic field gradient to squeeze the initial spin state, the sensitivity can further surpass the standard quantum limit as a scaling law of N^{-5/6}. To fully assess the protocol performance, we further analyze the effects of decoherence and control errors, which are negligible under experimentally achievable conditions. Specifically, the sensitivity reaches ∼18 μGal/sqrt[Hz] for the nanodiamond containing only one N-V center over a free-fall distance of ∼20 μm, while exceeds 0.4 μGal/sqrt[Hz] for 100 N-V centers. Our results will further facilitate research on compact and high-sensitivity gravimeters.
Gyroscopes find wide applications in everyday life from navigation and inertial sensing to rotation sensors in hand-held devices and automobiles. Current devices, based on either atomic or solid-state systems, impose a choice between long-time stability and high sensitivity in a miniaturized system. Here, we introduce a quantum sensor that overcomes these limitations by providing a sensitive and stable three-axis gyroscope in the solid state. We achieve high sensitivity by exploiting the long coherence time of the 14{}^{14}14N nuclear spin associated with the nitrogen-vacancy center in diamond, combined with the efficient polarization and measurement of its electronic spin. Although the gyroscope is based on a simple Ramsey interferometry scheme, we use coherent control of the quantum sensor to improve its coherence time and robustness against long-time drifts. Such a sensor can achieve a sensitivity of $\ensuremath{\eta}\ensuremath{\sim}0.5\phantom{\rule{0.28em}{0ex}}(\mathrm{mdeg}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})/\sqrt{\mathrm{Hz}\phantom{\rule{0.16em}{0ex}}{\mathrm{mm}}^{3}}$ while offering enhanced stability in a small footprint. In addition, we exploit the four axes of delocalization of the nitrogen-vacancy center to measure not only the rate of rotation, but also its direction, thus obtaining a compact three-axis gyroscope.
There is a severe impediment in Stern-Gerlach interferometry with a spin-embedded nanoparticle. This is because particle rotation creates a significant mismatch of the wave function of angular degrees of freedom during the creation and recombination of the spatial superposition, resulting in an inferior visibility contrast. We show that imparting angular momentum along the direction of a defect, such as the nitrogen-vacancy (NV) center, during the Stern-Gerlach interferometry provides excellent gyroscopic quantum stability to a nanodiamond, which opens up a way to maintain significant visibility in the quantum interference. The spin contrast improves by many folds for a wide-ranging value of the initial angular momentum, e.g., 10^3–10^6 Hz for a mass of order 10^{-14}–10^{-17} kg nanodiamond. Our scheme is independent of the material and is pertinent to any nanoparticle that can be used to create massive and large spatial superpositions with an embedded spin defect.
The nitrogen-vacancy (NV) center is one of the major platforms in the evolving field of quantum technologies. The inertial surveying technology based on NV centers in diamond is a developing field with both scientific and technological importance. Quantum measurement using the solid-state spin of the NV center has demonstrated potential in both high-precision and small-volume low-cost devices. In terms of rotation measurement, the optically detected magnetic resonance has provided a perspective of the rotation measurement mechanism via the solid-state spin of the NV center. A new type of gyroscope based on the solid-state spin in diamond according to the theory has attracted considerable attention. In addition, combined with the ingenious quantum mechanics manipulation and coupling mechanism, acceleration measurement can be achieved through an efficient quantum detection technology of the NV center. This review summarizes the recent research progress in diamond-based inertial measurement, including sensitivity optimization methods for inertial measurement systems based on the NV center.
We propose a current-carrying-chip scheme for generating spatial quantum superpositions using a levitating nanodiamond with a built-in nitrogen-vacancy (NV) centre defect. Our setup is quite versatile and we aim to create the superposition for a mass range of 10−19 kg<m<10−15 kg10^{-19}~{\rm kg}< m< 10^{-15}~{\rm kg}10−19 kg<m<10−15 kg and a superposition size O(10)μm<Δx<O(1)nm{\cal O}(10) {\rm μm} < Δx < {\cal O}(1){\rm nm}O(10)μm<Δx<O(1)nm, respectively, in t≤0.1t\leq 0.1t≤0.1s, depending on the position we launch from the center of the diamagnetic trap. We provide an in-depth analysis of two parallel chips that can create levitation and spatial superposition along the xxx-axis, while producing a very tight trap in the yyy direction, and the direction of gravity, i.e., the zzz direction. Numerical simulations demonstrate that our setup can create a one-dimensional spatial superposition state along the x-axis. Throughout this process, the particle is stably levitated in the z-direction, and its motion is effectively confined in the y-direction for a Gaussian initial condition. This setup presents a viable platform for a diamagnetically levitated nanoparticle for a table-top experiment exploring the possibility of creating a macroscopic Schrödinger Cat state to test the quantum gravity induced entanglement of masses (QGEM) protocol.