Session N39: Quantum Metrology and Sensing I

Optimally entangled atomic states for quantum metrology

Optical lattice clocks operating near the standard quantum limit (SQL) employ uncorrelated ensembles of cold trapped atoms to reach unprecedented accuracy. Their precision is proportional to the square root of the number of atoms. Going beyond the SQL requires correlations between the atoms. That is, nonlinear interactions such as the one-axis twisting Hamiltonian may be used to generate many-body entangled states such as spin squeezed states (SSS). For a SSS, noise is reduced for one quadrature and enhanced for the orthogonal quadrature. Although SSS improve the precision scaling beyond the SQL, they are limited due to the curvature of the Bloch sphere and cannot reach the fundamental Heisenberg limit (HL) of quantum metrology where the precision scales linearly with the number of atoms. Moreover, experimental limitations further reduce the metrological gain and scaling. For example, photon scattering into free space when using light-mediated interactions to implement one-axis twisting induces contrast loss in the measured signal.

In our presentation, we introduce a family of entangled states that leads to an improvement in the precision scaling proportional to the Heisenberg limit. We show how to create these entangled states using a combination of standard controls and the one-axis twisting Hamiltonian. The required types of controls have already been used previously to achieve the best sensitivity improvement beyond the SQL to date. Thus, we expect the proposed family of quantum states to be achievable with only small modifications to existing experimental setups, improving metrological scaling beyond the current state of the art. We discuss general considerations for the experimental implementation and their impact on the final metrological gain and precision scaling.   

Detection of Nuclear Quadrupolar Resonance of a nanoscale 2D material by optimized nitrogen vacancy ensembles in diamond.

Nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) of bulk quantum materials has provided significant insight into magnetic phenomena such as quantum phase criticality, magnetism, and superconductivity. With the emergence of nanoscale 2-D materials with magnetic phenomena, inductively detected NMR is not sufficiently sensitive to detect the small nuclear density in these materials. The nitrogen-vacancy center in diamond (NV) has shown great promise in bringing the spectroscopic capabilities of NQR to the nanoscale. Single NV spins provide excellent spatial resolution but can be unstable and maybe less sensitive to NMR than NV ensembles. However, NV NMR detection of 2D materials has yet to be demonstrated with NV ensembles. Furthermore, the optimal NV layer for NMR detection will require an optimized depth calibration which trades off sample-NV standoff (closer to the diamond surface) and higher activation/better spin properties (further from diamond surface).

In this work, we prepare six near-surface NV ensembles, determine their depths by 19F NMR, and determine their NMR sensitivities using a home-built fluorescence microscope with a 40 μm excitation diameter. We use one of our most sensitive NV ensembles for detection of 11B NQR in hBN exfoliated onto the diamond surface.  To prepare our near surface NV ensembles, we implant nitrogen at energies from 1.5 to 7 keV.  We experimentally demonstrate that minimizing sample sensor stand-off minimizes measurement time to achieve SNR = 3, t(SNR=3).  We then exfoliated 100nm thick flakes of hBN on a diamond and measured the NQR signal intensity of 11B with CPMGXY8-N, to demonstrate the sensitivity of these samples. We estimate these NV ensembles should have shorter t(SNR=3) than a single NV for 11B in hBN for excitation diameters as small as 8 μm.

SAND2021-13251 A   

Nanoscale Nuclear magnetic resonance with quantum sensors enhanced by nanostructures

Quantum sensors based on Nitrogen vacancy (NV) centers in diamond have demonstrated highly sensitive nanoscale detection of nuclear spins [1,2]. For the application in biochemistry, however, several challenges of the technique must be overcome. The spectral resolution achieved so far is low, mainly due to diffusion in liquid-state samples [3]. In addition to this the sample molecules and the sensor are typically not colocalized, which hinders practical application of the method. We overcome these limitations by fabricating nanostructures in diamond and trapping samples in them. We furthermore show the deterministic creation of NV centers within these nanostructures and characterize them by coherence measurements. To enhance the optical readout, we apply a single nuclear spin as a quantum memory. These improvements allow the nuclear magnetic resonance (NMR) detection of nanoconfined liquid-state samples.

[1] T. Staudacher et al. Science 339 (2013) 561

[2] H. Mamin et al. Science 339 (2013) 557

[3] N. Aslam et al. Science 357 (2017) 67   

Simulating Quantum Sensing with NV- Centers

NV centers in diamond have served an important role in quantum sensing and its applications to optically detected NMR. To understand the full breadth of the NV spin dynamics, we will discuss NV simulations under different pulse sequences and conditions using the python QuTiP package. Particularly interesting are the effects of different pulse shapes on the NV spin and how the dynamical decoupling sequences play a role in detecting AC signals. Furthermore, we will explore the double quantum resonance, and how we can use it to improve sensitivity.   

Probing spin dynamics in atomically thin materials with quantum sensors

Investigating the dimension dependence of spin-dynamics in solid-state systems gives more insight into the many-body physics at play. However, realizing a two-dimensional array of spins in a solid-state system is challenging and the experiments are further complicated due to the presence of disorder. Here two-dimensional materials can be useful with their variable thickness, well-defined geometry and low disorder. In this project we use shallow Nitrogen vacancy (NV) centers in diamond to detect the spin dynamics of nuclear spins in layered materials such as hBN [1]. Thanks to a quantum-memory enhanced sensing protocol, we can measure spin diffusion in atomically thin materials placed on the diamond surface. In the sensing protocol, the probe is the NV electron spin which prints phase information onto the memory, the NV nitrogen nuclear spin, through entanglement. The nitrogen nuclear spin being less sensitive to the environment, allows the storage of information on a longer timescale compared to the standard sensing scheme [2]. Furthermore, the optical readout is enhanced by single shot readout of the memory spin.

[1] I. Lovchinsky et al. Science 355 (2017) 6324

[2] N. Aslam et al. Science 357 (2017) 67   

Dual-space Compressed Sensing

Compressed sensing (CS) is routinely utilized to accelerate sampling processes, and attempts have been made to employ it into quantum sensing and quantum information processing. Here we present a dual-space CS approach that is suited for application of dual-mode imaging of nanodiamonds, combining optical imaging and dynamical nuclear polarization (DNP) enhanced magnetic resonance imaging [1]. This novel CS regime harnesses the ability to sample in two Fourier reciprocal spaces (e.g. k- and x-space) simultaneously. In contrast to conventional CS that only samples in single k-space, we show that dual-space CS offers significant acceleration in imaging speed and enhancement in robustness to noise. We will also describe its application towards edge detection. This work suggests a way to strategically sample two incoherent spaces to gain imaging acceleration, and can be generalized to images sampled over multiple uncorrelated spaces. Application of these ideas to quantum sensing will be discussed.

 

[1] Lv, Xudong, et al. "Background-free dual-mode optical and 13C magnetic resonance imaging in diamond particles." Proceedings of the National Academy of Sciences 118.21 (2021).   

High Magnetic Field Quantum Sensing via Hyperpolarized Nuclei

In the quest towards high-resolution quantum sensors for applications in sub-micronscale NMR, the high-field

regime is advantageous since it naturally enables chemical shift discrimination and allows higher analyte polarization.

Here we propose and demonstrate a high-field (7T) quantum sensor constructed from hyperpolarized

13C nuclear spins in diamond. The 13C nuclei are initialized via Nitrogen-Vacancy (NV) centers and protected

along a transverse Bloch sphere axis for minute-long periods. When exposed to a time-varying (AC) magnetic

field, they undergo secondary precessions that contain a direct imprint of its frequency. We demonstrate that

high sensitivity and resolution is feasible by harnessing the long rotating frame 13C sensor lifetimes T2'>20 s, over

106 greater than their NV center counterparts, and their ability to be continuously interrogated. For quantum

sensing at 7 T, we demonstrate spectral resolution better than 70 mHz (corresponding to a precision 1 ppm) and

sensitivity better than 20 nT/vHz for a single crystal sample. We discuss the advantages of nuclear magnetometers over conventional NV center

sensors, including deployability in randomly-oriented diamond particles, in optically scattering media, and in a

wide range of bias field environments (1-20 T). Fundamentally, our technique with densely-packed 13C nuclei

demonstrates a new approach for quantum sensing in the “coupled-sensor” limit. This work points to intriguing

opportunities for “targeted” microscale NMR chemical sensors constructed from hyperpolarized

nanodiamonds and portends applications of dynamic nuclear polarization (DNP) in quantum sensing.   

NMR spectroscopy using NV-centers in diamond

Solid-state systems including the nitrogen-vacancy (NV) center in diamond have attracted increasing interest as quantum sensing platforms. Due to their atomic size, NV-centers have allowed for nuclear magnetic resonance (NMR) spectroscopy of nano and micro scale volumes. After recent advances have achieved part per million spectral resolution, they are of particular interest for the analysis of surfaces as well as small biological systems such as single proteins or cells. Furthermore, they allow for electron spin polarization transfer and therefore NMR signal enhancement. While most experiments are done with single NV-centers, we have integrated a dense ensemble of defects within a layer of micron scale thickness with a microfluidic chip. This allows for faster measurement times due to millions of defects being probed simultaneously, as well as fast sample switching and confinement within the micro fluidic channel. We have used this setup for performing NMR microscopy in these channels and performed first steps towards hyperpolarization with NV-centers in diamond.   

NMR quantum sensing using Nitrogen–Vacancy Centers in Diamond

Elucidating molecular structure at the single- to few-molecule level is an important topic in analytical chemistry, biochemistry, and molecular biology. The nitrogen–vacancy (NV) center in diamond is a promising sensing tool to achieve this resolution for nanoscale nuclear magnetic resonance (NMR) spectroscopy and imaging.

In this talk, we report on recent strategies to improve NMR spectroscopy methods by new measurement schemes with NV centers. These allow us to physically map the nuclear spin signals of individual ¹³C atoms and to measure their inter-nuclear couplings at room temperature. Individual ¹³C atoms in the atomistic environment of the NV center serve as an ideal test bed for the long-term goal of imaging individual molecules that are attached to the diamond surface. Towards this goal, we report on our ongoing work on bringing NV centers close to the surface and preparing surfaces in a controlled manner. We chemically functionalize the diamond surface with monolayers of fluorinated molecules and show that ¹⁹F NMR signals can be detected using single NVs. We give an outlook on the steps needed to perform NMR measurements at the single-molecule level and to expand the suite of characterization methods necessary for spin mapping above the diamond surface.   

Detection of Molecular Transitions with Nitrogen-Vacancy Centers and Electron-Spin Labels

We present a protocol that detects molecular conformational changes with two nitroxide electron-spin labels and a nitrogen-vacancy (NV) center in diamond. More specifically, we demonstrate that the NV can detect energy shifts induced by the coupling between electron-spin labels. The protocol relies on the judicious application of microwave and radiofrequency pulses in a range of parameters that ensures stable nitroxide resonances. Furthermore, we demonstrate that our scheme is optimized by using nitroxides with distinct nitrogen isotopes. Finally, we use detailed numerical simulations and Bayesian inference techniques to show that our method enables the detection of conformational changes under realistic conditions. In particular, we show that random molecular tumbling can be exploited to extract the associated changes in inter-label distance. In addition, we account for strong NV dephasing rates as a consequence of the diamond surface proximity and for nitroxide decoherence and thermalization mechanisms.   

High-resolution spectroscopy of single nitrogen-vacancy defects at zero magnetic field

Nitrogen-vacancy (NV) centers in diamond are excellent and versatile quantum sensors, even at room temperature and pressure. The extraordinary sensitivity of NV centers to the external and internal fields, including electric, magnetic, stress/strain fields and temperature, makes them susceptible to these perturbations, thus making the study of their effect on the NV centers essential. In this work, we discuss the effect of intrinsic electric and strain fields, collectively known as the effective field, on the energy level structure of the NV center. Our work is a vital step in understanding the consequence of the coupling of the NV center with its surrounding effective field.   

Spatially selective universal quantum operation of a nitrogen-vacancy center in diamond

Solid-state spin systems have long coherence time and are inherently small, making them ideal for large-scale integrated quantum storage. However, selective, and precise manipulation of spatially aligned spins is challenging. We realize spatially selective universal quantum gates by using microwave for holonomic manipulation while inducing an optical Stark shift in the electron spin of a nitrogen-vacancy center in diamond. By using highly localized light for addressing and highly controllable microwaves for gate manipulation, we demonstrate optically addressed quantum gates with <300 nm resolution and >90% fidelity. Our method, based on alternating microwave pulses, allows high fidelity control even for inactive spins, which is difficult to achieve with conventional all-optical manipulation [1-3]. By applying this technique, we also show initialization, arbitrary state preparation, readout, and spin echo. Furthermore, we show local electron-nuclear spin entanglement generation by utilizing the selectivity of electron spins. This enables selective quantum teleportation transfer from photons to nuclear spins [4, 5], paving the way for the realization of distributed quantum computers and the quantum Internet implementing large-scale quantum storage.