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arXiv:2101.10049 · Physical review. B./Physical review. B

Optimal control of a nitrogen-vacancy spin ensemble in diamond for sensing in the pulsed domain

Andreas F. L. Poulsen, Joshua D. Clement, James Luke Webb, Rasmus Høy Jensen, Luca Troise, Kirstine Berg‐Sørensen, Alexander Huck, Ulrik L. Andersen

Published Jul 5, 2022• 28 citations
arXivHTMLPDF

Abstract

Defects in solid-state materials provide an ideal, robust platform for quantum sensing. To deliver maximum sensitivity, a large ensemble of noninteracting defects hosting quantum states with long coherence is required. Control of such an ensemble is challenging due to the spatial variation in both the defect energy levels and in any control field across a macroscopic sample. In this work, we experimentally demonstrate that we can overcome these challenges using Floquet theory and optimal control optimization methods to efficiently and coherently control a large defect ensemble, suitable for sensing. We apply our methods experimentally to a spin ensemble of up to $4\ifmmode\times\else\texttimes\fi{}{10}^{9}$ nitrogen-vacancy centers in diamond. By explicitly including the hyperfine interaction to the intrinsic $^{14}\mathrm{N}$ nuclear spin in the optimization, we design shaped microwave control pulses that can outperform conventional ($\ensuremath{\pi}$) pulses when applied to sensing schemes, with an improvement in the strength of ensemble response of between 11% and 78%. Through simulation of the ensemble dynamics, we shed light on the bandwidth limitations of large-ensemble reinitialization and propose alternative routes for further improvement.

DOI
10.1103/physrevb.106.014202

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During the last ten years, basic quantum operations on a single electronic spins in the nitrogen-vacancy defect center in diamond have been a rich field of study. Quantum operations coherently manipulating the spin of the nitrogen-vacancy center have become promising candidates for easy to manipulate qubits. However in order to implement these qubits in quantum computers robust high-fidelity control is needed. Building on an existing confocal microscopy setup, pulsed and quadrature-amplitude modulated microwave signals were used to realize coherent spin manipulation measurements. Especially designed Smooth Optimal Control pulses (robust against detuning and different control amplitudes) were used to develop measurement schemes resulting in the aforementioned increase of fidelity. The first part of the thesis describes the implementation of these pulses into the existing experimental setup and the calibration work necessary prior to measurements, due to imperfections of devices in the microwave chain. The second part is dedicated to the analysis of the pulses applied to a single spin by comparing the experimental results to theoretical simulations. This was done not only for one resonant spin with accurate control amplitude, but also for a range of different detunings and amplitudes. A more thorough analysis of the pulses was then achieved by using state/process tomography, resulting in a complete description of the process induced by these optimized pulses. Finally, after verifying the effect of the pulses, measurement schemes for sensing alternating magnetic fields were implemented, resulting in measurements with improved sensitivity for magnetic fields.
Quantum technologies are transitioning from proof-of-principle experiments to practical everyday applications. As this transition unfolds, it remains unclear which quantum system will offer the most suitable platform for specific tasks. While many candidate systems offer excellent control and demonstrate rapid progress, they often require demanding operating conditions such as cryogenic temperatures down to the millikelvin range. The nitrogen-vacancy (N-V) center in diamond is a notable exception. This optically active defect allows full control of its electronic spin state at room temperature and maintains long coherence times under ambient conditions, a prerequisite for many applications. This accessibility makes the N-V center uniquely suited for translating fundamental quantum concepts into deployable technologies. The applicability of N-V centers in quantum sensing, quantum control, and quantum simulation is the central focus of this thesis. After an introductory overview of the field, the thesis introduces the experimental and theoretical concepts that are necessary to understand the presented results. It proceeds to show how the operating regime of N-V centers as sensors for AC magnetic fields and nuclear spins can be extended to low and zero magnetic bias fields. Many commonly used sensing protocols require a magnetic bias field, which can alter the investigated dynamics or may be infeasible to apply due to experimental constraints. This work describes how established sensing protocols can be adjusted for operation under these conditions, and presents novel sensing protocols that enable the detection of AC magnetic fields and nuclear spins in a regime where conventional protocols fail. These results highlight that precise control of the underlying quantum system is a must. Such control can be optimized using quantum optimal control, which allows one to improve the underlying gate operations in a closed-loop, black-box manner, provided a figure of merit can be found which reliably evaluates the gate-set's performance. As this performance can depend on the specific application, the following part of this thesis defines and benchmarks several figures of merit for closed-loop optimal control using an ensemble of N-V centers. The strengths and limitations of these figures of merit are discussed, and the dependence of the optimization performance on several control and experimental parameters is analyzed. The achieved results are applicable to a broad range of other physical platforms, and can serve as a reference for experimental groups that aim to optimize their gate operations using optimal control. Building upon these insights into quantum control, the next part of this thesis presents the fabrication, control, and application of a room-temperature quantum simulator based on thin nuclear spin layers in diamond. A detailed assessment of the growth process is provided, and the dynamics that allow nearby N-V centers to initialize and read out the nuclear spins are thoroughly investigated. Furthermore, the nuclear spin layer is employed to create and study discrete time-crystalline order. The results demonstrate a scalable route for exploring quantum many-body phenomena under ambient conditions. The thesis concludes with a summary and discussion of all results and provides an outlook on future work based on these findings. In conclusion, this thesis demonstrates and expands the versatile use of N-V centers in diamond for quantum sensing, control, and simulation, highlighting their potential as a practical platform for future quantum technologies.
Solid-state electron spin qubits, like the nitrogen-vacancy center in diamond, rely on control sequences of population inversion to enhance sensitivity and improve device coherence. But even for this paradigmatic system, the fundamental limits of population inversion and potential impacts on applications like quantum sensing have not been assessed quantitatively. Here, we perform high accuracy simulations beyond the rotating wave approximation, including explicit unitary simulation of neighboring nuclear spins. Using quantum optimal control, we identify analytical pulses for the control of a qubit subspace within the spin-1 ground state and quantify the relationship between pulse complexity, control duration, and fidelity. We find exponentially increasing amplitude and bandwidth requirements with reduced control duration and further quantify the emergence of non-Markovian effects for multipulse sequences using sub-nanosecond population inversion. From this, we determine that the reduced fidelity and non-Markovianity is due to coherent interactions of the electron spin with the nuclear spin environment. Ultimately, we identify a potentially realizable regime of nanosecond control duration for high-fidelity multipulse sequences. These results provide key insights into the fundamental limits of quantum information processing using electron spin defects in diamond.
Nitrogen-vacancy (NV) centers in diamond are a promising platform for ambient, high-spatial resolution magnetometry relevant to biological signals such as cardiac and muscle activity. One of the challenges is the development of pulse sequences tailored to biological signals in the near DC-range. The spatial environment of NV centers within the diamond lattice is highly complex, e.g. due to magnetic field inhomogeneities, limiting the sensors performance. To overcome these experimental constraints, quantum optimal control (QOC) aims at a precise manipulation of the systems dynamics via optimally shaped microwave pulses increasing the overall robustness of spin-based quantum sensors.
Nitrogen-vacancy (NV) center ensembles have the potential to improve a wide range of applications, including nuclear magnetic resonance spectroscopy at the microscale and nanoscale, wide-field magnetometry, and hyperpolarization of nuclear spins via the transfer of optically induced NV polarization to nearby nuclear spin clusters. These NV ensembles can be coherently manipulated with microwave cavities, that deliver strong and homogeneous drivings over large volumes. However, the pulse shaping for microwave cavities presents the challenge that the external controls and intracavity field amplitudes are not identical, leading to adverse effects on the accuracy of operations on the NV ensemble. In this paper, we introduce a method based on gradient ascent pulse engineering (GRAPE) to optimize external controls, resulting in robust pulses within the cavity while minimizing the effects of cavity ringings. The effectiveness of the method is demonstrated by designing both π and π / 2 pulses. These optimized controls are then integrated into a PulsePol sequence, where numerical simulations reveal a resilience to detunings five times larger than those tolerated by the sequence constructed using standard controls.
Solid-state spin defects, particularly the nitrogen-vacancy (NV) center in diamond, have emerged as powerful platforms for exploring quantum many-body physics and quantum metrology. Their exceptional coherence properties and strong dipolar interactions offer unique opportunities to simulate complex quantum dynamics and engineer entangled states for enhanced sensing beyond the standard quantum limit. However, achieving scalable entanglement in these systems is notoriously difficult due to intrinsic disorder and the complex nature of long-range dipole-dipole interactions. This thesis presents both theoretical and experimental advancements in harnessing quantum dynamics in interacting spin ensembles for quantum-enhanced metrology. A central result is the experimental realization of spin squeezing in a dense ensemble of NV centers, demonstrating a clear path toward overcoming classical limits in solid-state platforms. To further formalize and scale these phenomena, this work develops theoretical frameworks for generating robust spin squeezing under realistic experimental conditions. We show that finite-temperature easy-plane magnetism can be actively leveraged to create scalable squeezed states for the dipolar spin systems on regular lattices. Building upon this, we further extend the result to spatially disordered quantum dipoles. We demonstrate that strongly coupled spin pairs suppress squeezing through dynamical heating, and we propose a selective shelving protocol to mitigate this problem. Furthermore, we also propose a universal protocol for quantum-enhanced sensing that exploits information scrambling, utilizing the natural, scrambling dynamics of strongly interacting many-body systems to effectively amplify weak external signals. Together, the findings detailed in this thesis establish a foundational paradigm for controlling and utilizing solid-state spin ensembles, paving the way for entanglement-enhanced quantum sensors.