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Applied Physics Letters

Effective and robust quantum state tomography of electron-nuclear spins in diamond by time-resolved fluorescence

Rujian Zhang, Yuhang Ye, Fei Liu, Jianpei Geng, Baiqiang Zhu, Peng Qian, Bing Chen

Published Aug 12, 2024• 2 citations
Publisher

Abstract

Quantum state tomography (QST) of electron-nuclear spins of nitrogen-vacancy (NV) center in diamond commonly requires a sequence of population flipping operations and frequent calibration of basis states by fluorescence photon-counting. Here, we realize an effective and robust quantum state tomography of electron-nuclear spins based on time-resolved fluorescence, which can enhance the signal-to-noise ratio between different basis states up to 29.6% compared to the photon-counting method. Meanwhile, our method can directly obtain the population of four basis states with only one measurement, which significantly improves the efficiency of tomography. Furthermore, the photon count rate fluctuation of time-resolved fluorescence can be reduced to the standard quantum limit by normalization operation, indicating that the time-resolved method is calibration-free. This method could be easily applied to multi-nuclear spins of NV center in diamond and extended to other solid-state spin systems.

DOI
10.1063/5.0211842

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Quantum state tomography (QST) of electron-nuclear spins of nitrogen-vacancy (NV) center in diamond commonly requires a sequence of population flipping operations and frequent calibration of basis states by fluorescence photon-counting. Here, we realize an effective and robust quantum state tomography of electron-nuclear spins based on time-resolved fluorescence, which can enhance the signal-to-noise ratio between different basis states up to 29.6% compared to the photon-counting method. Meanwhile, our method can directly obtain the population of four basis states with only one measurement, which significantly improves the efficiency of tomography. Furthermore, the photon count rate fluctuation of time-resolved fluorescence can be reduced to the standard quantum limit by normalization operation, indicating that the time-resolved method is calibration-free. This method could be easily applied to multi-nuclear spins of NV center in diamond and extended to other solid-state spin systems.
Quantum state tomography is the procedure for reconstructing unknown quantum states from a series of measurements of different observables. Depending on the physical system, different sets of observables have been used for this procedure. In the case of spin qubits, the most common procedure is to measure the transverse magnetization of the system as a function of time. Here, we present a different scheme that relies on time-independent observables and therefore does not require measurements at different evolution times, thereby greatly reducing the overall measurement time. To recover the full density matrix, we use a set of unitary operations that transform the density operator elements into the directly measurable observable. We demonstrate the performance of this scheme in the electron-nuclear spin system of the nitrogen vacancy center in diamond.
For quantum sensing, it is vital to develop an efficient technique for determining the quantum state of the sensor. We optimize the weighting of the photoluminescence intensity for readout of the spin state of the nitrogen-vacancy (NV) center in diamond. We find that adopting a physical model that considers the optical transitions and relaxations of the NV center allows for an efficient readout. Our method improves the signal-to-noise ratio of the readout by 5.4% in a short time of 3 s, while the existing methods typically require 1 min of integration time. We also show that our technique enhances the readout of the nuclear spin memory. The demonstrated way is helpful for a wide range of measurements, from a few minutes to several days.
Room-temperature fluorescence detection of the nitrogen-vacancy center electronic spin typically has low signal to noise, requiring long experiments to reveal an averaged signal. Here, we present a simple approach to analysis of time-resolved fluorescence data that permits an improvement in measurement precision through signal processing alone. Applying our technique to experimental data reveals an improvement in signal to noise, which is equivalent to a 14% increase in photon collection efficiency. We further explore the dependence of the signal-to-noise ratio on excitation power and analyze our results using a rate equation model. Our results provide a rubric for optimizing fluorescence spin detection, which has direct implications for improving precision of nitrogen-vacancy-based sensors.
We report on a quantum state characterization method, which we call Rabi-based quantum state tomography (RQST), that we have validated on single-qubit quantum states, in particular on the electron and nuclear spins of a single nitrogen-vacancy (NV) center in diamond, demonstrating high fidelities. The difference of RQST with conventional tomography methods is in the implementation of rotation operators and construction of the density matrix from the measured datasets. We demonstrate efficient quantum state control of the electron spin at room temperature with an average fidelity of 0.995 over more than 40 measurements on different states on the Bloch sphere. Also, we apply the methodology to the dark NV nuclear spin state. The state is read via the electron spin using the C-NOT two-qubit entanglement gate and demonstrates fidelities of the same order.
This thesis describes a series of experiments on the control of the optical properties of the nitrogen-vacancy (NV) center in diamond, and on control of the electron and nuclear spin states associated with the NV center. The NV center is a fluorescing atomic defect center in diamond, consisting of a substitutional nitrogen atom adjacent to a vacancy in the diamond carbon lattice. The electron spin of the NV center can be initialized and read out optically, and coherently manipulated with high fidelity even at room temperature. This unique combination of properties has attracted much attention to the NV center in recent years for application in quantum information technologies. The experiments in this work focus on exploiting the intrinsic hybrid nature of the NV center. The NV center forms a hybrid spin register, as its electron spin is always coupled to the nuclear spin of its own nitrogen nucleus, and can furthermore be coupled to additional nuclear carbon-13 spins in the diamond. In addition, the electronic spin state can be mapped onto the state of a photon, in principle allowing long range transmission of quantum information and measurement-based entanglement of distant NV center registers. The long-term goal is to achieve a large scale quantum network where the different constituents each perform the task they are most well suited for: the stable nuclear spins store the quantum information, photons transfer quantum information over long distances, and the fast electron spin interfaces between spin and photon states. For measurement-based entanglement of distant NV centers it is of primary importance to maximize the emission and detection of coherent photons emitted by the NV center. Spontaneous emission can be controlled and enhanced by coupling an emitter to a photonic cavity. Chapters 3, 4, and 5 of this thesis describe experiments aimed at maximizing the coherent photon emission rate of an NV center by coupling the NV center to a photonic crystal cavity. One of the main challenges is to position a single NV center into the nanometer-sized cavity mode. Chapter 3 describes the development of a nanopositioning technique, which allows diamond nanocrystals ~50 nm in size containing single NV centers to be placed at arbitrary locations on a chip, with nanometer precision. By using a sharp etched tungsten tip, individual nanocrystals can be picked up, moved and placed under real-time imaging with an electron microscope. We explicitly demonstrate that the unique optical and spin properties of the NV center are conserved by the nanopositioning process. In chapter 4, we apply the nanopositioning technique to couple single NV centers contained in a diamond nanocrystals to gallium phosphide photonic crystal cavities. These cavities resonate in the visible with high quality factors, and are designed to have the lowest energy mode coincide with the zero-phonon line of the NV center. Efficient coupling is evidenced by a strong enhancement of NV center emission at the cavity wavelength. The high quality factor of a photonic crystal cavity is a result of careful design and fabrication. The introduction of a nanocrystal may therefore be expected to have a detrimental effect on the optical properties of a cavity. In chapter 5 we investigate the effect of a nanocrystal on the optical properties of photonic crystal cavities. Our simulations and measurements show that the effect of a nanocrystal is in fact only minor, a promising result for future work on cavity-QED systems in the solid state and with diamond defect centers in particular. Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Chapter 6 describes experiments that exploit quantum control of the NV center and recently developed dynamical decoupling techniques to study the properties of the surrounding bath of spins belonging to single substitutional nitrogen atoms. The coherence properties of a single NV center are affected by changes in the state of the bath spins, allowing a single NV center to be used as a probe to detect bath spin resonances and study the quantum dynamics of the spin bath. We use quantum control of the spin bath to extend the dephasing time of the NV center, important for the application of the NV center in DC magnetometry. In chapter 7 we describe the development and implementation of decoherence protected quantum gates for the hybrid spin register formed by the NV center electron spin that is coupled to the nuclear spin of its own nitrogen atom. Electron and nuclear spins evolve and decohere at vastly different rates, making it challenging to use such a hybrid system as a fully functional quantum register. We create a universal set of two-qubit quantum gates by integrating dynamical decoupling techniques into the gate operation. We demonstrate the power of our gate design by implementing for the first time Grover's quantum search algorithm on a solid-state spin register.
Nitrogen-vacancy (NV) centers in diamond have been used in recent years for a wide range of applications, from nanoscale NMR to quantum computation. These applications depend strongly on the efficient readout of the NV center's spin state, which is currently limited. Here we suggest a method of reading the NV center's spin state, using the weak optical transition in the singlet manifold. We numerically calculate the number of photons collected from each spin state using this technique, and show that an order of magnitude enhancement in spin-readout signal-to-noise ratio is expected, making single-shot spin readout within reach. Thus, this method could lead to an order of magnitude enhancement in sensitivity for ubiquitous NV-based sensing applications, and remove a major obstacle from using NVs for quantum information processing.