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arXiv:quant-ph/0409067 · Physical Review B

Energy levels and decoherence properties of single electron and nuclear spins in a defect center in diamond

I. Popa, T. Gaebel, Michael Domhan, Christoffer Wittmann, Fedor Jelezko, Jörg Wrachtrup

Published Nov 5, 2004• 28 citations
arXivHTMLPDF

Abstract

The coherent behavior of the single electron and single nuclear spins of a defect center in diamond and a $^{13}\mathrm{C}$ nucleus in its vicinity, respectively, are investigated. The energy levels associated with the hyperfine coupling of the electron spin of the defect center to the $^{13}\mathrm{C}$ nuclear spin are analyzed. Methods of magnetic resonance, together with the optical readout of single defect centers, have been applied in order to observe the coherent dynamics of the electron and nuclear spins. Long coherence times, in the order of microseconds for electron spins and tens of microseconds for nuclear spins, recommend the studied system as a good experimental approach for implementing a two-qubit gate.

DOI
10.1103/physrevb.70.201203

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Nitrogen vacancy (NV-) color centers in diamond are a prime candidate for use in quantum information devices, owing to their spin-1 ground state, straightforward optical initialization and readout, and long intrinsic coherence times in a room-temperature solid. While the 13C nuclear spin is often a dominant source of magnetic noise, we observe transitions between electron-nuclear hyperfine states of NV- centers in 99% 13C diamond that are robust to decoherence. At magnetic field strengths ranging from 550 - 900 G, these transitions are observable by optically detected magnetic resonance (ODMR), and exhibit linewidths narrowed by factors as high as ~130 at room temperature over typical electron-type transitions observed from this spin system. We anticipate the use of these decoherence-protected transitions, in combination with dynamical decoupling methods, for storage of quantum information.

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Quantum control of single spins and single photons in diamond

Toeno van der Sar

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. 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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.

•Mar 27, 2012•0 citations

Manipulation and measurement of quantum states of single spins

Jörg Wrachtrup

Defects determine the mechanical, electrical and optical properties in solids. Often their chemical nature is very simple, comprising for example just a simple lattice vacancy or a single atom impurity. Some defects are optically active, i.e. they show allowed optical transitions. Those defect are called colour centers and often determine the optical properties of the respective solid. Famous examples are colour centers in ruby or alkali halides. By careful control of defect center concentration in combination with optical microscopy it became recently possible to investigate single defect centers optically. One of the materials that was investigated in particular detail is diamond. Pure diamond is an optically transparent medium. However more than 100 colour centers have been identified in diamond. Owing to its energy level structure the nitrogen vacancy center in diamond is a particularly interesting one to investigate. This defect center has a paramagnetic ground and first excited state. The resulting fine structure splitting can be resolved by low temperature fluorescence excitation spectroscopy. Ground as well as first excited state are spin triplets, i.e. S=1. When spin angular momentum is conserved during optical excitation one thus expects to find three optical excitation lines owing to the three spin sub levels in each electronic state. Indeed conservation of spin angular momentum during excitation seems to be fulfilled, however only a single excitation line is found. Experimentally this is due to unfavourable photophysical properties of the other transitions. Because of low electron phonon coupling of the center the linewidth of the transition is limited by the lifetime of the optically excited state and not, as in most cases, by dephasing due to electron-phonon coupling. Due to this low electron-phonon coupling all of the oscillator strength of the optical transition is concentrated in a narrow frequency interval giving rise to a large on resonance absorption cross section. This large cross section allows for ms averaging times, which are much smaller than the spin lattice relaxation times. One thus is able to determine the specific electron spin state the defect center is in. In diamonds isotopically enriched with 13C, the electron spin of the defect center is coupled to the nuclear spins of the surrounding 13C nuclei by hyperfine interaction. The hyperfine coupling depends on the distance of the center of the defect to the nuclei. For nuclei in the first coordination shell around the defect the coupling strength is around 250 MHz for nuclei in the second shell it is roughly 60 MHz. The hyperfine coupling is thus resolvable in single defect center excitation spectra. The spin relaxation times of nuclei in diamond are even longer than those of the electron. One thus is also able to determine the nuclear spin states around the defect center. Simultaneous radiation with radio frequency generates magnetic dipole transition and thus allows to control the nuclear spin states around the center. The system provides an interesting example for readout and manipulation of single spin degrees of freedom which may be interesting as hardware in future quantum information processing application.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations
The coherent behavior of the single electron and single nuclear spins of a defect center in diamond and a 13C^{13}\mathrm{C}13C nucleus in its vicinity, respectively, are investigated. The energy levels associated with the hyperfine coupling of the electron spin of the defect center to the 13C^{13}\mathrm{C}13C nuclear spin are analyzed. Methods of magnetic resonance, together with the optical readout of single defect centers, have been applied in order to observe the coherent dynamics of the electron and nuclear spins. Long coherence times, in the order of microseconds for electron spins and tens of microseconds for nuclear spins, recommend the studied system as a good experimental approach for implementing a two-qubit gate.
We discuss the possibility of realizing quantum computation on the basis of a cluster of single interacting nuclear spins in solids. This idea seems to be feasible because of the combination of two techniques—Single Molecule Spectroscopy and Optically Detected Electron Nuclear Double Resonance. Compared to the well-known bulk Nuclear Magnetic Resonance (NMR), the proposed method of quantum computation has the advantage that quantum computation is performed with pure spin states and the quantum processor is more easily scalable. At the same time, the advantages of NMR quantum computation are kept: long coherence time and easy construction of quantum gates. As a specific system to implement the above idea, we discuss the 13 C-nuclear spins in the nearest vicinity of a single nitrogen-vacancy (NV) defect center in diamond, which can be optically detected using the technique of scanning confocal microscopy. Owing to the hyperfine coupling of the ground state electron paramagnetic spin S =1 of the center to 13 C nuclear spins in a diamond lattice, the states of nuclear spins in the vicinity of the defect-center can be addressed individually. Preliminary consideration shows that it should be possible to address up to 12 individual 13 C nuclear spins. The dephasing time of the nuclear spin states at low temperatures allows realization up to 10 5 gates.
Individual nuclear spins in diamond can be optically detected through hyperfine couplings with the electron spin of a single nitrogen-vacancy (NV) center; such nuclear spins have outstandingly long coherence times. Among the hyperfine couplings in the NV center, the nearest neighbor 13C nuclear spins have the largest coupling strength. Nearest neighbor 13C nuclear spins have the potential to perform fastest gate operations, providing highest fidelity in quantum computing. Herein, we report on the control of coherences in the NV center where all three nearest neighbor carbons are of the 13C isotope. Coherence among the three and four qubits are generated and analyzed at room temperature.
Abstract We employ the electronic spin of a single nitrogen-vacancy (NV) defect in diamond to detect and control the quantum state of remote nuclear spins coupled by hyperfine interaction. More precisely, our work focuses on individual 13C^{13}\text {C}13C 13 C nuclei featuring a moderate hyperfine coupling strength ( ∼1\sim 1∼1 ∼ 1 MHz) with the NV’s electron spin. Two different methods providing an efficient room-temperature polarization of these peculiar 13C^{13}\text {C}13C 13 C nuclear spins are described. The first one is based on a polarization transfer from the NV electron spin to the 13C^{13}\text {C}13C 13 C nucleus, which is mediated by the anisotropic component of the hyperfine interaction. The second one relies on coherent population trapping (CPT) within a Λ\Lambda Λ Λ -type energy-level configuration in the microwave domain, which enables to initialize the 13C^{13}\text {C}13C 13 C nuclear spin in any quantum state superposition on the Bloch sphere. This CPT protocol is performed in an unusual regime for which relaxation from the excited level of the Λ\Lambda Λ Λ -scheme is externally triggered by optical pumping and separated in time from coherent microwave excitations. For these two polarization techniques, we investigate the impact of optical illumination on the nuclear spin polarization efficiency. This work adds new methods to the quantum toolbox used for coherent control of individual nuclear spins in diamond, which might find applications in quantum metrology. Graphical Abstract
Nitrogen vacancy (NV-) color centers in diamond are a prime candidate for use in quantum information devices, owing to their spin-1 ground state, straightforward optical initialization and readout, and long intrinsic coherence times in a room-temperature solid. While the 13C nuclear spin is often a dominant source of magnetic noise, we observe transitions between electron-nuclear hyperfine states of NV- centers in 99% 13C diamond that are robust to decoherence. At magnetic field strengths ranging from 550 - 900 G, these transitions are observable by optically detected magnetic resonance (ODMR), and exhibit linewidths narrowed by factors as high as ~130 at room temperature over typical electron-type transitions observed from this spin system. We anticipate the use of these decoherence-protected transitions, in combination with dynamical decoupling methods, for storage of quantum information.
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.
Defects determine the mechanical, electrical and optical properties in solids. Often their chemical nature is very simple, comprising for example just a simple lattice vacancy or a single atom impurity. Some defects are optically active, i.e. they show allowed optical transitions. Those defect are called colour centers and often determine the optical properties of the respective solid. Famous examples are colour centers in ruby or alkali halides. By careful control of defect center concentration in combination with optical microscopy it became recently possible to investigate single defect centers optically. One of the materials that was investigated in particular detail is diamond. Pure diamond is an optically transparent medium. However more than 100 colour centers have been identified in diamond. Owing to its energy level structure the nitrogen vacancy center in diamond is a particularly interesting one to investigate. This defect center has a paramagnetic ground and first excited state. The resulting fine structure splitting can be resolved by low temperature fluorescence excitation spectroscopy. Ground as well as first excited state are spin triplets, i.e. S=1. When spin angular momentum is conserved during optical excitation one thus expects to find three optical excitation lines owing to the three spin sub levels in each electronic state. Indeed conservation of spin angular momentum during excitation seems to be fulfilled, however only a single excitation line is found. Experimentally this is due to unfavourable photophysical properties of the other transitions. Because of low electron phonon coupling of the center the linewidth of the transition is limited by the lifetime of the optically excited state and not, as in most cases, by dephasing due to electron-phonon coupling. Due to this low electron-phonon coupling all of the oscillator strength of the optical transition is concentrated in a narrow frequency interval giving rise to a large on resonance absorption cross section. This large cross section allows for ms averaging times, which are much smaller than the spin lattice relaxation times. One thus is able to determine the specific electron spin state the defect center is in. In diamonds isotopically enriched with 13C, the electron spin of the defect center is coupled to the nuclear spins of the surrounding 13C nuclei by hyperfine interaction. The hyperfine coupling depends on the distance of the center of the defect to the nuclei. For nuclei in the first coordination shell around the defect the coupling strength is around 250 MHz for nuclei in the second shell it is roughly 60 MHz. The hyperfine coupling is thus resolvable in single defect center excitation spectra. The spin relaxation times of nuclei in diamond are even longer than those of the electron. One thus is also able to determine the nuclear spin states around the defect center. Simultaneous radiation with radio frequency generates magnetic dipole transition and thus allows to control the nuclear spin states around the center. The system provides an interesting example for readout and manipulation of single spin degrees of freedom which may be interesting as hardware in future quantum information processing application.