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Conference on Lasers and Electro-Optics

Model systems and photo-kinetics of single N-V defect centers in diamond

S. Ya. Kilin, Alexander P. Nizovtsev, Tatiana M. Maevskaya, Fedor Jelezko, C. Tietz, Jörg Wrachtrup

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. Fluorescence excitation method of single molecule spectroscopy has been applied recently to study individual nitrogen-vacancy (N-V) defect centers in diamond. These objects are of great interest owing to the proposal to build quantum computer at /sup 13/C nuclear spins neighboring the N-V center. Based on new spectroscopic information we have developed simple models of the N-V center and used them to describe a wide range of experiments dealing both with single centers and with their ensembles. The first model emphasizes possible tunneling of N atom into vacancy and describes that in terms of double well potentials. The second model takes into account the spin-triplet character of the ground electronic state of the center and allows to describe a variety of fluorescence detected magnetic resonance phenomena.

DOI
10.1109/iqec.2000.907880

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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
Summary form only given. Fluorescence excitation method of single molecule spectroscopy has been applied recently to study individual nitrogen-vacancy (N-V) defect centers in diamond. These objects are of great interest owing to the proposal to build quantum computer at /sup 13/C nuclear spins neighboring the N-V center. Based on new spectroscopic information we have developed simple models of the N-V center and used them to describe a wide range of experiments dealing both with single centers and with their ensembles. The first model emphasizes possible tunneling of N atom into vacancy and describes that in terms of double well potentials. The second model takes into account the spin-triplet character of the ground electronic state of the center and allows to describe a variety of fluorescence detected magnetic resonance phenomena.
To describe experiments on fluorescence excitation of single N-V defect centers in diamond we have used the double well potential (DWP) model which incorporates the possibility of tunneling the nitrogen atom into the vacancy both in ground and excited electronic states of the center. Fluorescence and linear absorption spectra are calculated, DWP's parameter values for N-V centers are determined and manifestations of their variations due to local diamond lattice distortions in fluorescence spectra of various single N-V centers are studied.
Over the past few years, the detection of single N-V centers in diamond has attracted much interest, since it is expected to lead to innovative applications in various domains of quantum information. The N-V center in diamond is a defectconsisting of a substitutional nitrogen atom adjacent to a carbon-atom vacancy. The optical transition between the 3A ground state and the 3E excited state has a very high quantum efficiency allowing single defect spectroscopy. Because of the paramagnetic nature of the ground electronic state, single N-V defects are believed to be promising candidates for solid state quantum computation. To date, however, the photophysics of the defect is not entirely understood. The existence of a singlet metastable state 1A was challenged in a series of papers reporting hole-burning, optically detected magnetic resonance and single molecule experiments. We present here an overview of recent low and room temperature data, indicating the important role of a metastable state of the defect in single center experiments.
In an effort to realize a two-bit processor for a quantum computer on the basis of single nitrogen-vacancy defect centers (NV centers) in diamond, the optically detected nutations of the electron spin of a single NV center in the ground state and of the nuclear spin of a 13 C atom located at a diamond lattice site nearest to the NV center are studied. The photodynamics of NV and NV + 13 C centers under different temperatures and optical excitation conditions is discussed. A seven-level model of a center excited by radiation from an Ar + laser at room temperature is proposed. On the basis of this model, the experimental spectra of optically detected electron paramagnetic and electron-nuclear double resonances of single NV and NV + 13 C centers in diamond nanocrystals, as well as experimental data on the optically detected nutations of the electron and nuclear spins of these centers caused by the actions of pulsed microwave and radiofrequency fields, respectively, are interpreted.
Abstract The nitrogen vacancy and some nickel related defects in diamond can be observed as single quantum systems in diamond by their fluorescence. The fabrication of single colour centres occurs via generation of vacancies or via controlled nitrogen implantation in the case of the nitrogen vacancy (NV) centre. The NV centre shows an electron paramagnetic ground and optically excited state. As a result electron and nuclear magnetic resonance can be carried out on single defects. Due to the localized nature of the electron spin wavefunction hyperfine coupling to nuclei more than one lattice constant away from the defect as dominated by dipolar interaction. As a consequence the coupling to close nuclei leads to a splitting in the spectrum which allows for optically detected electron nuclear double resonance. The contribution discusses the physics of the NV and other defect centre from the perspective of single defect centre spectroscopy. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The nitrogen-vacancy (N-V⁻) colour centre in diamond has potential applications in quantum information processing and single photon generation. It is currently the only known defect in a solid detected at a single site level that has a non-zero spin in the electronic ground state. For the proposed applications it is desirable to have a good understanding of the electronic structure and photodynamics of the centre, however this is currently not the case. Various models have been proposed to explain the fluorescence characteristics observed in single site experiments. The challenge has been to also account for the properties of the centre well-known from observations of the fluorescence from large ensembles of N-V⁻ in diamond. Firstly, that a non-Boltzmann population distribution between the. ground state spin levels is induced by optical excitation. Secondly, that the fluorescence intensity exhibits a strong dependence on the spin orientation. The models proposed to date either cannot account for these properties, or do so only by invoking optical processes that are arbitrary or, in some cases, not physical. In this thesis an alternative model is presented. The derivation of the model, from group theoretical considerations, does not form part of this thesis. This thesis is concerned primarily with a series of independent measurements to determine the transition rates which govern the photodynamics of the centre. When these transition rates are known, there will be no free parameters in the model and the N-V⁻ emission can be simulated for an arbitrary optical field by solving the classical rate equations. To conclude the first part of this thesis, a two-pulse optical excitation is considered and the results of experiment are compared to the predictions of the model. The latter part of t his thesis is concerned with optically detecting single N-V⁻ centres. A confocal microscope system, to enable single site detection, was developed as part of this work. The photon statistics from a single N-V⁻ centre is compared to the statistics predicted by the model. The implications for the modelling of individual N-V⁻ photon statistics are discussed.
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.