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Optics and Spectroscopy

Spin-selective low temperature spectroscopy on single molecules with a triplet-triplet optical transition: Application to the NV defect center in diamond

Alexander P. Nizovtsev, S. Ya. Kilin, Fedor Jelezko, I. Popa, A. Gruber, C. Tietz, Jörg Wrachtrup

Published Jun 1, 2003• 42 citations
Publisher

Abstract

The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T 0–T 1, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g (2)(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T 1→S→T 0 to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T 0) state sublevels can be obtained from the spectra and g (2)(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet 3 A-3 E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m S =0 sublevel of the excited 3 E state to the singlet 1 A state (~1 kHz) is much slower than the rates from the m S =±1 substates, while the rates of ISC transitions to different m S substates of the ground 3 A state are close to each other (~1 Hz). As a result, only the optical transition between m S =0 sublevels in the 3 A-3 E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g (2)(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T 0(m S )=0) transition and (ii) the S→T 0(m S =±1) transitions followed by the slow spin-lattice relaxation T 0(m S =±1)→T 0(m S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.

DOI
10.1134/1.1586735

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Manipulation and measurement of quantum states of single spins

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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.

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Electronic structure of the nitrogen-vacancy color center in diamond.

David A. Redman

The nitrogen - vacancy (N-V) center is a point defect found in diamonds containing substitutional nitrogen impurities. It arises after exposure to ionizing radiation and subsequent thermal annealing. The physical structure of the center has previously been identified as a substitutional nitrogen atom located adjacent to a neutral carbon vacancy, but prior to this work knowledge of its electronic structure was very incomplete. The results presented here are intended to establish the energy level structure of the N-V center unambiguously, using nonlinear laser spectroscopy in concert with paramagnetic resonance experiments. A new technique which achieves sub-Hertz resolution in nearly degenerate four-wave mixing (NDFWM) and optical two-beam coupling experiments was applied to determine the decay rates of excited states in the N-V center. Laser-enhanced EPR experiments were performed to assign spin character to the ground state. Fluorescent emission of the center was used to determine excited state energies. In particular, these results resolve earlier conflicting reports of the N-V ground state structure and offer a picture of state energies and dynamics consistent with all observations to date. The principal results of this thesis may be summarized as follows. We show that the ground state of the center consists of a spin triplet ground state with a zero-field splitting of 2.88 GHz and a spin-lattice relaxation time of 1.170 $\pm$ 0.003 ms. The first parity-allowed transition occurs to a triplet excited state at 1.944 eV with a lifetime of 13.3 $\pm$ 0.2 ns. The first metastable singlet excited state is shown to have a lifetime of 265.3 $\pm$ 0.6 ms at room temperature and its temperature dependence measured between 77 and 295 K. Through low temperature studies the mechanism for ground state spin-lattice relaxation is determined to be a two-phonon process involving 63 meV optical phonons. Finally, the origin of satellite lines in the persistent hole-burning spectrum is tentatively explained using our picture of the energy level structure and used to infer a zero-field spin splitting in the excited triplet state of 0.6 GHz.

•Jan 1, 1991•0 citations
The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T 0–T 1, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g (2)(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T 1→S→T 0 to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T 0) state sublevels can be obtained from the spectra and g (2)(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet 3 A-3 E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m S =0 sublevel of the excited 3 E state to the singlet 1 A state (~1 kHz) is much slower than the rates from the m S =±1 substates, while the rates of ISC transitions to different m S substates of the ground 3 A state are close to each other (~1 Hz). As a result, only the optical transition between m S =0 sublevels in the 3 A-3 E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g (2)(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T 0(m S )=0) transition and (ii) the S→T 0(m S =±1) transitions followed by the slow spin-lattice relaxation T 0(m S =±1)→T 0(m S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.
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.
We investigate spin-dependent decay and intersystem crossing (ISC) in the optical cycle of single negatively charged nitrogen-vacancy (NV) centres in diamond. We use spin control and pulsed optical excitation to extract both the spin-resolved lifetimes of the excited states and the degree of optically induced spin polarization. By optically exciting the centre with a series of picosecond pulses, we determine the spin-flip probabilities per optical cycle, as well as the spin-dependent probability for ISC. This information, together with the independently measured decay rate of singlet population, provides a full description of spin dynamics in the optical cycle of NV centres. The temperature dependence of the singlet population decay rate provides information about the number of singlet states involved in the optical cycle.
Spin-lattice relaxation within the nitrogen-vacancy (NV) center's electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center's |m_{s}=0⟩↔|m_{s}=±1⟩ and |m_{s}=-1⟩↔|m_{s}=+1⟩ transitions as a function of temperature from 9 to 474 K in high-purity samples. We show that the temperature dependencies of the rates are reproduced by an ab initio theory of Raman scattering due to second-order spin-phonon interactions, and we discuss the applicability of the theory to other spin systems. Using a novel analytical model based on these results, we suggest that the high-temperature behavior of NV spin-lattice relaxation is dominated by interactions with two groups of quasilocalized phonons centered at 68.2(17) and 167(12) meV.
The nitrogen-vacancy (NV) center in diamond is of high importance in quantum information processing applications. The operation of the NV center relies on the efficient optical polarization of its electron spin. However, the full optical spin-polarization process, which involves the intersystem crossing between the shelving singlet state and the ground-state triplet, is not understood. Here we develop a detailed theory of this process which involves a combination of pseudo- and dynamic Jahn-Teller interactions together with spin-orbit interaction. Our theory provides an explanation for the asymmetry between the observed emission and absorption spectra of the singlet states. We apply density functional theory to calculate the intersystem crossing rates and the optical spectra of the singlets, and we obtain a good agreement with the experimental data. Since the NV center serves as a template for other solid-state-defect quantum bit systems, our theory provides a toolkit to study them that might help optimize their quantum bit operation.
The nitrogen - vacancy (N-V) center is a point defect found in diamonds containing substitutional nitrogen impurities. It arises after exposure to ionizing radiation and subsequent thermal annealing. The physical structure of the center has previously been identified as a substitutional nitrogen atom located adjacent to a neutral carbon vacancy, but prior to this work knowledge of its electronic structure was very incomplete. The results presented here are intended to establish the energy level structure of the N-V center unambiguously, using nonlinear laser spectroscopy in concert with paramagnetic resonance experiments. A new technique which achieves sub-Hertz resolution in nearly degenerate four-wave mixing (NDFWM) and optical two-beam coupling experiments was applied to determine the decay rates of excited states in the N-V center. Laser-enhanced EPR experiments were performed to assign spin character to the ground state. Fluorescent emission of the center was used to determine excited state energies. In particular, these results resolve earlier conflicting reports of the N-V ground state structure and offer a picture of state energies and dynamics consistent with all observations to date. The principal results of this thesis may be summarized as follows. We show that the ground state of the center consists of a spin triplet ground state with a zero-field splitting of 2.88 GHz and a spin-lattice relaxation time of 1.170 ±\pm± 0.003 ms. The first parity-allowed transition occurs to a triplet excited state at 1.944 eV with a lifetime of 13.3 ±\pm± 0.2 ns. The first metastable singlet excited state is shown to have a lifetime of 265.3 ±\pm± 0.6 ms at room temperature and its temperature dependence measured between 77 and 295 K. Through low temperature studies the mechanism for ground state spin-lattice relaxation is determined to be a two-phonon process involving 63 meV optical phonons. Finally, the origin of satellite lines in the persistent hole-burning spectrum is tentatively explained using our picture of the energy level structure and used to infer a zero-field spin splitting in the excited triplet state of 0.6 GHz.