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Physical review. B./Physical review. B

Circularly polarized zero-phonon transitions of vacancies in diamond at high magnetic fields

D. Braukmann, Evan R. Glaser, Thomas A. Kennedy, M. Bayer, J. Debus

Published May 29, 2018• 21 citations
Publisher

Abstract

We study the circularly polarized photoluminescence of negatively charged (${\mathrm{NV}}^{\ensuremath{-}}$) and neutral (${\mathrm{NV}}^{0}$) nitrogen-vacancy ensembles and neutral vacancies (${\mathrm{V}}^{0}$) in diamond crystals exposed to magnetic fields of up to 10 T. We determine the orbital and spin Zeeman splitting as well as the energetic ordering of their ground and first-excited states. The spin-triplet and -singlet states of the ${\mathrm{NV}}^{\ensuremath{-}}$ are described by an orbital Zeeman splitting of about 9 $\ensuremath{\mu}\mathrm{eV}/\mathrm{T}$, which corresponds to a positive orbital $g$-factor of ${g}_{L}=0.164$ under application of the magnetic field along the (001) and (111) crystallographic directions, respectively. The zero-phonon line (ZPL) of the ${\mathrm{NV}}^{\ensuremath{-}}$ singlet is defined as a transition from the ${}^{1}{E}^{\ensuremath{'}}$ states, which are split by ${g}_{L}{\ensuremath{\mu}}_{\text{B}}B$, to the ${}^{1}{A}_{1}$ state. The energies of the zero-phonon triplet transitions show a quadratic dependence on intermediate magnetic field strengths, which we attribute to a mixing of excited states with nonzero orbital angular momentum. Moreover, we identify slightly different spin Zeeman splittings in the ground (gs) and excited (es) triplet states, which can be expressed by a deviation between their spin $g$-factors: ${g}_{S,\text{es}}={g}_{S,\text{gs}}+\mathrm{\ensuremath{\Delta}}g$ with values of $\mathrm{\ensuremath{\Delta}}g=0.014$ and 0.029 in the (001) and (111) geometries, respectively. The degree of circular polarization of the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs depends significantly on the temperature, which is explained by an efficient spin-orbit coupling of the excited states mediated through acoustic phonons. We further demonstrate that the sign of the circular polarization degree is switched under rotation of the diamond crystal. A weak Zeeman splitting similar to $\mathrm{\ensuremath{\Delta}}g{\ensuremath{\mu}}_{\text{B}}B$ measured for the ${\mathrm{NV}}^{\ensuremath{-}}$ ZPLs is also obtained for the ${\mathrm{NV}}^{0}$ zero-phonon lines, from which we conclude that the ground state is composed of two optically active states with compensated orbital contributions and opposite spin-1/2 momentum projections. The zero-phonon lines of the ${\mathrm{V}}^{0}$ show Zeeman splittings and degrees of the circular polarization with opposite signs. The magnetophotoluminescence data indicate that the electron transition from the $^{1}T_{2}$ states to the $^{1}A$ ground state defines the zero-phonon emission at 1.674 eV, while the $^{1}T_{2}\ensuremath{\rightarrow}^{1}E$ transition is responsible for the zero-phonon line at 1.666 eV. The $^{1}T_{2}$ ($^{1}E$) states are characterized by an orbital Zeeman splitting with ${g}_{L}=0.071$ (0.128).

DOI
10.1103/physrevb.97.195448

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We study the circularly polarized photoluminescence of negatively charged (NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath−) and neutral (NV0{\mathrm{NV}}^{0}NV0) nitrogen-vacancy ensembles and neutral vacancies (V0{\mathrm{V}}^{0}V0) in diamond crystals exposed to magnetic fields of up to 10 T. We determine the orbital and spin Zeeman splitting as well as the energetic ordering of their ground and first-excited states. The spin-triplet and -singlet states of the NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath− are described by an orbital Zeeman splitting of about 9 \ensuremathμeV/T\ensuremath{\mu}\mathrm{eV}/\mathrm{T}\ensuremathμeV/T, which corresponds to a positive orbital ggg-factor of gL=0.164{g}_{L}=0.164gL​=0.164 under application of the magnetic field along the (001) and (111) crystallographic directions, respectively. The zero-phonon line (ZPL) of the NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath− singlet is defined as a transition from the 1E\ensuremath′{}^{1}{E}^{\ensuremath{'}}1E\ensuremath′ states, which are split by gL\ensuremathμBB{g}_{L}{\ensuremath{\mu}}_{\text{B}}BgL​\ensuremathμB​B, to the 1A1{}^{1}{A}_{1}1A1​ state. The energies of the zero-phonon triplet transitions show a quadratic dependence on intermediate magnetic field strengths, which we attribute to a mixing of excited states with nonzero orbital angular momentum. Moreover, we identify slightly different spin Zeeman splittings in the ground (gs) and excited (es) triplet states, which can be expressed by a deviation between their spin ggg-factors: gS,es=gS,gs+\ensuremathΔg{g}_{S,\text{es}}={g}_{S,\text{gs}}+\mathrm{\ensuremath{\Delta}}ggS,es​=gS,gs​+\ensuremathΔg with values of \ensuremathΔg=0.014\mathrm{\ensuremath{\Delta}}g=0.014\ensuremathΔg=0.014 and 0.029 in the (001) and (111) geometries, respectively. The degree of circular polarization of the NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath− ZPLs depends significantly on the temperature, which is explained by an efficient spin-orbit coupling of the excited states mediated through acoustic phonons. We further demonstrate that the sign of the circular polarization degree is switched under rotation of the diamond crystal. A weak Zeeman splitting similar to \ensuremathΔg\ensuremathμBB\mathrm{\ensuremath{\Delta}}g{\ensuremath{\mu}}_{\text{B}}B\ensuremathΔg\ensuremathμB​B measured for the NV\ensuremath−{\mathrm{NV}}^{\ensuremath{-}}NV\ensuremath− ZPLs is also obtained for the NV0{\mathrm{NV}}^{0}NV0 zero-phonon lines, from which we conclude that the ground state is composed of two optically active states with compensated orbital contributions and opposite spin-1/2 momentum projections. The zero-phonon lines of the V0{\mathrm{V}}^{0}V0 show Zeeman splittings and degrees of the circular polarization with opposite signs. The magnetophotoluminescence data indicate that the electron transition from the 1T2^{1}T_{2}1T2​ states to the 1A^{1}A1A ground state defines the zero-phonon emission at 1.674 eV, while the 1T2\ensuremath→1E^{1}T_{2}\ensuremath{\rightarrow}^{1}E1T2​\ensuremath→1E transition is responsible for the zero-phonon line at 1.666 eV. The 1T2^{1}T_{2}1T2​ (1E^{1}E1E) states are characterized by an orbital Zeeman splitting with gL=0.071{g}_{L}=0.071gL​=0.071 (0.128).
We study the linear polarization properties of the photoluminescence of ensembles of neutral and negatively charged nitrogen vacancies and neutral vacancies in diamond crystals as a function of their symmetry and their response to strong external magnetic fields. The linear polarization degree, which exceeds 10% at room temperature, and rotation of the polarization plane of their zero-phonon lines significantly depend on the crystal rotation around specific axes demonstrating anisotropic angular evolutions. The sign of the polarization plane rotation is changed periodically through the crystal rotation, which indicates a switching between electron excited states of orthogonal linear polarizations. At external magnetic fields of up to 10 T, the angular dependencies of the linear polarization degree experience a remarkable phase shift. Moreover, the rotation of the linear polarization plane increases linearly with rising magnetic field at 6 K and room temperature, for the negatively charged nitrogen vacancies, which is attributed to magneto-optical Faraday rotation.
We report on the polarization-dependent optical characterization of nitrogen vacancies in a (001)-oriented diamond crystal subjected to high magnetic fields. A strong optical alignment of the zero-phonon line photoluminescence of up to about 40% is observed for an ensemble of negatively charged nitrogen vacancies. We demonstrate an anisotropy in the linear polarization degree as well as in the rotation of the linear polarization plane of the photoluminescence, which can be tuned from positive to negative values. A phenomenological approach, which takes into account symmetry aspects of the diamond crystal, explains well the anisotropy observed experimentally.
The time-averaged emission spectrum of single nitrogen-vacancy defects in diamond gives zero-phonon lines of both the negative charge state at 637 nm (1.945 eV) and the neutral charge state at 575 nm (2.156 eV). This occurs through photoconversion cycling between the two charge states. Due to strain in the diamond the zero-phonon lines of both charge states are split and it is found that the splitting and polarization of the two zero-phonon lines are the same. From this observation and consideration of the electronic structure of the nitrogen-vacancy center it is concluded that the excited state of the neutral center has A2{A}_{2}A2​ orbital symmetry. The assignment of the 575-nm transition to a 2E{}^{2}E2E-2A2{}^{2}{A}_{2}2A2​ transition has not been established previously.
The 1E^{1}E1E--1A1^{1}A_{1}1A1​ singlet manifold of the negatively charged nitrogen vacancy ($\mathrm{N}{V}^{\ensuremath{-}}$) center in diamond plays a central role in its quantum-information and quantum-sensing applications. However, the energy gap between the 1E^{1}E1E singlet state and diamond band edges or the 3A2^{3}A_{2}3A2​--3E^{3}E3E triplet manifold has not been measured directly. Using the magnetic-field quenching effect on the $\mathrm{N}{V}^{\ensuremath{-}}$ photoluminescence (PL) spectra, we measure these energy gaps as a function of temperature, applied magnetic field, excitation wavelength, and excitation power in a heavily nitrogen-doped sample. Increased PL and decreased zero-phonon line width from the NV0\mathrm{N}{V}^{0}NV0 center were observed in the presence of an applied magnetic field, indicating ionization from the long-lived 1E^{1}E1E singlet state. A temperature-dependent ionization threshold between 532 and 550 nm was found, locating the singlet states within the diamond band gap.
Spectroscopy of photoionization from the 1E^1E1E singlet state in nitrogen−-−vacancy centers in diamond
The 1E−1A1^1E-^1A_11E−1A1​ singlet manifold of the negatively charged nitrogen vacancy (NV−)(NV^-)(NV−) center in diamond plays a central role in the quantum information and quantum sensing applications of the NV−NV^-NV− center. However, the energy of this manifold within the diamond bandgap and with respect to the 3A2−3E^3A_2-^3E3A2​−3E triplet manifold has not been measured directly. Using field-quenching effects on photoluminescence (PL) spectra, we report on the energy gap between the 1E−1A1^1E-^1A_11E−1A1​ singlet manifold and the 3A2^3A_23A2​ and 3E^3E3E ground and excited triplet states of the NV−NV^-NV− as a function of excitation wavelength and power, temperature, and applied magnetic field in a heavily nitrogen-doped sample. Increased PL and decreased zero-phonon line width from the NV0NV^0NV0 were observed in the presence of an applied magnetic field, indicating ionization from the long-lived 1E^1E1E singlet state. A temperature-dependent ionization threshold between 532 nm and 550 nm was found, locating the singlet states within the diamond band gap.
With the creation of nitrogen (NV) in 1b diamond it is common to find that the absorption and emission is predominantly of negatively charged NV centres. This occurs because electrons tunnel from the substitutional nitrogen atoms to NV to form NV − –N + pairs. There can be a small percentage of neutral charge NV 0 centres and a linear increase of this percentage can be obtained with optical intensity. Subsequent to excitation it is found that the line width of the NV − zero-phonon has been altered. The alteration arises from a change of the distribution of N + ions and a modification of the average electric field at the NV − sites. The consequence is a change to the Stark shifts and splittings giving the change of the zero-phonon line (ZPL) width. Exciting the NV − centres enhances the density of close N + ions and there is a broadening of the ZPL. Alternatively exciting and ionizing N 0 in the lattice results in more distant distribution of N + ions and a narrowing of the ZPL. The competition between NV − and N 0 excitation results in a significant dependence on excitation wavelength and there is also a dependence on the concentration of the NV − and N 0 in the samples. The present investigation involves extensive use of low temperature optical spectroscopy to monitor changes to the absorption and emission spectra particularly the widths of the ZPL. The studies lead to a good understanding of the properties of the NV − –N + pairs in diamond. There is a critical dependence on pair separation. When the NV − –N + pair separation is large the properties are as for single sites and a high degree of optically induced spin polarization is attainable. When the separation decreases the emission is reduced, the lifetime shortened and the spin polarization downgraded. With separations of <12 A 0 there is even no emission. The deterioration occurs as a consequence of electron tunneling in the excited state from NV – to N + and an optical cycle that involves NV 0 . The number of pairs with the smaller separations and poorer properties will increase with the number of nitrogen impurities and it follows that the degree of spin polarization that can be achieved for an ensemble of NV − in 1b diamond will be determined and limited by the concentration of single substitutional nitrogen. The information will be invaluable for obtaining optimal conditions when ensembles of NV − are required. As well as extensive measurements of the NV − optical ZPL observations of Stark effects associated with the infrared line at 1042 nm and the optically detected magnetic resonance at 2.87 GHz are also reported.