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 study the circularly polarized photoluminescence of negatively charged (${\mathrm{NV}}^{\ensuremath{-}}$) and neutral (
NV0) nitrogen-vacancy ensembles and neutral vacancies (
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 ${\mathrm{NV}}^{\ensuremath{-}}$ 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
gL=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
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
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
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 show Zeeman splittings and degrees of the circular polarization with opposite signs. The magnetophotoluminescence data indicate that the electron transition from the
1T2 states to the
1A 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
1T2 (
1E) states are characterized by an orbital Zeeman splitting with
gL=0.071 (0.128).
The dependence of the luminescence of diamonds with negatively charged nitrogen-vacancy centers (NV-) vs. applied magnetic field (magnetic spectrum) was studied. A narrow line in zero magnetic field was discovered. The properties of this line are considerably different from those of other narrow magnetic spectrum lines. Its magnitude is weakly dependent of the orientation of the single-crystal sample to the external magnetic field. This line is also observed in a powdered sample. The shape of the line changes greatly when excitation light polarization is varied. The magnitude of the line has a non-linear relation to excitation light intensity. For low intensities this dependence is close to a square law. To explain the mechanism giving rise to this line in the magnetic spectrum, we suggest a model based on the dipole-dipole interaction between different NV- centers.
The low-magnetic-field feature in the magnetic field dependence of the luminescence of negatively charged nitrogen-vacancy (NV − ) centers in diamond has been experimentally observed for the first time. This feature, centered at the zero magnetic field—henceforth the zero field line—and observed with a magnetic field sweep of NV − center luminescence (magnetic spectrum), is quite narrow. The properties of this line are considerably different from those of other narrow NV − magnetic spectrum lines. Its amplitude is weakly dependent on the orientation of the single-crystal sample with respect to the external magnetic field. This line is also observed in a powdered sample. The shape of the line changes drastically with a change in the polarization of excitation light. The amplitude of the line non-linearly depends on excitation light intensity. For low intensities this dependence is close to the square law. We attribute the occurrence of this line to the dipole–dipole interaction between different NV − centers.
The
1E--
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 singlet state and diamond band edges or the
3A2--
3E 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 center were observed in the presence of an applied magnetic field, indicating ionization from the long-lived
1E singlet state. A temperature-dependent ionization threshold between 532 and 550 nm was found, locating the singlet states within the diamond band gap.
Nitrogen-vacancy (
N-
V) centers in diamond are among the best-studied quantum-based sensors for a wide range of applications. Here, we demonstrate an optical polarization-based method for full vector magnetometry using ensembles of
N-
V centers. The anisotropy of the electric dipole moments of the
N-
V centers enables the assignment of the different magnetic field split transitions in the optically detected magnetic resonance spectra by appropriately setting the optical polarization in the excitation and/or detection of the
N-
V photoluminescence signal. By further employing the optical-selection rules for the driving microwave field, we show how the full vector of the investigated magnetic field can be restored without the need to apply external bias fields. We discuss different
N-
V-center orientation implementations and limitations toward common approximations used in the
N-
V magnetometry literature for our approach.