Photoluminescence at the ground-state level anticrossing of the nitrogen-vacancy center in diamond: A comprehensive study

The nitrogen-vacancy center (NV center) in diamond at magnetic fields corresponding to the ground-state level anticrossing (GSLAC) region gives rise to rich photoluminescence (PL) signals due to the vanishing energy gap between the electron spin states, which enables for a broad variety of environmental couplings to have an effect on the NV center's luminescence. Previous works have addressed several aspects of the GSLAC photoluminescence, however, a comprehensive analysis of the GSLAC signature of NV ensembles in different spin environments at various external fields is missing. Here we employ a combination of experiments and recently developed numerical methods to investigate in detail the effects of transverse electric and magnetic fields, strain, P1 centers, NV centers, and the ${}^{13}\mathrm{C}$ nuclear spins on the GSLAC photoluminescence. Our comprehensive analysis provides a solid ground for advancing various microwave-free applications at the GSLAC, including but not limited to magnetometry, spectroscopy, dynamic nuclear polarization (DNP), and nuclear magnetic resonance (NMR) detection. We demonstrate that not only the most abundant ${}^{14}\mathrm{NV}$ center but the ${}^{15}\mathrm{NV}$ can also be utilized in such applications.

Figure 1

(a) Energy level diagram of the ${}^{14}\mathrm{NV}$ center. Greek letters denote the spin eigenenergies and green dashed circles with capital letters denote crossings where external perturbations may open gaps. (b) Theoretical PL signal vs longitudinal magnetic field at the GSLAC with different values of transverse magnetic field. (c) Experimental PL signal obtained from sample IS vs longitudinal magnetic field at the GSLAC with different values of transverse magnetic field. (d) Transverse magnetic field dependence of the full width at half maximum of the central dip E. Maroon open circles, maroon solid line, and blue solid line depict the experimental points, a linear fit, and the theoretical results, respectively.

Figure 2

(a) Energy level diagram of the ${}^{15}\mathrm{NV}$ center. Greek letters denote the spin eigenenergies and green dashed circles with capital Greek letters denote crossings where external perturbations may open a gap. (b) Theoretical PL signal vs longitudinal magnetic field at the GSLAC with different values of transverse magnetic field. (c) Transverse magnetic field dependence of the FWHM of the pronounced dip at $\approx 102.4$ mT.

Figure 3

PL and polarization of ${}^{14}\mathrm{NV}$ center-${}^{13}\mathrm{C}$ spin bath system at the GSLAC. (a) Measured PL at the GSLAC in sample W4. The PL signal indicates polarization of the ${}^{13}\mathrm{C}$ nuclear spin bath, where the sign of the polarization is opposite at the side dips, see text for further discussion. (b) Closeup of the energy levels structure of ${}^{14}\mathrm{NV}–{}^{13}\mathrm{C}$ weakly coupled three spin system at the GSLAC. Greek letter with arrows specify the corresponding states, see Table 2, while capital alphabet letters indicate level crossings where hyperfine interaction may give site to additional spin mixing. Maroon and blue curves depict ${}^{13}\mathrm{C}$ nuclear spin up and down states, respectively. (c) Theoretical ensemble and site averaged polarization of a 128-spin ${}^{13}\mathrm{C}$ spin bath obtained after optical pumping of varying duration. (d) Theoretical PL signal obtained by starting from different initial ${}^{13}\mathrm{C}$ polarization. The solid maroon curve shows the case of initially nonpolarized spin bath, green and blue dashed lines show the PL signal obtained for initially up and down polarized spin bath, respectively. Initial polarization of the spin bath makes side dip amplitudes asymmetric.

Figure 4

PL and polarization of ${}^{15}\mathrm{NV}$ center-${}^{13}\mathrm{C}$ spin bath system at the GSLAC. (a) PL spectrum of ${}^{15}\mathrm{NV}–{}^{13}\mathrm{C}$ system (solid blue curve) as compared to the PL spectrum of the ${}^{14}\mathrm{NV}–{}^{13}\mathrm{C}$ system (dashed maroon curve). (b) Energy-level structure at the GSLAC. Blue and maroon curves correspond to $\left|-1/2\right.〉$ and $\left|+1/2\right.〉$ nuclear spin states, respectively. Relevant crossings of the energy levels are indicated with green dashed circles and labeled by capital letters. (c) and (d) depict the polarization of ${}^{15}\mathrm{N}$ nuclear spin and ensemble and site averaged polarization of ${}^{13}\mathrm{C}$ nuclear spin bath, respectively. For comparison ${}^{13}\mathrm{C}$ nuclear spin bath polarization induced by a ${}^{14}\mathrm{NV}$ center at the GSLAC is also depicted in (d).

Figure 5

Interaction with P1 centers at the GSLAC. (a) Experimental PL spectrum recorded in two samples of different P1 concentration, see Table 1. PL intensities were scaled to be comparable with each other. (b) Energy-level structure of P1 centers. Maroon and blue curves show the case of magnetic field aligned and ${109}^{\circ }$ aligned P1 centers, respectively. (c) Theoretical PL spectrum for different P1 center concentrations. (d) Ensemble and site averaged electron and ${}^{14}\mathrm{N}$ nuclear spin polarization of the P1 center.

Figure 6

Photoluminescence of ${}^{14}\mathrm{NV}$ center-${}^{14}\mathrm{NV}$ center spin-bath system at the GSLAC. (a) Simulated PL spectrum of ${}^{14}\mathrm{NV}$ center-magnetic field aligned ${}^{14}\mathrm{NV}$ spin-bath system at different concentrations ranging from 1 ppm to 100 ppm. (b) Transition energy curves, see text for clarification, at the GSLAC. Wide solid curves highlight transitions associated to the highest populated $\alpha$ state of individual NV centers. Dashed curves show transition energies associated to transitions between less populated energy levels. Green dashed circle labeled by A mark the place of level crossing where the central NV center precesses in the transverse field of other NV centers. Crossing B between the transition energy curves represents a place of effective cross relaxation between the NV centers that gives rise to dip B in the PL scan. (c) Experimental GSLAC PL spectrum obtained in our IS diamond sample as compared with simulation of 0.5 ppm field oriented NV center spin bath and 15 $\mu \mathrm{T}$ transverse magnetic field. Signatures of both the transverse field and the parallel NV centers are visible on the experimental and theoretical curves. (d) Simulated PL spectrum with ${109}^{\circ }$ aligned NV center spin bath.

Figure 7

Optimization of the simulation parameters. (a), (b), (c), and (d) show the GSLAC PL signal of ${}^{14}\mathrm{NV}–{}^{13}\mathrm{C}$ system for different order parameter, ensemble size, bath size, and ground-state dwell time, respectively.

Figure 8

(a) PL signal and (b) ${}^{13}\mathrm{C}$ polarization after varying length of optical pumping of a ${}^{14}\mathrm{NV}$ center at the GSLAC.