Magnetic-Field-Assisted Spectral Decomposition and Imaging of Charge States of $\mathrm{N}$-$V$ Centers in Diamond

With the advent of quantum technology, nitrogen vacancy ($\mathrm{N}$-$V$) centers in diamond turn out to be a frontier that provides an efficient platform for quantum computation, communication, and sensing applications. Due to the coupled spin-charge dynamics of the $\mathrm{N}$-$V$ system, knowledge of $\mathrm{N}$-$V$ charge-state dynamics can help to formulate efficient spin-control sequences strategically. Here, we report two spectroscopy-based deconvolution methods to create charge-state mapping images of ensembles of $\mathrm{N}$-$V$ centers in diamond. First, relying on the fact that an off-axis external magnetic field mixes the electronic spins and selectively modifies the photoluminescence (PL) of $\mathrm{N}$-$V^{-}$, we perform decomposition of the optical spectrum for an ensemble of $\mathrm{N}$-$V$ and extract the spectra for $\mathrm{N}$-$V^{-}$ and $\mathrm{N}$-$V^0$ states. Next, we introduce an optical-filter-based decomposition protocol and perform PL imaging for $\mathrm{N}$-$V^{-}$ and $\mathrm{N}$-$V^0$. Previously obtained spectra for $\mathrm{N}$-$V^{-}$ and $\mathrm{N}$-$V^0$ states are used to calculate their transmissivities through a long-pass optical filter. These results help us to determine the spatial distribution of the $\mathrm{N}$-$V$ charge states in a diamond sample.

Figure 1

Schematic diagram of the home-built confocal setup, which is combined with a spectrometer. Permanent magnet is used to apply the magnetic field to the $\mathrm{N}$-$V$ system.

Figure 2

(a) Measured $\mathrm{N}$-$V$ emission spectra at low ($\sim 170$ G) and high ($\sim 975$ G) magnetic fields shown by green and red curves, respectively. Spectra show the ZPL for $\mathrm{N}$-$V^0$ at 575 nm and for $\mathrm{N}$-$V^{-}$ at 637 nm. Blue curve denotes the spectrum obtained by subtracting the spectrum at high field from the one recorded at low field. Inset shows an expanded view of the region near the $\mathrm{N}$-$V^0$ ZPL. (b) Extracted $\mathrm{N}$-$V^0$ (blue curve) and $\mathrm{N}$-$V^{-}$ spectra (red curve). $\mathrm{N}$-$V^{-}$ spectrum is manually shifted along the $y$ axis to make both spectra visible.

Figure 3

(a) $\mathrm{N}$-$V$ spectrum (red curve) measured at an applied field of 170 G and its fit to $A_{\text{N-}V}(\lambda ;B)$ (black curve). (b) Variation of $\mathrm{N}$-$V^{-}$ and $\mathrm{N}$-$V^0$ PL as a function of applied magnetic field strength. (c) Dependence of $f(B_1;B_2)$ on magnetic field variation. Dashed curve connects data points that correspond to $B_2=829$ G for different $B_1$ values.

Figure 4

PL maps for an $\mathrm{N}$-$V$ ensemble at (a) 170 G and (b) 975 G magnetic fields. Contribution of (c) $\mathrm{N}$-$V^0$ and (d) $\mathrm{N}$-$V^{-}$ PL to the map shown in (a).

Figure 5

Mapping ratio of concentrations of $\mathrm{N}$-$V^{-}$ to $\mathrm{N}$-$V^0$ centers.

Figure 6

Measured PL mapping images (a) without and (b) with the 645-nm long-pass filter. Mapping image of the fraction of PL-signal contributions from (c) $\mathrm{N}$-$V^0$ and (d) $\mathrm{N}$-$V^{-}$ centers into the image shown in (a), as calculated using our decomposition method.

Figure 7

Extracted $\mathrm{N}$-$V^0$ spectrum (thin red curve) and its transmission through a 645-nm long-pass filter (thick red curve), extracted $\mathrm{N}$-$V^{-}$ spectrum (thin blue curve) and its transmission through a 645-nm long-pass filter (thick blue curve).

Figure 8

Simulated PL mapping images (a) without and (b) with the 645-nm long-pass filter. Mapping images for (c) $\mathrm{N}$-$V^0$ and (d) $\mathrm{N}$-$V^{-}$ centers decomposed using Eqs. (18) and (19).