Improving the Energy and Angular Resolutions of X-ray Telescopes with Nitrogen-Vacancy Centers in Diamond

TL;DR

This work proposes a novel X-ray focal-plane detector that integrates a metallic magnetic microcalorimeter (MMC) array with nitrogen-vacancy (NV) centers in diamond to achieve simultaneous, high-fidelity measurements of X-ray energy and incoming direction. By using NV-based wide-field optical readout of magnetization transients in Er-doped Au absorbers, the approach eliminates cryogenic multiplexing electronics and scales to large, high-resolution arrays. Projected performance shows energy resolutions on the order of $\delta E$ in the eV range and angular resolutions down to the sub-arcsecond level (e.g., ~0.17 arcsec for $L=10\ \mu$m at $f=12$ m), potentially rivaling or surpassing current TES and MMC readouts. If realized, this NV-MMC scheme would enable wide-field, high-precision X-ray imaging with reduced cryogenic overhead, offering a practical path toward next-generation X-ray astronomy missions and broader applications requiring precise X-ray spectroscopy and imaging.

Abstract

We introduce a focal-plane detector for advancing the energy and angular resolutions of current X-ray telescopes. The architecture integrates a metallic magnetic microcalorimeter (MMC) array of paramagnetic absorber pads with a thin layer of nitrogen-vacancy (NV) centers in diamond for simultaneous optical readout. An impinging X-ray photon induces a temperature transient in an absorber pad, kept at ~35 mK. This time- and temperature-dependent magnetic field transient is then optically imaged by diamond NV centers, kept at 4 K and positioned directly below the pad. For a 10 $μ$m absorber length used with a 12 m focal length telescope, our design yields an optimal angular resolution of ~0.17 arcseconds and energy resolution of ~0.70 eV. Our NV-MMC design improves upon current transition-edge sensors (TES) or MMCs read-out by superconducting quantum interference devices (SQUID) by enabling simultaneous optical readout of the entire MMC array. Because no additional cryogenic multiplexing electronics are required, our approach scales naturally to larger and finer arrays, supporting finer angular resolutions and wider fields of view.

Figures (5)

• Figure 1: Schematic of the NV-MMC setup, and of its detection procedure.(a) An array of erbium-doped gold absorbers, each of dimension $L~\mu$m $\times$$L~\mu$m $\times$ 5 $\mu$m, is supported by thin layers of graphite and silver 100 nm above the diamond plate. The diamond contains a dense ensemble of NV sensors (red dots) within the top 1 $\mu$m of the diamond, produced via an ion implantation and annealing process. The paramagnetic absorber pads are cooled to $\sim$35 mK, whereas the diamond stage is connected to the $\sim$4 K stage; the overall cryostat is indicated by the shaded box. The green excitation laser (see Fig. \ref{['fig:fig3']}) for the NV centers is delivered in from one side window of the cryostat, undergoes total internal reflection at the top surface of the diamond, and leaves the cryostat through another window on the opposite side. The NV fluorescence then exits the cryostat via another window at the bottom of the cryostat, where it is focused by an objective lens onto an imaging CCD camera below the lens. The placement of the CCD outside the cryostat greatly reduces the heat load that would otherwise need to be cooled by the cryogenics. For optimal absorber performance, the interior of the cryostat maintains a 5 mT field. The gold strip for delivering the needed microwave power (also see Fig. \ref{['fig:fig3']}) is located at the bottom of the diamond. (b)-(d) A zoomed-in schematic, showing each step of the detection process. An incident X-ray photon strikes and heats an absorber pad. The paramagnetic absorber, having a temperature-dependent magnetization, thus produces a magnetic transient. This magnetic field change shifts the NV center energy transition frequencies and thus alters the fluorescence produced by the NV centers below the relevant pad (Fig. \ref{['fig:fig2']}b and c). By imaging that fluorescence as a function of time and frequency with a CCD camera, the incident X-ray event can thus be sensed with high spatial and energy resolution.
• Figure 2: Principle, and demonstration, of magnetic field sensing with NV centers.(a) The lattice structure of NV centers in diamond: two adjacent carbon atoms (black) in the lattice are replaced by a nitrogen atom (light blue) and a vacancy (dotted circle). In a single-crystal diamond, there are thus four possible orientations of the NV crystallographic axis. (b) Energy levels of (spin-1) NV centers: in the absence of a magnetic field, the system exhibits only a zero-field splitting of $D_\mathrm{gs} = 2870$ MHz between the $|m_s = 0\rangle$ and $|m_s = \pm1\rangle$ sublevels. By applying an external magnetic field, the degeneracy between the $|m_s = \pm1\rangle$ sublevels is lifted due to the Zeeman effect, leading to an additional splitting of $2\gamma B_\mathrm{NV}$, where $B_\mathrm{NV}$ is the projection of the external magnetic field onto the nitrogen-vacancy (NV) bond axis. (c) An example of the electron spin resonance (ESR) spectrum of a NV ensemble with an external magnetic field of approximately 3 mT. The spectrum is divided into four groups of resonances (marked by the shaded areas), with each group corresponding to one of the four NV crystallographic axes. The splitting exhibited by each group is determined by the magnitude of the projection of the external magnetic field onto the respective NV axis. (We note that the resonance peaks within each shaded area also exhibit a small hyperfine splitting of about 3 MHz, originating from the hyperfine interaction between the NV center and the $^{15}$N nuclear spin smeltzer2009robust.) (d) A wide-field magnetic field image of the dipole due to a magnetic bead deposited on top of a diamond surface, acquired with our NV diamond microscope. The image demonstrates sub-$\mu$T precision and has a spatial resolution of $\sim$ 1 $\mu$m after applying a Gaussian filter with $\delta=1.5~\mu$m to reduce background noise.
• Figure 3: Magnetic field sensitivity calculations for the NV-MMC.(a) The calculated distribution of magnetic field change in the $z$-direction at the location of the NV centers, $100$ nm beneath a $10~\mu \rm m \times 10~\mu \rm m \times 5~\mu \rm m$ absorber pad, given a $1$ mK increase in the temperature of that absorber. (b) The calculated magnetic field volume sensitivity of the NV ensemble, using the sample parameters listed in Table \ref{['tab:SampleParameters']}, as a function of microwave (MW) strength and laser intensity. The optimal sensitivity, 27 ${\rm nT}~{\rm Hz}^{-\frac{1}{2}}~\mu$m$^{\frac{3}{2}}$, is marked with the black dot at $I_{\mathrm{opt}}\approx 51~\mathrm{W/mm^2}$ and $\Omega_{\mathrm{opt}}\approx (2\pi)\times0.16~$MHz. The black dashed circle displays the contour for all parameter combinations that yield a sensitivity of 30 ${\rm nT}~{\rm Hz}^{-\frac{1}{2}}~\mu$m$^{\frac{3}{2}}$ or better. Thus, the laser intensity and microwave strengths can both be roughly halved without significantly changing the sensitivity.
• Figure 4: Energy and angular resolutions of the NV-MMC, compared to other missions and detectors. Energy resolutions as a function of absorber pixel width (top horizontal axis) and angular resolution (bottom horizontal axis) for the NV-MMC, with the absorber pads kept at a distance of 100 nm above the diamond. These results are compared with those from some current state-of-the-art X-ray detectors (data for other missions/detector designs are taken from ChandraCalWebsiteAcis2022arXiv220205399X2015ApPhL.107v3503L2016JLTP..184..344K2020JLTP..199..916Y). The Chandra energy resolution is given for 1.5 keV; the XRISM and MMC energy resolutions are given for 6 keV; and the TES energy resolution is given for 1.5 keV. For test arrays not yet fully implemented on missions, their angular resolution is given assuming a focal length of 12 m. The darker (lighter) shaded region indicates an ability to spatially differentiate an angular resolution on the scale of one-thousandth (one-ten-thousandth) the rough angular extent of the Crab Nebula, a pulsar wind nebula and prototypical high-flux source for X-ray astronomy.
• Figure S1: Principle of NV layer volume selection.(a) The calculated distribution of magnetic field change at the location of the NV centers in diamond, 0.1 $\mu$m beneath a $10~\mu \rm m \times 10~\mu \rm m \times 5~\mu \rm m$ (for example) absorber pad, given a $1$ mK increase in the temperature of the absorber. Calculations, such as the one done for this figure, were done for all of the absorber widths shown in Figure 4. (b) Magnetic field strength at the depth of a given NV layer as a function of the X-coordinate and of the distance between the layer and the absorber pad, taken along the dashed line-cut axis shown in (a). The reference field magnitude, $B_\mathrm{ref}$ (measured at the location given by the diamond), is defined as the field strength at a position of X = 0 at a distance of 0.1 $\mu$m below the absorber. The red dashed line marks the region where the field magnitude stays above 80% of $B_\mathrm{ref}$. The hatched area, with width $W_{\mathrm{eff}}$ and height $H_{\mathrm{opt}}$, is then taken to be the effective volume within which we accumulate NV signals for each magnetic field measurement.