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Nitrogen vacancy (NV) centers in diamond are atom-scale defects with long spin coherence times that can be used to sense magnetic fields with high sensitivity and spatial resolution. Typically, the magnetic field projection at a single point is measured by averaging many sequential measurements with a single NV center, or the magnetic field distribution is reconstructed by taking a spatial average over an ensemble of many NV centers. In averaging over many single-NV center experiments, both techniques discard information. Here we propose and implement a new sensing modality, whereby two or more NV centers are measured simultaneously, and we extract temporal and spatial correlations in their signals that would otherwise be inaccessible. We analytically derive the measurable two-point correlator in the presence of environmental noise, quantum projection noise, and readout noise. We show that optimizing the readout noise is critical for measuring correlations, and we experimentally demonstrate measurements of correlated applied noise using spin-to-charge readout of two NV centers. We also implement a spectral reconstruction protocol for disentangling local and nonlocal noise sources, and demonstrate that independent control of two NV centers can be used to measure the temporal structure of correlations. Our covariance magnetometry scheme has numerous applications in studying spatiotemporal structure factors and dynamics, and opens a new frontier in nanoscale sensing.

Strong gravitational lensing provides unique opportunities to investigate the mass distribution at the cores of galaxy clusters and to study high redshift galaxies. Using $94$ strong lensing models of $74$ cluster fields from the \textit{Hubble} Frontier Fields (HFF), Reionization Lensing Cluster Survey (RELICS), and Sloan Giant Arcs Survey (SGAS), modeled with three parametric approaches, we evaluate the lensing strength of each cluster (area with $|\mu|\geq3$ for $z_s=9$). We assess how large scale mass, projected inner core mass, and the inner slope of the projected mass density profile relate to lensing strength. While we do not identify a strong correlation between lensing strength and large scale mass, we reveal that the inner slope ($50$ kpc~$\leq r \leq~200$ kpc) of the projected mass density profile is indicative of lensing strength and can set an upper bound on the possible lensing strength of a cluster. We find that the effective Einstein area correlates with lensing strength, and that a large ($\gtrsim 30^{''}0$) radial extent of lensing evidence is a strong indicator of a powerful lens. These results can help to more efficiently design future observations to maximize lensing strength., Comment: 28 pages, 12 figures, Accepted for publication in ApJ

Extensive surveys with the \textit{Hubble Space Telescope} (HST) over the past decade, targeting some of the most massive clusters in the sky, have uncovered dozens of galaxy-cluster strong lenses. The massive cluster strong-lens scale is typically $\theta_{E}\sim10\arcsec$ to $\sim30-35\arcsec$, with only a handful of clusters known with Einstein radii $\theta_{E}\sim40\arcsec$ or above (for $z_{source}=2$, nominally). Here we report another very large cluster lens, RXC J0032.1+1808 ($z=0.3956$), the second richest cluster in the redMapper cluster catalog and the 85th most massive cluster in the Planck Sunyaev-Zel'dovich catalog. With our Light-Traces-Mass and fully parametric (dPIEeNFW) approaches, we construct strong lensing models based on 18 multiple images of 5 background galaxies newly identified in the \textit{Hubble} data mainly from the \textit{Reionization Lensing Cluster Survey} (RELICS), in addition to a known sextuply imaged system in this cluster. Furthermore, we compare these models to Lenstool and GLAFIC models that were produced independently as part of the RELICS program. All models reveal a large effective Einstein radius of $\theta_{E}\simeq40\arcsec$ ($z_{source}=2$), owing to the obvious concentration of substructures near the cluster center. Although RXC J0032.1+1808 has a very large critical area and high lensing strength, only three magnified high-redshift candidates are found within the field targeted by RELICS. Nevertheless, we expect many more high-redshift candidates will be seen in wider and deeper observations with \textit{Hubble} or \emph{JWST}. Finally, the comparison between several algorithms demonstrates that the total error budget is largely dominated by systematic uncertainties., Comment: 23 pages, accepted for publication in ApJ

Large surveys of galaxy clusters with the Hubble and Spitzer Space Telescopes, including CLASH and the Frontier Fields, have demonstrated the power of strong gravitational lensing to efficiently deliver large samples of high-redshift galaxies. We extend this strategy through a wider, shallower survey named RELICS, the Reionization Lensing Cluster Survey. This survey, described here, was designed primarily to deliver the best and brightest high-redshift candidates from the first billion years after the Big Bang. RELICS observed 41 massive galaxy clusters with Hubble and Spitzer at 0.4-1.7um and 3.0-5.0um, respectively. We selected 21 clusters based on Planck PSZ2 mass estimates and the other 20 based on observed or inferred lensing strength. Our 188-orbit Hubble Treasury Program obtained the first high-resolution near-infrared images of these clusters to efficiently search for lensed high-redshift galaxies. We observed 46 WFC3/IR pointings (~200 arcmin^2) with two orbits divided among four filters (F105W, F125W, F140W, and F160W) and ACS imaging as needed to achieve single-orbit depth in each of three filters (F435W, F606W, and F814W). As previously reported by Salmon et al., we discovered 322 z ~ 6 - 10 candidates, including the brightest known at z ~ 6, and the most distant spatially-resolved lensed arc known at z ~ 10. Spitzer IRAC imaging (945 hours awarded, plus 100 archival) has crucially enabled us to distinguish z ~ 10 candidates from z ~ 2 interlopers. For each cluster, two HST observing epochs were staggered by about a month, enabling us to discover 11 supernovae, including 3 lensed supernovae, which we followed up with 20 orbits from our program. We delivered reduced HST images and catalogs of all clusters to the public via MAST and reduced Spitzer images via IRSA. We have also begun delivering lens models of all clusters, to be completed before the JWST GO call for proposals., Comment: 29 pages, 6 figures, submitted to ApJ. For reduced images, catalogs, lens models, and more, see relics.stsci.edu

Strong gravitational lensing by clusters of galaxies probes the mass distribution at the core of each cluster and magnifies the universe behind it. MACS J0417.5-1154 at z=0.443 is one of the most massive clusters known based on weak lensing, X-ray, and Sunyaev-Zel'dovich analyses. Here we compute a strong lens model of MACS J0417 based on Hubble Space Telescope imaging observations collected, in part, by the Reionization Lensing Cluster Survey (RELICS), and recently reported spectroscopic redshifts from the MUSE instrument on the Very Large Telescope (VLT). We measure an Einstein radius of ThetaE=36'' at z = 9 and a mass projected within 200 kpc of M(200 kpc) = 1.78+0.01-0.03x10**14Msol. Using this model, we measure a ratio between the mass attributed to cluster-member galaxy halos and the main cluster halo of order 1:100. We assess the probability to detect magnified high-redshift galaxies in the field of this cluster, both for comparison with RELICS HST results and as a prediction for the James Webb Space Telescope (JWST) Guaranteed Time Observations upcoming for this cluster. Our lensing analysis indicates that this cluster has similar lensing strength to other clusters in the RELICS program. Our lensing analysis predicts a detection of at least a few z~6-8 galaxies behind this cluster, at odds with a recent analysis that yielded no such candidates in this field. Reliable strong lensing models are crucial for accurately predicting the intrinsic properties of lensed galaxies. As part of the RELICS program, our strong lensing model produced with the Lenstool parametric method is publicly available through the Mikulski Archive for Space Telescopes (MAST)., Comment: 20 pages, 8 figures. Accepted to ApJ