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Recent years have seen significant growth of quantum technologies, and specifically quantum sensing, both in terms of the capabilities of advanced platforms and their applications. One of the leading platforms in this context is nitrogen-vacancy (NV) color centers in diamond, providing versatile, high-sensitivity, and high-resolution magnetic sensing. Nevertheless, current schemes for spin resonance magnetic sensing (as applied by NV quantum sensing) suffer from tradeoffs associated with sensitivity, dynamic range, and bandwidth. Here we address this issue, and implement machine learning tools to enhance NV magnetic sensing in terms of the sensitivity/bandwidth tradeoff in large dynamic range scenarios. We experimentally demonstrate this new approach, reaching an improvement in the relevant figure of merit by a factor of up to 5. Our results promote quantum machine learning protocols for sensing applications towards more feasible and efficient quantum technologies., Comment: 12 pages including supplementary, 6 figures

Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar [Phys. Rev. Appl. 20, 064046 (2023)]. In this work, we identify the optimal waveforms for distinguishing the range resolution between two reflectors of identical strength. We discuss both the unnormalized optimal waveform as well as the best square-integrable pulse, and their variants. Using orthogonal function theory, we give an explicit algorithm to optimize the wave pulse in finite time to have the best performance. We also explore range resolution estimation with unnormalized waveforms with multi-parameter methods to also independently estimate loss and time of arrival. These results are consistent with the earlier single parameter approach of range resolution only and give deeper insight into the ranging estimation problem. Experimental results are presented using radio pulse reflections inside coaxial cables, showing robust range resolution smaller than a tenth of the inverse bandedge, with uncertainties close to the derived Cram\'er-Rao bound., Comment: 8 pages, 8 figures

We establish fundamental bounds on subwavelength resolution for the radar ranging problem, ``super radar''. Information theoretical metrics are applied to probe the resolution limits for the case of both direct electric field measurement and photon-counting measurements. To establish fundamental limits, we begin with the simplest case of range resolution of two point targets from a metrology perspective. These information-based metrics establish fundamental bounds on both the minimal discrimination distance of two targets as well as the precision on the separation of two subwavelength resolved targets. For the minimal separation distance, both the direct field method and photon counting method show that the discriminability vanishes quadratically as the target separation goes to zero, and is proportional to the variance of the second derivative of the electromagnetic field profile. Nevertheless, robust subwavelength estimation is possible. Several different band-limited function classes are introduced to optimize discrimination. We discuss the application of maximum likelihood estimation to improve the range precision with optimal performance. The general theory of multi-parameter estimation is analyzed, and a simple example of estimating both the separation and relative strength of the two point reflectors is presented., Comment: 11 pages, 3 figures

Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehavior of this operator occurs whenever the operator's weak value exceeds its eigenvalue bound. We give illustrative examples of this effect for total angular momentum and energy. In the later case, we demonstrate a sequence of harmonic oscillator potentials where a finite energy state converges everywhere on the real line, using only bounded superpositions of states whose asymptotic energy vanishes - "energy out of nothing". This limit requires postselecting the particle in a region whose size diverges in the considered limit. We further show that superenergy behavior implies that the state superoscillates in time with a rate given by the superenergy divided by the reduced Planck's constant. This example demonstrates the possibility of mimicking a high-energy state with coherent superpositions of nearly zero-energy states for as wide a spatial region as desired. We provide numerical evidence of these features to further bolster and elucidate our claims., Comment: 9 pages, 5 figures, expanded treatment of time

We simplify the Ashworth-Davies special relativistic theory of a uniformly translating mirror with an arbitrary angle of incidence and direction of propagation in the non-relativistic limit. We show that it is in good agreement with a more intuitive derivation that only considers the constancy of the speed of light. We experimentally confirm the theory predictions with phase-insensitive frequency measurements using a liquid crystal light valve.