Quantum interpolation for high-resolution sensing

Significance Nanoscale magnetic resonance imaging enabled by quantum sensors is a promising path toward the outstanding goal of determining the structure of single biomolecules at room temperature. We develop a technique, which we name “quantum interpolation,” to improve the frequency resolution of these quantum sensors far beyond limitations set by the experimental controlling apparatus. The method relies on quantum interference to achieve high-fidelity interpolation of the quantum dynamics between hardware-allowed time samplings, thus allowing high-resolution sensing. We demonstrate over two orders of magnitude resolution gains, and discuss applications of our work to high-resolution nanoscale magnetic resonance imaging. Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.