Quantum interpolation for high-resolution sensing

Abstract

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.quantum sensing | quantum control | nanoscale NMR | NV centers P recision metrology often needs to strike a compromise between signal contrast and resolution, because the hardware apparatus sets limits on the precision and sampling rate at which the data can be acquired. In some cases, classical interpolation techniques have become a standard tool to achieve a significantly higher resolution than the bare recorded data. For instance, the Hubble Space Telescope uses classical digital image processing algorithms like variable pixel linear reconstruction [Drizzle (1)] to construct a supersampled image from multiple low-resolution images captured at slightly different angles. Unfortunately, this classical interpolation method would fail for signals obtained from a quantum sensor, where the information is encoded in its quantum phase (2). Here we introduce a technique, which we call "quantum interpolation," that can recover the intermediary quantum phase, by directly acting on the quantum probe dynamics, and effectively engineer an interpolated Hamiltonian. Crucially, by introducing an optimal interpolation construction, we can exploit otherwise deleterious quantum interferences to achieve high fidelity in the resulting quantum phase signal.Quantum systems, such as trapped ions (3), superconducting qubits (4, 5), and spin defects (6, 7) have been shown to perform as excellent spectrum analyzers and lock-in detectors for both classical and quantum fields (8-10). This sensing technique relies on modulation of the quantum probe during the interferometric detection of an external field. Such a modulation is typically achieved by a periodic sequence of π-pulses that invert the sign of the coupling of the external field to the quantum probe, leading to an effective time-dependent modulation f (t) of the field (11-13). These sequences, more frequently used for dynamical decoupling (14, 15), can be described by sharp bandpass filter functions obtained from the Fourier transform of f (t). This description lies at the basis of their application for precision spectroscopy, as the fil...

Identifying and Mitigating Charge Instabilities in Shallow Diamond Nitrogen-Vacancy Centers

“…S6(a) For the plotted measurement we apply an external bias field of 330.5 Gauss aligned to the NV symmetry axis and use k = 5 (40 π pulses). We supersample beyond the 2-ns timing resolution of our hardware by use of a quantum interpolation technique developed in [52]. The solid red curve is a fit to the model developed in [51] with 2τ spacing between π pulses and tπ π pulse duration, and we fit with a finite nuclear spin dephasing time T * 2n (here T * 2n = 26(4) µs).…”

“…NV centers are formed by 14 N ion implantation at 4 keV with a dosage of 5.2×10 10 ions / cm 2 into a 150-µm thick Element 6 electronic grade (100) diamond substrate, followed by subsequent annealing at 850 • C for 2.5 hours (see Supplementary Information SI Note 1 [50] for full details on sample preparation). The NV center depth is experimentally measured via proton NMR [51,52] and ranges between ∼ 3-17 nm (see SI Fig. S5 [50]).…”

Optimal Control for One-Qubit Quantum Sensing

“…Optimal control can indeed be exploited to find optimal distributions of the π-pulse positions. Sequences of non-equally distributed pulse spacings, devised by means of analytical models, have been indeed demonstrated to correct for selectivity of CP in certain cases [49][50][51]. In the case of multitone AC signals to be measured, such sequences enable to simultaneously collect signal from all the various frequency components thus achieving a faster phase accumulation.…”

Hamiltonian identifiability assisted by a single-probe measurement

“…By acquiring 2j sampling points (with 2j M total measurements) we can construct the (noisy) j × j Hankel matricesH j (0) andH j (1). Using the ERA algorithm we can extract a set of parameters {θ m + δθ m } M m=1 that differ from the true parameters…”

“…In particular, characterizing many-body qubit Hamiltonians is essential in the quest of building a scalable quantum information processor. The development of system identification techniques is expected to have impact in diverse fields, such as structural determination of a complex molecule [1][2][3], biosensing [4,5], and studying magnetism at the nanoscale [6,7].…”