Precise timekeeping is critical to metrology, forming the basis by which standards of time, length, and fundamental constants are determined. Stable clocks are particularly valuable in spectroscopy because they define the ultimate frequency precision that can be reached. In quantum metrology, the qubit coherence time defines the clock stability, from which the spectral linewidth and frequency precision are determined. We demonstrate a quantum sensing protocol in which the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock. Using this technique, we observed a precision in frequency estimation scaling in time as for classical oscillating fields. The narrow linewidth magnetometer based on single spins in diamond is used to sense nanoscale magnetic fields with an intrinsic frequency resolution of 607 microhertz, which is eight orders of magnitude narrower than the qubit coherence time.

Nitrogen‐vacancy (NV) center ensemble in synthetic diamond is a promising and emerging platform for quantum sensing technologies. Realization of such a solid‐state based quantum sensor is widely studied and requires reproducible manufacturing of NV centers with controlled spin properties, including the spin bath environment within the diamond crystal. Here, a non‐invasive method is reported to benchmark NV ensembles regarding their suitability as ultra‐sensitive magnetic field sensors. Imaging and electron spin resonance techniques are presented to determine operating figures and precisely define the optimal material for NV‐driven diamond engineering. The functionality of the methods is manifested on examples of chemical vapor deposition synthesized diamond layers containing preferentially aligned, isotopically controlled 15NV center ensembles. Quantification of the limiting 15N P1 spin bath, in an otherwise 12C enriched environment, and the reduction of its influence by applying dynamical decoupling protocols, complete the suggested set of criteria for the analysis of NV ensemble with potential use as magnetometers.

We propose an iterative scheme to factor numbers based on the quantum dynamics of an ensemble of interacting bosonic atoms stored in a trap where the single-particle energy spectrum depends logarithmically on the quantum number. When excited by a time-dependent interaction these atoms perform Rabi oscillations between the ground state and an energy state characteristic of the factors. The number to be factored is encoded into the frequency of the sinusoidally modulated interaction. We show that a measurement of the energy of the atoms at a time chosen at random yields the factors with probability one half. We conclude by discussing a protocol to obtain the desired prime factors employing a logarithmic energy spectrum which consists of prime numbers only.