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.

We report on the noise spectrum experienced by few nanometer deep nitrogen-vacancy centers in diamond as a function of depth, surface coating, magnetic field and temperature. Analysis reveals a double-Lorentzian noise spectrum consistent with a surface electronic spin bath in the low frequency regime, along with a faster noise source attributed to surface-modified phononic coupling. These results shed new light on the mechanisms responsible for surface noise affecting shallow spins at semiconductor interfaces, and suggests possible directions for further studies. We demonstrate dynamical decoupling from the surface noise, paving the way to applications ranging from nanoscale NMR to quantum networks.Nanoscale magnetic imaging and magnetic resonance spectroscopy, recently demonstrated using nitrogenvacancy (NV) color centers in diamond [1][2][3][4], are capable of yielding unique insights into chemistry, biology and physical sciences. The sensitivity and resolution of these techniques relies heavily on the NV coherence properties, which empirically are much worse for shallow NV centers than those deep within bulk diamond [5]. An understanding of the origin of surface related noise enables optimal decoupling or surface passivation to be performed. It is critical not only for improving NV applications in quantum sensing [6,7], quantum information processing [8], and photonics [9], but is also an outstanding problem in many solid-state quantum systems (e.g. [10,11]). Furthermore, overcoming noise at the diamond interface is a significant obstacle to realizing hybrid quantum systems with NV centers [12,13], which are expected to play an important role in realistic devices.For NV centers in bulk diamond, noise sources limiting coherence times have been identified with internal nuclear and electronic spin baths, and interactions with phonons [14,15]. Although additional noise sources related to the diamond surface, and affecting shallow NVs, have been observed [16], their origin is not currently well understood. This phenomenon is general and has been observed at various semiconductor interfaces, resulting in the development of several theoretical models, which are still without significant experimental confirmation [17,18]. Here we use shallow implanted NV centers as nanoscale sensors to perform spectroscopy of the diamond surface. We use dynamical decoupling techniques together with measurements of longitudinal (T 1 ) relaxation under varying conditions (surface coating, magnetic field, temperature) in order to characterize the surface-induced noise. The strength and frequency dependence of fluctuations as a function of the NV distance from the surface are investigated with nanometer precision. We directly measure the noise spectrum experienced by shallow NV centers, revealing an unexpected double-Lorentzian structure which indicates contributions from two distinct noise sources. We find that the low frequency noise experienced by shallow NVs is consistent with electronic spin impurities on the surface [ Fig. 1(a)], w...

We experimentally demonstrate the protection of a room-temperature hybrid spin register against environmental decoherence by performing repeated quantum error correction whilst maintaining sensitivity to signal fields. We use a long-lived nuclear spin to correct multiple phase errors on a sensitive electron spin in diamond and realize magnetic field sensing beyond the time scales set by natural decoherence. The universal extension of sensing time, robust to noise at any frequency, demonstrates the definitive advantage entangled multiqubit systems provide for quantum sensing and offers an important complement to quantum control techniques.

Qudi is a general, modular, multi-operating system suite written in Python 3 for controlling laboratory experiments. It provides a structured environment by separating functionality into hardware abstraction, experiment logic and user interface layers. The core feature set comprises a graphical user interface, live data visualization, distributed execution over networks, rapid prototyping via Jupyter notebooks, configuration management, and data recording. Currently, the included modules are focused on confocal microscopy, quantum optics and quantum information experiments, but an expansion into other fields is possible and encouraged. Qudi is available from https://github.com/Ulm-IQO/ qudi and is freely useable under the GNU General Public Licence.