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We investigate the effects of a novel approach to diamond nanofabrication and nitrogen vacancy (NV) center formation on the optical linewidth of the NV zero-phonon line (ZPL). In this post-implantation method, nitrogen is implanted after all fabrication processes have been completed. We examine three post-implanted samples, one implanted with $^{14}$N and two with $^{15}$N isotopes. We perform photoluminescence excitation (PLE) spectroscopy to assess optical linewidths and optically detected magnetic resonance (ODMR) measurements to isotopically classify the NV centers. From this, we find that NV centers formed from nitrogen naturally occuring in the diamond lattice are characterized by a linewidth distribution peaked at an optical linewidth nearly two orders of magnitude smaller than the distribution characterizing most of the NV centers formed from implanted nitrogen. Surprisingly, we also observe a number of $^{15}$NV centers with narrow ($<500\,\mathrm{MHz}$) linewidths, implying that implanted nitrogen can yield NV centers with narrow optical linewidths. We further use a Bayesian approach to statistically model the linewidth distributions, to accurately quantify the uncertainty of fit parameters in our model, and to predict future linewidths within a particular sample. Our model is designed to aid comparisons between samples and research groups, in order to determine the best methods of achieving narrow NV linewidths in structured samples.

We present high-resolution optically detected magnetic resonance (ODMR) spectroscopy on single nitrogen-vacancy (NV) center spins in diamond at and around zero magnetic field. The experimentally observed transitions depend sensitively on the interplay between the microwave (MW) probing field and the local intrinsic effective field comprising strain and electric fields, which act on the NV spin. Based on a theoretical model of the magnetic dipole transitions and the MW driving field, we extract both the strength and the direction of the transverse component of the effective field. Our results reveal that for the diamond crystal under study, strain is the dominant contribution to the effective field. Our experiments further yield a method for MW polarization analysis in a tunable, linear basis, which we demonstrate on a single NV spin. Our results are of importance to low-field quantum sensing applications using NV spins and form a relevant addition to the ever-growing toolset of spin-based quantum sensing., Comment: 12 pages, 5 figures. Including appendix

We demonstrate the use of shortcuts to adiabaticity protocols for initialisation, readout, and coherent control of dressed states generated by closed-contour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their two-level counterparts can offer. Our state transfer protocols yield a transfer fidelity of ~ 99.4(2) % while accelerating the transfer speed by a factor of 2.6 compared to the adiabatic approach. We show bi-directionality of the accelerated state transfer, which we employ for direct dressed state population readout after coherent manipulation in the dressed state manifold. Our results enable direct and efficient access to coherence-protected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing., Comment: 16 pages, 9 figures. Including supplementary material

Hybrid quantum systems, which combine quantum-mechanical systems with macroscopic mechanical oscillators, have attracted increasing interest as they are well suited as high-performance sensors or transducers in quantum computers. A promising candidate is based on diamond cantilevers, whose motion is coupled to embedded Nitrogen-Vacancy (NV) centers through crystal deformation. Even though this type of coupling has been investigated intensively in the past, several inconsistencies exist in available literature, and no complete and consistent theoretical description has been given thus far. To clarify and resolve these issues, we here develop a complete and consistent formalism to describe the coupling between the NV spin degree of freedom and crystal deformation in terms of stress, defined in the crystal coordinate system XYZ, and strain, defined in the four individual NV reference frames. We find that the stress-based approach is straightforward, yields compact expressions for stress-induced level shifts and therefore constitutes the preferred approach to be used in future advances in the field. In contrast, the strain-based formalism is much more complicated and requires extra care when transforming into the employed NV reference frames. Furthermore, we illustrate how the developed formalism can be employed to extract values for the spin-stress and spin-strain coupling constants from data published by Teissier et al.., Comment: 14 pages, 3 figures; SOM available for download under https://quantum-sensing.physik.unibas.ch/publications/research-articles.html

Many promising applications of single crystal diamond and its color centers as sensor platform and in photonics require free-standing membranes with a thickness ranging from several micrometers to the few 100 nm range. In this work, we present an approach to conveniently fabricate such thin membranes with up to about one millimeter in size. We use commercially available diamond plates (thickness 50 $\mu$m) in an inductively coupled reactive ion etching process which is based on argon, oxygen and SF$_6$. We thus avoid using toxic, corrosive feed gases and add an alternative to previously presented recipes involving chlorine-based etching steps. Our membranes are smooth (RMS roughness <1 nm) and show moderate thickness variation (central part: <1 $\mu$m over $\approx \,$200x200 $\mu$m$^2$). Due to an improved etch mask geometry, our membranes stay reliably attached to the diamond plate in our chlorine-based as well as SF$_6$-based processes. Our results thus open the route towards higher reliability in diamond device fabrication and up-scaling., Comment: 9 pages, 4 figures, version 2 accepted for publication in MDPI micromachines

Three-level quantum systems have formed a cornerstone of quantum optics since the discovery of coherent population trapping (CPT) and electromagnetically induced transparency. Key to these phenomena is quantum interference, which arises if two of the three available transitions are coherently driven at well-controlled amplitudes and phases. The additional coherent driving of the third available transition would form a closed-contour interaction (CCI) from which fundamentally new phenomena would emerge, including phase-controlled CPT and one atom interferometry. However, due to the difficulty in experimentally realising a fully coherent CCI, such aspects of three-level systems remain unexplored as of now. Here, we exploit recently developed methods for coherent driving of single Nitrogen-Vacancy (NV) electronic spins to implement highly coherent CCI driving. Our experiments reveal phase-controlled, single spin quantum interference fringes, reminiscent of electron dynamics on a triangular lattice, with the driving field phases playing the role of a synthetic magnetic flux. We find that for suitable values of this phase, CCI driving leads to efficient coherence protection of the NV spin, yielding a nearly two orders of magnitude improvement of the coherence time, even for moderate drive strengths <~1MHz. Our results establish CCI driving as a novel paradigm in coherent control of few-level systems that offers attractive perspectives for applications in quantum sensing or quantum information processing., Comment: 18 pages, 11 figures. Including supplementary material. Comments are welcome. For further information visit https://quantum-sensing.physik.unibas.ch/news.html

St\"uckelberg interferometry describes the interference of two strongly coupled modes during a double passage through an avoided energy level crossing. In this work, we experimentally investigate finite time effects in St\"uckelberg interference and provide an exact analytical solution of the St\"uckelberg problem. Approximating this solution in distinct limits reveals uncharted parameter regimes of St\"uckelberg interferometry. Experimentally, we study these regimes using a purely classical, strongly coupled nanomechanical two-mode system of high quality factor. The classical two-mode system consists of the in-plane and out-of-plane fundamental flexural mode of a high stress silicon nitride string resonator, coupled via electric gradient fields. The dielectric control and microwave cavity enhanced universal transduction of the nanoelectromechanical system allows for the experimental access to all theoretically predicted St\"uckelberg parameter regimes. We exploit our experimental and theoretical findings by studying the onset of St\"uckelberg interference in dependence of the characteristic system control parameters and obtain characteristic excitation oscillations between the two modes even without the explicit need of traversing the avoided crossing. The presented theory is not limited to classical mechanical two-mode systems but can be applied to every strongly coupled (quantum) two-level system, for example a spin-1/2 system or superconducting qubit.

The transition from classical to quantum mechanics has intrigued scientists in the past and remains one of the most fundamental conceptual challenges in state-of-the-art physics. Beyond the quantum mechanical correspondence principle, quantum-classical analogies have attracted considerable interest. In this work, we present classical two-mode interference for a nanomechanical two-mode system, realizing classical St\"uckelberg interferometry. In the past, St\"uckelberg interferometry has been investigated exclusively in quantum mechanical two-level systems. Here, we experimentally demonstrate a classical analog of St\"uckelberg interferometry taking advantage of coherent energy exchange between two-strongly coupled, high quality factor nanomechanical resonator modes. Furthermore, we provide an exact theoretical solution for the double passage St\"uckelberg problem which reveals the analogy of the return probabilities in the quantum mechanical and the classical version of the problem. This result qualifies classical two-mode systems at large as a testbed for quantum mechanical interferometry.