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Hands-on experimental experience with quantum systems in the undergraduate physics curriculum provides students with a deeper understanding of quantum physics and equips them for the fast-growing quantum science industry. Here we present an experimental apparatus for performing quantum experiments with single nitrogen-vacancy (NV) centers in diamond. This apparatus is capable of basic experiments such as single-qubit initialization, rotation, and measurement, as well as more advanced experiments investigating electron-nuclear spin interactions. We describe the basic physics of the NV center and give examples of potential experiments that can be performed with this apparatus. We also discuss the options and inherent trade-offs associated with the choice of diamond samples and hardware. The apparatus described here enables students to write their own experimental control and data analysis software from scratch all within a single semester of a typical lab course, as well as to inspect the optical components and inner workings of the apparatus. We hope that this work can serve as a standalone resource for any institution that would like to integrate a quantum instructional lab into its undergraduate physics and engineering curriculum.

The temperature dependence of the zero-field splitting (ZFS) between the $|m_{s}=0\rangle$ and $|m_{s}=\pm 1\rangle$ levels of the nitrogen-vacancy (NV) center's electronic ground-state spin triplet can be used as a robust nanoscale thermometer in a broad range of environments. However, despite numerous measurements of this dependence in different temperature ranges, to our knowledge no analytical expression has been put forward that captures the scaling of the ZFS of the NV center across all relevant temperatures. Here we present a simple, analytical, and physically motivated expression for the temperature dependence of the NV center's ZFS that matches all experimental observations, in which the ZFS shifts in proportion to the occupation numbers of two representative phonon modes. In contrast to prior models our expression does not diverge outside the regions of fitting. We show that our model quantitatively matches experimental measurements of the ZFS from 15 to 500 K in single NV centers in ultra-pure bulk diamond, and we compare our model and measurements to prior models and experimental data., Comment: Main text: 7 pages, 4 figures, 1 table, 44 references. Supplemental Material: 12 pages, 5 figures, 2 tables, 23 references

Owing to the ubiquity of cellular communication signals, positioning with the fifth generation (5G) signal has emerged as a promising solution in global navigation satellite system-denied areas. Unfortunately, although the widely employed antenna arrays in 5G remote radio units (RRUs) facilitate the measurement of the direction of arrival (DOA), DOA-based positioning performance is severely degraded by array errors. This paper proposes an in-situ calibration framework with a user terminal transmitting 5G reference signals at several known positions in the actual operating environment and the accessible RRUs estimating their array errors from these reference signals. Further, since sub-6GHz small-cell RRUs deployed for indoor coverage generally have small-aperture antenna arrays, while 5G signals have plentiful bandwidth resources, this work segregates the multipath components via super-resolution delay estimation based on the maximum likelihood criteria. This differs significantly from existing in-situ calibration works which resolve multipaths in the spatial domain. The superiority of the proposed method is first verified by numerical simulations. We then demonstrate via field test with commercial 5G equipment that, a reduction of 46.7% for 1-${\sigma}$ DOA estimation error can be achieved by in-situ calibration using the proposed method., Comment: 14 pages, 11 figures, accepted by IEEE Transactions on Microwave Theory and Techniques

We present an approach to experimental radar systems education based on a combination of commercial low-cost hardware with modern open-source software technologies. Following a discussion of the general top-level architecture of flexible, software-defined radar systems, we introduce the specific selection of subsystems, their capabilities, and current system limitations. Compared to existing approaches to practical radar education, a more top-level modular design with a greater focus on performance and flexibility of baseband processing is selected while reducing the complexity of circuit and subsystem assembly and total system cost. We present example measurements obtained from the radar kit. The radar kit allows for bringing a radar lab to the students instead of students into the labs. It enables practical hands-on radar education also in distance-only-learning scenarios., Comment: Presented at the European Microwave Week 2021, Focussed Session on on Teaching Methods for Microwave Engineering

An approach towards wireless ranging and synchronization using commercial of-the-shelf software-defined radio payloads for small satellites, esp. CubeSats is studied. The approach only relies on the programmable logic configuration and processing system software. No hardware modifications or additions to the payloads are necessary. Experimental evaluation of the initial implementation shows a standard deviation of time-of-flight-based ranging measurements in the order of 1 cm, which renders the concept of interest for distributed satellite system missions.

Spin-lattice relaxation within the nitrogen-vacancy (NV) center's electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center's $|m_{s}=0\rangle \leftrightarrow |m_{s}=\pm 1\rangle$ and $|m_{s}=-1\rangle \leftrightarrow |m_{s}=+1\rangle$ transitions as a function of temperature from 9 to 474 K in high-purity samples. We show that the temperature dependencies of the rates are reproduced by an ab initio theory of Raman scattering due to second-order spin-phonon interactions, and we discuss the applicability of the theory to other spin systems. Using a novel analytical model based on these results, we suggest that the high-temperature behavior of NV spin-lattice relaxation is dominated by interactions with two groups of quasilocalized phonons centered at 68.2(17) and 167(12) meV., Comment: Main text: 7 pages, 4 figures, 44 references. Supplement: 14 pages, 11 figures, 4 tables, 25 references. Revised version v2 includes changes to improve clarity

Super-resolution imaging techniques enable nanoscale microscopy in fields such as physics, biology, and chemistry. However, many super-resolution techniques require specialized optical components, such as a helical-phase mask. We present a novel technique, Super-resolution Airy disk Microscopy (SAM) that can be used in a standard confocal microscope without any specialized optics. We demonstrate this technique, in combination with ground state depletion, to image and control nitrogen-vacancy (NV) centers in bulk diamond below the diffraction limit. A greater than 14-fold improvement in resolution compared to the diffraction limit is achieved, corresponding to a spatial resolution of 16.9(8) nm for a 1.3 NA microscope with 589 nm light. We make use of our enhanced spatial resolution to control the spins states of individual NV centers separated from each other by less than the diffraction limit, including pairs sharing the same orientation that are indistinguishable with a conventional electron spin resonance measurement., Comment: Main text: 6 pages, 4 figures, 31 references. Supplement: 14 pages, 10 figures, 15 references. Version 2 contains updated figures and modified text to improve clarity and readability

Control over the charge states of color centers in solids is necessary in order to fully utilize them in quantum technologies. However, the microscopic charge dynamics of deep defects in wide-bandgap semiconductors are complex, and much remains unknown. Here, we utilize single shot charge state readout of an individual nitrogen-vacancy (NV) center to probe charge dynamics of the surrounding defects in diamond. We show that the NV center charge state can be converted through the capture of holes produced by optical illumination of defects many microns away. With this method, we study the optical charge conversion of silicon-vacancy (SiV) centers and provide evidence that the dark state of the SiV center under optical illumination is SiV2-. These measurements illustrate that charge carrier generation, transport, and capture are important considerations in the design and implementation of quantum devices with color centers, and provide a novel way to probe and control charge dynamics in diamond., Comment: Main text: 18 pages, 4 figures, 32 references. Supporting Information: 20 pages, 9 figures, 2 tables, 12 references

Understanding the limits to the spin-coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system. We show that relaxation on the $|m_{s}=-1\rangle \leftrightarrow |m_{s}=+1\rangle$ transition occurs approximately twice as fast as relaxation on the $|m_{s}=0\rangle \leftrightarrow |m_{s}=\pm 1\rangle$ transitions under ambient conditions in native NVs in high-purity bulk diamond. The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions. We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms. Finally, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind $|m_{s}=-1\rangle \leftrightarrow |m_{s}=+1\rangle$ relaxation, motivating future measurements of the temperature dependence of this relaxation rate., Comment: Main text: 7 pages, 4 figures, 31 references. Supplemental materials: 12 pages, 1 table, 1 figure

Thanks to their versatility, nitrogen-vacancy (NV) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to NVs in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on qutrit transitions between the energy eigenstates composed of the $m_s = \pm1$ states of the NV$^-$ electronic ground state in $\sim40$-nm nanodiamonds under ambient conditions. For frequency splittings between these states of $\sim20~$MHz or less the maximum theoretically achievable coherence time of the NV spin is $\sim2~$orders of magnitude shorter than would be expected if the NV spin is treated as a qubit. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the qutrit relaxation rate with the splitting between the states, suggesting that, whenever possible, measurements with NVs in nanodiamonds should be performed at moderate axial magnetic fields ($>60$ G). We also observe that the qutrit relaxation rate changes with time. These findings indicate that surface electric field noise is a major source of decoherence for NVs in nanodiamonds., Comment: Main text: 8 pages, 4 figures, 1 table, 37 references. Supplemental materials: 5 pages, 8 figures, 1 table. Changes in v4: Accepted manuscript