Ideal projective quantum measurement makes the system state collapse in one of the observable operator eigenstates | ϕ α ⟩ , making it a powerful tool for preparing the system in the desired pure state. Nevertheless, experimental realisations of projective measurement are not ideal. During the measurement time needed to overcome the classical noise of the apparatus, the system state is often (slightly) perturbed, which compromises the fidelity of initialisation. In this paper, we propose an analytical model to analyse the initialisation fidelity of the system performed by the single-shot readout. We derive a method to optimise parameters for the three most used cases of photon counting based readouts for NV colour centre in diamond, charge state, nuclear spin and low temperature electron spin readout. Our work is of relevance for the accurate description of initialisation fidelity of the quantum bit when the single-shot readout is used for initialisation via post-selection or real-time control.

Nitrogen vacancy (NV) centers are a major platform for the detection of nuclear magnetic resonance (NMR) signals at the nanoscale. To overcome the intrinsic electron spin lifetime limit in spectral resolution, a heterodyne detection approach is widely used. However, application of this technique at high magnetic fields is yet an unsolved problem. Here, we introduce a heterodyne detection method utilizing a series of phase coherent electron nuclear double resonance sensing blocks, thus eliminating the numerous Rabi microwave pulses required in the detection. Our detection protocol can be extended to high magnetic fields, allowing chemical shift resolution in NMR experiments. We demonstrate this principle on a weakly coupled 13 C nuclear spin in the bath surrounding single NV centers, and compare the results to existing heterodyne protocols. Additionally, we identify the combination of NV-spin-initialization infidelity and strong sensor-target-coupling as linewidth-limiting decoherence source, paving the way towards high-field heterodyne NMR protocols with chemical resolution.

The ability to follow the dynamics of a quantum system in a quantitative manner is of key importance for quantum technology. Despite its central role, justifiable deduction of the quantum dynamics of a single quantum system in terms of a macroscopical observable remains a challenge. Here we show that the relation between the readout signal of a single electron spin and the quantum dynamics of the single nuclear spin is given by a parameter related to the measurement strength. We determine this measurement strength in independent experiments and use this value to compare our analysis of the quantum dynamics with experimental results. We prove the validity of our approach by measuring violations of the Leggett-Garg inequality.

Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.

Nanoscale nuclear magnetic resonance (NMR) signals can be measured through hyperfine interaction to paramagnetic electron sensor spins. A heterodyne approach is widely used to overcome the electron spin lifetime limit in spectral resolution. It uses a series of modified Hahn echo pulse sequences applied coherently with precession signal resulting in a subsampled NMR signal. Due to challenges with applying high electron Rabi frequencies its application is limited to low fields, thus the full potential of the method is not yet exploited at high magnetic fields, beneficial for NMR. Here we present heterodyne detection utilizing a series of phase coherent electron nuclear double resonance sensing blocks which extends nanoscale NMR protocols to arbitrary magnetic fields. We demonstrate this principle on a single NV center, both with an intrinsic $^{14}$N and a weekly coupled $^{13}$C nuclear spin in the bath surrounding single NV centres. We compare our protocol to existing heterodyne protocols and discuss its prospects. This work paves the way towards high field nanoscale heterodyne NMR protocols with NV centres which is crucial for reducing sample volumes and improving chemical resolution.

Quantum sensors are known for their high sensitivity in sensing applications. However, this sensitivity often comes with severe restrictions on other parameters which are also important. Examples are that in measurements of arbitrary signals, limitation in linear dynamic range could introduce distortions in magnitude and phase of the signal. High frequency resolution is another important feature for reconstructing unknown signals. Here, we demonstrate a distortion-free quantum sensing protocol that combines a quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the capability of reconstructing audio frequency signals with an extended linear dynamic range and high frequency resolution. Melody and speech based signals are used for demonstrating the features. The methods could broaden the horizon for quantum sensors towards applications, e.g. telecommunication in challenging environment, where low-distortion measurements are required at multiple frequency bands within a limited volume.

The quantum Fourier transformation (QFT) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize QFT to enhance the performance of a quantum sensor. We implement the QFT algorithm in a hybrid quantum register consisting of a nitrogen-vacancy (NV) center electron spin and three nuclear spins. The QFT runs on the nuclear spins and serves to process the sensor—i.e., the NV electron spin signal. Specifically, we show the application of QFT for correlation spectroscopy, where the long correlation time benefits the use of the QFT in gaining maximum precision and dynamic range at the same time. We further point out the ability for demultiplexing the nuclear magnetic resonance (NMR) signals using QFT and demonstrate precision scaling with the number of used qubits. Our results mark the application of a complex quantum algorithm in sensing which is of particular interest for high dynamic range quantum sensing and nanoscale NMR spectroscopy experiments.

Vadim V. Vorobyov, ∗ Jonas Meinel, 2 Hitoshi Sumiya, Shinobu Onoda, Junichi Isoya, Oleg Gulinsky, 2, † and Jörg Wrachtrup 2, ‡ 3rd Institute of Physics, IQST and Centre for Applied Quantum Technologies, University of Stuttgart, 70569, Stuttgart, Germany Max-Planck Institute for Solid State Research, Stuttgart, Germany Advanced Materials Laboratory, Sumitomo Electric Industries Ltd., Itami 664-0016, Japan Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology, Takasaki 370-1292, Japan Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan

Quantum sensors are keeping the cutting-edge sensitivities in metrology. However, for high-sensitive measurements of arbitrary signals, limitations in linear dynamic range could introduce distortions when sensing the frequency, magnitude and phase of unknown signals. Here, we overcome these limitations with advanced sensing protocol that combines quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the ability to sense radio signals with a 98 dB linear dynamic range, a 31 pT/Hz$^{1/2}$ sensitivity, and arbitrary frequency resolution. Further, we use the sensor as a quantum radio receiver to show the capability in detecting audio signals (melody piece, speech) with high fidelity. The methods developed here could broaden the horizon for quantum sensors towards applications in telecommunication, where high-fidelity and low-distortion at multiple frequency bands within small sensing volumes are required.

Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system’s resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.

We report results of a new technique to measure the electric dipole moment of ^{129}Xe with ^{3}He comagnetometry. Both species are polarized using spin-exchange optical pumping, transferred to a measurement cell, and transported into a magnetically shielded room, where SQUID magnetometers detect free precession in applied electric and magnetic fields. The result from a one week measurement campaign in 2017 and a 2.5 week campaign in 2018, combined with detailed study of systematic effects, is d_{A}(^{129}Xe)=(1.4±6.6_{stat}±2.0_{syst})×10^{-28}  e cm. This corresponds to an upper limit of |d_{A}(^{129}Xe)|<1.4×10^{-27}  e cm (95% C.L.), a factor of 5 more sensitive than the limit set in 2001.

We report results of a new technique to measure the electric dipole moment of $^{129}\mathrm{Xe}$ with $^{3}\mathrm{He}$ comagnetometry. Both species are polarized using spin-exchange optical pumping, transferred to a measurement cell, and transported into a magnetically shielded room, where SQUID magnetometers detect free precession in applied electric and magnetic fields. The result from a one week measurement campaign in 2017 and a 2.5 week campaign in 2018, combined with detailed study of systematic effects, is ${d}_{A}(^{129}\mathrm{Xe})=(1.4\ifmmode\pm\else\textpm\fi{}6.{6}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}2.{0}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}28}\text{ }\text{ }e\text{ }\mathrm{cm}$. This corresponds to an upper limit of $|{d}_{A}(^{129}\mathrm{Xe})|<1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\text{ }\text{ }e\text{ }\mathrm{cm}$ (95% C.L.), a factor of 5 more sensitive than the limit set in 2001.

Polarized nuclei are a powerful tool in nuclear-spin studies and in the search for physics beyond the standard model. Systems which compare two nuclear species have thus far been limited by anomalous yet reproducible frequency variations of unknown origin. We studied the self-interactions in a He-3-Xe-129 system by independently addressing, controlling, and measuring the influence of each component of the nuclear-spin polarization. Our results directly rule out prior explanations of the shifts and demonstrate experimentally that they can be explained by species-dependent self-interactions. We also report a gas-phase frequency shift induced by Xe-129 on He-3.

— Precision measurements of co-located and hyper-polarized 3 He- 129 Xe gases are a promising technique for searches for a wide variety of new physics that couples to nuclear spin, most of which are in principle inaccessible at accelerators. Especially important are measurements of: Lorentz-violation; CP-violation in the form of a Xe EDM; relics of high-energy symmetry breaking; and ultra-light dark matter axion scenar-ios. The power of such measurements stems from very high signal-to-noise ratios and long interrogation times, enabling extreme precision in the determination of the precession frequencies of the spins of the species. Unfortunately, so far such He-Xe co-magnetometers have not realized their potential due to a systematic shift between the 3 He and 129 Xe frequencies that changes by a few (cid:22) Hz during each measurement, and limits the ability of this technique to identify new physics. This systematic has also been a subject to notable controversies in the community. I will present careful studies where we traced the issue back to residual longitudinal magnetization of the He and Xe, which affects the precession frequency of the two spin-species differ-ently. Reducing this effect will greatly increase the potential physics reach of He-Xe co-magnetometers.

Permanent electric dipole moments (EDMs) arise due to the breaking of time-reversal or, equivalently, CP-symmetry. Although EDM searches have so far only set upper limits, which are many orders of magnitude larger than Standard Model (SM) predictions, the motivation for more sensitive searches is stronger than ever. A new effort at FRM-II incorporating 129 Xe and 3 He as a co-magnetometer can potentially improve the current limit. The noble gas mixture of 129 Xe and 3 He is simultanously polarized by spin-exchange optical pumping and then transferred into a high-performance magnetically shielded room. Inside, both species can freely precess in the presence of applied magnetic and electric fields. The precession signals are detected by LTc SQUID sensors. In EDM cells with silicon electrodes we observed spin lifetimes in excess of 2500 s without and with high-voltage applied. This meets one requirement to achieve our goal of improving the EDM limit on 129 Xe by several orders of magnitude.