J. Cerrillo, S. Oviedo Casado, and J. Prior. 6/3/2021. “Low Field Nano-NMR via Three-Level System Control.” PHYSICAL REVIEW LETTERS, 126, 22. Publisher's Version Abstract
Conventional control strategies for nitrogen-vacancy centers in quantum sensing are based on a two-level model of their triplet ground state. However, this approach fails in regimes of weak bias magnetic fields or strong microwave pulses, as we demonstrate. To overcome this limitation, we propose a novel control sequence that exploits all three levels by addressing a hidden Raman configuration with microwave pulses tuned to the zero-field transition. We report excellent performance in typical dynamical decoupling sequences, opening up the possibility for nano-NMR operation in low field environments.
Simon Schmitt, Tuvia Gefen, Daniel Louzon, Christian Osterkamp, Nicolas Staudenmaier, Johannes Lang, Matthew Markham, Alex Retzker, Liam P. McGuinness, and Fedor Jelezko. 4/1/2021. “Optimal frequency measurements with quantum probes.” npj quantum information . Publisher's Version Abstract
Precise frequency measurements are important in applications ranging from navigation and imaging to computation and communication. Here we outline the optimal quantum strategies for frequency discrimination and estimation in the context of quantum spectroscopy, and we compare the effectiveness of different readout strategies. Using a single NV center in diamond, we implement the optimal frequency discrimination protocol to discriminate two frequencies separated by 2 kHz with a single 44 μs measurement, a factor of ten below the Fourier limit. For frequency estimation, we achieve a frequency sensitivity of 1.6 µHz/Hz2 for a 1.7 µT amplitude signal, which is within a factor of 2 from the quantum limit. Our results are foundational for discrimination and estimation problems in nanoscale nuclear magnetic resonance spectroscopy.
Yaoming Chu, Pengcheng Yang, Musang Gong, Min Yu, Baiyi Yu, Martin B. Plenio, Alex Retzker, and Jianming Cai. 1/19/2021. “Precise Spectroscopy of High-Frequency Oscillating Fields with a Single-Qubit Sensor.” PHYSICAL REVIEW APPLIED, 15, 1. Publisher's Version Abstract
Precise spectroscopy of oscillating fields plays a significant role in many fields. Here, we propose an experimentally feasible scheme to measure the frequency of a fast-oscillating field using a single-qubit sensor. By invoking a stable classical clock, the signal phase correlations between successive measurements enable us to extract the target frequency with extremely high precision. In addition, we integrate dynamical decoupling technique into the framework to suppress the influence of slow environmental noise. Our framework is feasible with a variety of atomic and single solid-state spin systems within the state-of-the-art experimental capabilities as a versatile tool for quantum spectroscopy.
Santiago Oviedo-Casado, Amit Rotem, Ramil Nigmatullin, Javier Prior, and Alex Retzker. 11/12/2020. “Correlated noise in Brownian motion allows for super resolution.” Scientific Reports . Publisher's Version Abstract
Diffusion broadening of spectral lines is the main limitation to frequency resolution in non-polarized liquid state nano-NMR. This problem arises from the limited amount of information that can be extracted from the signal before losing coherence. For liquid state NMR as with most generic sensing experiments, the signal is thought to decay exponentially, severely limiting resolution. However, there is theoretical evidence that predicts a power law decay of the signal’s correlations due to diffusion noise in the non-polarized nano-NMR scenario. In this work we show that in the NV based nano-NMR setup such diffusion noise results in high spectral resolution.
D. Cohen, T.Gefen, L.Ortiz, and A.Retzker. 9/18/2020. “Achieving the ultimate precision limit with a weakly interacting quantum probe.” npj Quantum Information , 6, 83. Publisher's Version Abstract
The ultimate precision limit in estimating the Larmor frequency of N unentangled qubits is well established, and is highly important for magnetometers, gyroscopes, and other types of quantum sensors. However, this limit assumes perfect projective measurements of the quantum registers. This requirement is not practical in many physical systems, such as NMR spectroscopy, where a weakly interacting external probe is used as a measurement device. Here, we show that in the framework of quantum nano-NMR spectroscopy, in which these limitations are inherent, the ultimate precision limit is still achievable using control and a finely tuned measurement.
Yotam V, Benedikt T, Tuvia G, Ilai S, Martin P, and Alex R. 9/8/2020. “Robustness of the NV-NMR Spectrometer Setup to Magnetic Field Inhomogeneities.” Physical Review Letters, 125, 110502. Publisher's Version Abstract
The NV-NMR spectrometer is a promising candidate for detection of NMR signals at the nanoscale. Field inhomogeneities, however, are a major source of noise that limits spectral resolution in state of the art NV-NMR experiments and constitutes a major bottleneck in the development of nanoscale NMR. Here we propose, a route in which this limitation could be circumvented in NV-NMR spectrometer experiments, by utilizing the nanometric scale and the quantumness of the detector.
Genko T. Genov, Yachel Ben-Shalom, Fedor Jelezko, Alex Retzker, and Nir Bar-Gill. 8/7/2020. “Efficient and robust signal sensing by sequences of adiabatic chirped pulses.” Phys. Rev. Research , 2, 3. Publisher's Version Abstract
We propose a scheme for sensing of an oscillating field in systems with large inhomogeneous broadening and driving field variation by applying sequences of phased, adiabatic, chirped pulses. These act as a double filter for dynamical decoupling, where the adiabatic changes of the mixing angle during the pulses rectify the signal and partially remove frequency noise. The sudden changes between the pulses act as instantaneous π pulses in the adiabatic basis for additional noise suppression. We also use the pulses' phases to correct for other errors, e.g., due to nonadiabatic couplings. Our technique improves significantly the coherence time in comparison to standard XY8 dynamical decoupling in realistic simulations in NV centers with large inhomogeneous broadening. Beyond the theoretical proposal, we also present proof-of-principle experimental results for quantum sensing of an oscillating field in NV centers in diamond, demonstrating superior performance compared to the standard technique.
D. Cohen, R.Nigmatullin, M.Eldar, and A.Retzker. 6/15/2020. “Confined Nano‐NMR Spectroscopy Using NV Centers.” Advanced Quantum Technologies. Publisher's Version Abstract
Nano nuclear magnetic resonance (nano‐NMR) spectroscopy with nitrogen‐vacancy (NV) centers holds the potential to provide high‐resolution spectra of minute samples. This is likely to have important implications for chemistry, medicine, and pharmaceutical engineering. One of the main hurdles facing the technology is that diffusion of unpolarized liquid samples broadens the spectral lines thus limiting resolution. Experiments in the field are therefore impeded by the efforts involved in achieving high polarization of the sample which is a challenging endeavor. Here, a scenario where the liquid is confined to a small volume is examined. It is shown that the confinement “counteracts” the effect of diffusion, thus overcoming a major obstacle to the resolving abilities of the NV‐NMR spectrometer.
QY Cao, PC Yang, MS Gong, M Yu, A Retzker, MB Plenio, C Muller, N Tomek, B Naydenov, LP McGuinness, F Jelezko, and JM Cai. 2020. “Protecting Quantum Spin Coherence of Nanodiamonds in Living Cells.” Physical Review Applied, 13, 2. Publisher's Version Abstract
Because of its superior coherent and optical properties at room temperature, the nitrogen-vacancy (N-V) center in diamond has become a promising quantum probe for nanoscale quantum sensing. However, the application of N-V-containing nanodiamonds to quantum sensing suffers from their relatively short spin coherence times. Here we demonstrate energy-efficient protection of N-V spin coherence in nanodiamonds using concatenated continuous dynamical decoupling, which exhibits excellent performance with a less-stringent microwave-power requirement. When this is applied to nanodiamonds in living cells, we are able to extend the spin coherence time by an order of magnitude to the T1 limit of 30μs. Further analysis demonstrates concomitant improvements of sensing performance, which shows that our results provide an important step toward in vivo quantum sensing using N-V centers in nanodiamond.
Daniel Cohen, Ramil Nigmatullin, Oded Kenneth, Fedor Jelezko, Maxim Khodas, and Alex Retzker. 2020. “Utilising NV based quantum sensing for velocimetry at the nanoscale.” Scientific Reports, 10, 1. Publisher's Version Abstract
Nitrogen-Vacancy (NV) centers in diamonds have been shown in recent years to be excellent magnetometers on the nanoscale. One of the recent applications of the quantum sensor is retrieving the Nuclear Magnetic Resonance (NMR) spectrum of a minute sample, whose net polarization is well below the Signal-to-Noise Ratio (SNR) of classic devices. The information in the magnetic noise of diffusing particles has also been shown in decoherence spectroscopy approaches to provide a method for measuring different physical parameters. Similar noise is induced on the NV center by a flowing liquid. However, when the noise created by diffusion effects is more dominant than the noise of the drift, it is unclear whether the velocity can be efficiently estimated. Here we propose a non-intrusive setup for measuring the drift velocity near the surface of a flow channel based on magnetic field quantum sensing using NV centers. We provide a detailed analysis of the sensitivity for different measurement protocols, and we show that our nanoscale velocimetry scheme outperforms current fluorescence based approaches even when diffusion noise is dominant. Our scheme can be applied for the investigation of microfluidic channels, where the drift velocity is usually low and the flow properties are currently unclear. A better understanding of these properties is essential for the future development of microfluidic and nanofluidic infrastructures.
Nati Aharon, Amit Rotem, Liam P. McGuinness, Fedor Jelezko, Alex Retzker, and Zohar Ringel. 11/28/2019. “NV center based nano-NMR enhanced by deep learning.” Scientific Reports, 9. Publisher's Version Abstract
The growing field of nano nuclear magnetic resonance (nano-NMR) seeks to estimate spectra or discriminate between spectra of minuscule amounts of complex molecules. While this field holds great promise, nano-NMR experiments suffer from detrimental inherent noise. This strong noise masks to the weak signal and results in a very low signal-to-noise ratio. Moreover, the noise model is usually complex and unknown, which renders the data processing of the measurement results very complicated. Hence, spectra discrimination is hard to achieve and in particular, it is difficult to reach the optimal discrimination. In this work we present strong indications that this difficulty can be overcome by deep learning (DL) algorithms. The DL algorithms can mitigate the adversarial effects of the noise efficiently by effectively learning the noise model. We show that in the case of frequency discrimination DL algorithms reach the optimal discrimination without having any pre-knowledge of the physical model. Moreover, the DL discrimination scheme outperform Bayesian methods when verified on noisy experimental data obtained by a single Nitrogen-Vacancy (NV) center. In the case of frequency resolution we show that this approach outperforms Bayesian methods even when the latter have full pre-knowledge of the noise model and the former has none. These DL algorithms also emerge as much more efficient in terms of computational resources and run times. Since in many real-world scenarios the noise is complex and difficult to model, we argue that DL is likely to become a dominant tool in the field.
T Gefen, A Rotem, and A Retzker. 11/1/2019. “Overcoming resolution limits with quantum sensing.” Nature Communications, 10. Publisher's Version Abstract
The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. While for static signals the main figure of merit is sensitivity, for time dependent signals it is spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.
Nati Aharon, Nicolas Spethmann, Ian D Leroux, Piet O Schmidt, and Alex Retzker. 8/2019. “Robust optical clock transitions in trapped ions using dynamical decoupling.” New Journal of Physics, 21. Publisher's Version Abstract
We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic field shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions, such as ${}^{40}{\mathrm{Ca}}^{+}$ , ${}^{88}{\mathrm{Sr}}^{+}$ , ${}^{138}{\mathrm{Ba}}^{+}$ and ${}^{176}{\mathrm{Lu}}^{+}$ . Taking a spherically symmetric Coulomb crystal formed by 400 ${}^{40}{\mathrm{Ca}}^{+}$ ions as an example, we show through numerical simulations that the inhomogeneous linewidth of tens of Hertz in such a crystal together with linear Zeeman shifts of order 10 MHz are reduced to form a linewidth of around 1 Hz. We estimate a two-order-of-magnitude reduction in averaging time compared to state-of-the art single ion frequency references, assuming a probe laser fractional instability of ${10}^{-15}$. Furthermore, a statistical uncertainty reaching 2.9 × 10−16 in 1 s is estimated for a cascaded clock scheme in which the dynamically decoupled Coulomb crystal clock stabilizes the interrogation laser for an ${}^{27}{\mathrm{Al}}^{+}$ clock.
Nati Aharon, Ilai Schwartz, and Alex Retzker. 3/29/2019. “Quantum Control and Sensing of Nuclear Spins by Electron Spins under Power Limitations.” Physical Review Letters, 122, 12. Publisher's Version Abstract
State of the art quantum sensing experiments targeting frequency measurements or frequency addressing of nuclear spins require one to drive the probe system at the targeted frequency. In addition, there is a substantial advantage to performing these experiments in the regime of high magnetic fields, in which the Larmor frequency of the measured spins is large. In this scenario we are confronted with a natural challenge of controlling a target system with a very high frequency when the probe system cannot be set to resonance with the target frequency. In this contribution we present a set of protocols that are capable of confronting this challenge, even at large frequency mismatches between the probe system and the target system, both for polarization and for quantum sensing.
Daniel Cohen, Maxim Khodas, Oded Keneth, and Alex Retzker. 3/1/2019. “Sensing nano-NMR diffusion spectra using a nitrogen vacancy center.” Optical, Opto-Atomic, and Entanglement-Enhanced Precision Metrology, 10934. Publisher's Version Abstract
Nano nuclear magnetic resonance (nano‐NMR) spectroscopy with nitrogen‐vacancy (NV) centers holds the potential to provide high‐resolution spectra of minute samples. This is likely to have important implications for chemistry, medicine, and pharmaceutical engineering. One of the main hurdles facing the technology is that diffusion of unpolarized liquid samples broadens the spectral lines thus limiting resolution. Experiments in the field are therefore impeded by the efforts involved in achieving high polarization of the sample which is a challenging endeavor. Here, a scenario where the liquid is confined to a small volume is examined. It is shown that the confinement “counteracts” the effect of diffusion, thus overcoming a major obstacle to the resolving abilities of the NV‐NMR spectrometer.
Amit Rotem, Tuvia Gefen, Santiago Oviedo-Casado, Javier Prior, Simon Schmitt, Yoram Burak, Liam McGuiness, Fedor Jelezko, and Alex Retzker. 2019. “Limits on Spectral Resolution Measurements by Quantum Probes.” Physical Review Letters, 122, 6. Publisher's Version Abstract
The limits of frequency resolution in nano-NMR experiments have been discussed extensively in recent years. It is believed that there is a crucial difference between the ability to resolve a few frequencies and the precision of estimating a single one. Whereas the efficiency of single frequency estimation gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific timescale of the signal and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and both are only limited by the Cramér-Rao bound of a single frequency estimation.
Genko T Genov, Nati Aharon, Fedor Jelezko, and Alex Retzker. 2019. “Mixed dynamical decoupling.” Quantum Science and Technology, 4, 3. Publisher's Version Abstract
We propose a scheme for mixed dynamical decoupling (MDD), where we combine continuous dynamical decoupling with robust sequences of phased pulses. Specifically, we use two fields for decoupling, where the first continuous driving field creates dressed states that are robust to environmental noise. Then, a second field implements a robust sequence of phased pulses to perform inversions of the dressed qubits, thus achieving robustness to amplitude fluctuations of both fields. We show that MDD outperforms standard concatenated continuous dynamical decoupling in realistic numerical simulations for dynamical decoupling in NV centers in diamond. Finally, we also demonstrate how our technique can be utilized for improved sensing.
Alexander Stark, Nati Aharon, Alexander Huck, Haitham A. R El-Ella, Alex Retzker, Fedor Jelezko, and Ulrik L. Andersen. 10/4/2018. “Clock transition by continuous dynamical decoupling of a three-level system.” Scientific Reports, 8. Publisher's Version Abstract
We present a novel continuous dynamical decoupling scheme for the construction of a robust qubit in a three-level system. By means of a clock transition adjustment, we first show how robustness to environmental noise is achieved, while eliminating drive-noise, to first-order. We demonstrate this scheme with the spin sub-levels of the NV-centre’s electronic ground state. By applying drive fields with moderate Rabi frequencies, the drive noise is eliminated and an improvement of 2 orders of magnitude in the coherence time is obtained compared to the pure dephasing time. We then show how the clock transition adjustment can be tuned to eliminate also the second-order effect of the environmental noise with moderate drive fields. A further detailed theoretical investigation suggests an additional improvement of more than 1 order of magnitude in the coherence time which is supported by simulations. Hence, our scheme predicts that the coherence time may be prolonged towards the lifetime-limit using a relatively simple experimental setup.
Nils Scharnhorst, Javier Cerrillo, Johannes Kramer, Ian D. Leroux, Jannes B. Wübbena, Alex Retzker, and Piet O. Schmidt. 8/27/2018. “Experimental and theoretical investigation of a multimode cooling scheme using multiple electromagnetically-induced-transparency resonances.” Physical Review a, 98, 2. Publisher's Version Abstract
We introduce and demonstrate double-bright electromagnetically-induced-transparency (D-EIT) cooling as an extension to EIT cooling. By involving an additional ground state, two bright states can be shifted individually into resonance for cooling of motional modes of frequencies that may be separated by more than the width of a single EIT cooling resonance. This allows three-dimensional ground-state cooling of a 40Ca+ ion trapped in a linear Paul trap with a single cooling pulse. Measured cooling rates and steady-state mean motional quantum numbers for this D-EIT cooling are compared with those of standard EIT cooling as well as concatenated standard EIT cooling pulses for multimode cooling. Experimental results are compared to full-density matrix calculations. We observe a failure of the theoretical description within the Lamb-Dicke regime that can be overcome by a time-dependent rate theory. Limitations of the different cooling techniques and possible extensions to multi-ion crystals are discussed.
J Cerrillo, A Retzker, and MB Plenio. 7/30/2018. “Double-path dark-state laser cooling in a three-level system.” Physical Review a, 98, 1. Publisher's Version Abstract
We present a detailed analysis of a robust and fast laser cooling scheme [J. Cerrillo et al., Phys. Rev. Lett. 104, 043003 (2010)] on a three-level system. A special laser configuration, applicable to trapped ions, atoms, or cantilevers, designs a double-path quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon interactions. As a consequence, cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very flexible under constraints of the physical parameters such as laser intensity, detuning, or optical access, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes. Its suitability as a cooling scheme for several ions in a trap and three-dimensional cooling is shown.