Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However the spectral resolution in such protocols is limited ultimately by 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 $1\ \rm{Hz}$ for a $4\ \rm{GHz}$ 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 highest sensitivity, the Floquet dynamics allows robust control independent from the systems resonance frequency. Our work is important for future studies in sensing weak microwave signals in wide frequency range with high spectral resolution.
Raman heterodyne spectroscopy is a powerful tool for characterizing the energy and dynamics of spins. The technique uses an optical pump to transfer coherence from a spin transition to an optical transition where the coherent emission is more easily detected. Here Raman heterodyne spectroscopy is used to probe an isotopically purified ensemble of erbium dopants, in a yttrium orthosilicate (Y$_2$SiO$_5$) crystal coupled to a microwave cavity. Because the erbium electron spin transition is strongly coupled to the microwave cavity, we observed Raman heterodyne signals at the resonant frequencies …
Homodyne and heterodyne detection represent "twin-pillars" of quantum displacement sensing using optical cavities, having permitted major breakthroughs including detection of gravitational waves and of the motion of quantum ground-state cooled mechanical oscillators. Both can suffer disadvantages as diagnostics in quantum optomechanics, either through symmetrisation (homodyne), or loss of correlations (heterodyne). We show that, for modest heterodyne beat frequencies ($Ω\sim ω_M/10 \gg Γ$), judicious construction of the autocorrelation of the measured current can either recover (i) a spectrum …
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 presen…
The efficiency of the frequency conversion process at the heart of Raman heterodyne spectroscopy was improved by nearly four orders of magnitude by resonant enhancement of both the pump and signal optical fields. Our results using an erbium doped Y$_2$SiO$_5$ crystal at temperatures near 4K suggest that such an approach is promising for the quantum conversion of microwave to optical photons.
The extraordinary sensitivity of the output field of an optical cavity to small quantum-scale displacements has led to breakthroughs such as the first detection of gravitational waves \cite{LIGO,LIGODC} and of the motions of quantum ground-state cooled mechanical oscillators \cite{Teufel2011,Chan2011}. While heterodyne detection of the cavity field preserves asymmetries which provide a key signature that mechanical oscillators has attained the quantum regime, detection of a rotating quadrature of the light averages out important quantum correlations, yielding a weaker signal and lower sensitiv…
Cryogenic rf-to-microwave transducer based on a dc-biased electromechanical system
Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS–Université PSL, Collège de France（卡斯勒-布罗塞尔实验室，索邦大学，法国国家科学研究中心，巴黎高等师范学院-巴黎文理研究大学，法兰西公学院）；Alice & Bob（爱丽丝与鲍勃公司）；Niels Bohr Institute, University of Copenhagen（尼尔斯·玻尔研究所，哥本哈根大学）；Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen（混合量子网络中心（Hy-Q），尼尔斯·玻尔研究所，哥本哈根大学）；Institut Universitaire de France (IUF)（法国高等研究院）
Phase-Sensitive Heterodyne Detection of MW using EIT Harmonics in Rydberg Atoms
Johns Hopkins University（约翰斯·霍普金斯大学）；Indian Institute of Science（印度科学学院）；Defence Institute of Advanced Technology (Deemed University)（国防先进技术研究所（认定大学））；University of Bristol（布里斯托大学）；Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）
We consider the interaction of a magnetically trapped Bose-Einstein condensate of Rubidium atoms with the stationary microwave radiation field sustained by a coplanar waveguide resonator. This coupling allows for the measurement of the magnetic field of the resonator by means of counting the atoms that fall out of the condensate due to hyperfine transitions to non-trapped states. We determine the quantum efficiency of this detection scheme and show that weak microwave fields at the single-photon level can be sensed with an integration time on the order of a second.
Developing robust microwave-field sensors is both fundamentally and practically important with a wide range of applications from astronomy to communication engineering. The Nitrogen-Vacancy (NV) center in diamond is an attractive candidate for such purpose because of its magnetometric sensitivity, stability and compatibility with ambient conditions. However, the existing NV center-based magnetometers have limited sensitivity in the microwave band. Here we present a continuous heterodyne detection method that can enhance the sensor's response to weak microwaves, even in the absence of spin cont…
Quantum communication is a holy grail to achieve secure communication among a set of partners, since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglement as an extra resource to determine parameters by either using less resources or attaining a precision unachievable in classical protocols. A paradigmatic example is the quantum radar, which allows one to detect an object without being detected oneself, by making use of the additional asset provided by quantum entanglement to reduce the intensity of the signal. In the optical regime, impressive technological…
Fast, high-fidelity measurement is a key ingredient for quantum error correction. Conventional approaches to the measurement of superconducting qubits, involving linear amplification of a microwave probe tone followed by heterodyne detection at room temperature, do not scale well to large system sizes. Here we introduce an alternative approach to measurement based on a microwave photon counter. We demonstrate raw single-shot measurement fidelity of 92%. Moreover, we exploit the intrinsic damping of the counter to extract the energy released by the measurement process, allowing repeated high-fi…
We present a square root law for active sensing of phase $θ$ of a single pixel using optical probes that pass through a single-mode lossy thermal-noise bosonic channel. Specifically, we show that, when the sensor uses an $n$-mode covert optical probe, the mean squared error (MSE) of the resulting estimator $\hatθ_n$ scales as $\langle (θ-\hatθ_n)^2\rangle=\mathcal{O}(1/\sqrt{n})$; improving the scaling necessarily leads to detection by the adversary with high probability. We fully characterize this limit and show that it is achievable using laser light illumination and a heterodyne receiver, e…
Real-Time Magnetic Field Sensing based on Microwave Frequency Modulated Photocurrent of Nitrogen-Vacancy Centers in Diamond
Henan Key Laboratory of Diamond Materials and Devices, Key Laboratory of Material Physics, Ministry of Education, School of Physics, Zhengzhou University（郑州大学物理学院）；Institute of Quantum Materials and Physics, Henan Academy of Sciences（河南省科学院量子材料与物理研究所）
An ensemble of nitrogen-vacancy (NV) centers in diamond is a fascinating candidate to realize a sensitive magnetic field sensor. In particular, since the axes of the NV centers are distributed along four directions, a collection of measurement data from NV centers with different axes provides information on the vector components of a magnetic field. However, in the conventional approach, the low measurement contrast of NV centers limits the sensitivity of vector magnetic field sensing. Recently, to overcome this problem, multi-frequency control of the NV centers has been proposed. The key idea…
We propose a scheme for covert active sensing using floodlight illumination from a THz-bandwidth amplified spontaneous emission (ASE) source and heterodyne detection. We evaluate the quantum-estimation-theoretic performance limit of covert sensing, wherein a transmitter's attempt to sense a target phase is kept undetectable to a quantum-equipped passive adversary, by hiding the signal photons under the thermal noise floor. Despite the quantum state of each mode of the ASE source being mixed (thermal), and hence inferior compared to the pure coherent state of a laser mode, the thousand-times hi…
Optomechanically controlled response amplification for enhanced quantum sensing
Joint Laboratory of Optics of Palacký University and Institute of Physics ASCR, Faculty of Science, Palacký University（帕拉茨基大学与捷克科学院物理研究所联合光学实验室，帕拉茨基大学理学院）
High-fidelity, efficient quantum nondemolition readout of quantum bits is integral to the goal of quantum computation. As superconducting circuits approach the requirements of scalable, universal fault tolerance, qubit readout must also meet the demand of simplicity to scale with growing system size. Here we propose a fast, high-fidelity, scalable measurement scheme based on the state-selective ring-up of a cavity followed by photodetection with the recently introduced Josephson photomultiplier (JPM), a current-biased Josephson junction. This scheme maps qubit state information to the binary d…
Superconducting circuits offer a scalable platform for the construction of large-scale quantum networks where information can be encoded in multiple temporal modes of propagating microwaves. Characterization of such microwave signals with a method extendable to an arbitrary number of temporal modes with a single detector and demonstration of their phase-robust nature are of great interest. Here we show the on-demand generation and Wigner tomography of a microwave time-bin qubit with superconducting circuit quantum electrodynamics architecture. We perform the tomography with a single heterodyne…
Individual nitrogen vacancy (NV) color centers in diamond are versatile, spin-based quantum sensors. Coherently controlling the spin of NV centers using microwaves in a typical frequency range between 2.5 and 3.5 GHz is necessary for sensing applications. In this work, we present a stripline-based, planar, Ω-shaped microwave antenna that enables to reliably manipulate NV spins. We find an optimal antenna design using finite integral simulations. We fabricate our antennas on low-cost, transparent glass substrate. We demonstrate highly uniform microwave fields in areas of roughly 400 x 400 μm^2 …
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…
Experiments with superconducting circuits require careful calibration of the applied pulses and fields over a large frequency range. This remains an ongoing challenge as commercial semiconductor electronics are not able to probe signals arriving at the chip due to its cryogenic environment. Here, we demonstrate how the on-chip amplitude and frequency of a microwave signal can be inferred from the ac Stark shifts of higher transmon levels. In our time-resolved measurements we employ Ramsey fringes, allowing us to detect the amplitude of the systems transfer function over a range of several hund…
The polarisation dynamics of nuclear spins weakly coupled to an NV center is highly sensitive to the parameters of the microwave control and the nuclear Larmor frequency. What is commonly regarded as a challenge, we propose here as a resource for quantum sensing. By varying a single experimental parameter in a suitable set-up, i.e., the Rabi frequency of a continual microwave driving or the nuclear Larmor frequency, we predict periodic reversals of the steady-state polarisation of the nuclear spin. Crucially, interference between the transverse and longitudinal dipolar interaction of electron …
While detection of optical photons is today achieved with very high efficiencies, the detection of microwave fields at the photon level still poses non-trivial experimental challenges. In this Letter we propose a model of microwave photodetector which is based on the use of an electro-opto-mechanical system. Using state of the art technology, we show how single microwave photons can efficiently be converted into optical photons which are then measured by standard optics. The overall quantum efficiency of our microwave detector tends to one for achievable values of the optical and microwave coo…
Low-loss fiber optic links have the potential to connect superconducting quantum processors together over long distances to form large scale quantum networks. A key component of these future networks is a quantum transducer that coherently and bidirectionally converts photons from microwave frequencies to optical frequencies. We present a platform for electro-optic photon conversion based on silicon-organic hybrid photonics. Our device combines high quality factor microwave and optical resonators with an electro-optic polymer cladding to perform microwave-to-optical photon conversion from 6.7 …
An inertial sensor design is proposed in this paper to achieve high sensitivity and large dynamic range in the sub-Hz frequency regime. High acceleration sensitivity is obtained by combining optical cavity readout systems with monolithically fabricated mechanical resonators. A high-sensitivity heterodyne interferometer simultaneously monitors the test mass with an extensive dynamic range for low-stiffness resonators. The bandwidth is tuned by optical feedback cooling to the test mass via radiation pressure interaction using an intensity-modulated laser. The transfer gain of the feedback system…
The recently discovered spin defects in hexagonal boron nitride (hBN), a layered van der Waals material, have great potential in quantum sensing. However, the photoluminescence and the contrast of the optically detected magnetic resonance (ODMR) of hBN spin defects are relatively low so far, which limits their sensitivity. Here we report a record-high ODMR contrast of 46$\%$ at room temperature, and simultaneous enhancement of the photoluminescence of hBN spin defects by up to 17-fold by the surface plasmon of a gold-film microwave waveguide. Our results are obtained with shallow boron vacancy…
Quantum sensing of low-frequency magnetic fields using nitrogen-vacancy (NV) center ensembles has been demonstrated in multiple experiments with sensitivities as low as $\sim$1 pT/$\sqrt{\text{Hz}}$. To date, however, demonstrations of high-frequency magnetometry in the GHz regime with NV diamond are orders of magnitude less sensitive, above the nT/$\sqrt{\text{Hz}}$ level. Here we adapt for microwave frequencies techniques that have enabled high-performance, low-frequency quantum sensors. Using a custom-grown NV-enriched diamond combined with a noise cancellation scheme designed for high-freq…
We investigate the use of a split-ring resonator (SRR) incorporated with an atomic-vapor cell to improve the sensitivity and the minimal detectable electric (E) field of Rydberg atom-based sensors. In this approach, a sub-wavelength SRR is placed around an atomic vapor-cell filled with cesium atoms for E-field measurements at 1.3~GHz. The SRR provides a factor of 100 in the enhancement of the E-field measurement sensitivity. Using electromagnetically induced transparency (EIT) with Aulter-Townes splitting, E-field measurements down to 5~mV/m are demonstrated with the SRR, while in the absence …
