The quality of a quantum operation determines the performance of quantum information processing, such as the sensitivity of quantum sensing. Different from the fidelity of quantum operation in quantum computation, we present an effective function to evaluate the performance and diagnose the imperfection of operations in multi-pulse based quantum sensing. The evaluation function directly links the realistic sensitivity with intrinsic sensitivity in a simple way. Moreover, guided by this evaluation function, we optimize a composite pulse sequence for high sensitivity nitrogen-vacancycenter based magnetometry against spectrum inhomogeneities and control errors to improve the signal-to-noise ratio of nanoscale nuclear magnetic resonance by 1 order of magnitude. It marks an important step towards quantitative quantum sensing with imperfect quantum control in practical applications.
We develop theoretically and demonstrate experimentally a universal dynamical decoupling method for robust quantum sensing with unambiguous signal identification. Our method uses randomisation of control pulses to suppress simultaneously two types of errors in the measured spectra that would otherwise lead to false signal identification. These are spurious responses due to finite-width $π$ pulses, as well as signal distortion caused by $π$ pulse imperfections. For the cases of nanoscale nuclear spin sensing and AC magnetometry, we benchmark the performance of the protocol with a single nitroge…
Dynamical decoupling sequences with multiple pulses can be considered to exhibit filter functions for the time evolution of a qubit superposition state. They contribute to the improvement of coherence time and qubit-phase accumulation due to a time-varying field and can thus achieve high-frequency-resolution spectroscopy. Such behaviors find useful application in highly sensitive detection based on qubits for various external fields such as a magnetic field. Hence, decoupling sequences are indispensable tools for quantum sensing. In this study, we experimentally and theoretically investigated …
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. The latter 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 non-adiabatic couplings. O…
Different hypotheses about a quantum system such as the logical state of a qubit or the value of physical interaction parameters can be investigated by the interaction with a probe field. Such fields may be prepared in particularly sensitive quantum states, and we can use quantum trajectories to model the stochastic measurement record and conditional evolution of the state of the quantum system subject to its interaction with a travelling pulse of radiation. Our analysis applies to different measurement strategies and to arbitrary input quantum states of the probe field pulse and it thus permi…
We present a method to identify spurious signals generated by finite-width pulses in quantum sensing experiments and apply it to recently proposed dynamical decoupling sequences for accurate spectral interpretation. We first study the origin of these fake resonances and quantify their behavior in a situation that involves the measurement of a classical magnetic field. Here we show that a change of the initial phase of the sensor or, equivalently, of the decoupling pulses leads to oscillations in the spurious signal intensity while the real resonances remain intact. Finally we extend our result…
We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen vacancy center in diamond and up to 10,000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6 ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2 ns hardware sampling. We apply the method for the detection of external AC magnetic fields and nuclear magnetic resonance signals of carbon-13 spins with h…
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 experimentally demonstrate single-spin magnetometry with multi-pulse sensing sequences. The use of multi-pulse sequences can greatly increase the sensing time per measurement shot, resulting in enhanced ac magnetic field sensitivity. We theoretically derive and experimentally verify the optimal number of sensing cycles, for which the effects of decoherence and increased sensing time are balanced. We perform these experiments for oscillating magnetic fields with fixed phase as well as for fields with random phase. Finally, by varying the phase and frequency of the ac magnetic field, we measu…
The nitrogen vacancy (NV) color center in diamond is an enormously important platform for the development of quantum sensors, including for single spin and single molecule NMR. Detection of weak single-spin signals is greatly enhanced by repeated sequences of microwave pulses; in these dynamical decoupling (DD) techniques, the key control parameters swept in the experiment are the time intervals, $τ$, between pulses. Here we show that, in fact, the pulse duration offers a powerful additional control parameter. While previously, a non-negligible pulse-width has been considered simply a source o…
A method for measuring small energy level shifts in a qubit by coherent amplification of their effect is proposed. It is based on the repeated application of the same interaction pulse in two manners: with the same phase of each subsequent pulse, and with an alternating phase shift of $π$ (i.e. a minus sign) from pulse to pulse. Two specific types of pulses are considered: a resonant $π$ pulse and an adiabatic chirped pulse, both of which produce complete population inversion with high fidelity. In the presence of a weak ambient external electric or magnetic field, the ensuing Stark or Zeeman …
Quantum sensors, qubits sensitive to external fields, have become powerful detectors for various small acoustic and electromagnetic fields. A major key to their success have been dynamical decoupling protocols which enhance sensitivity to weak oscillating (AC) signals. Currently, those methods are limited to signal frequencies below a few MHz. Here we harness a quantum-optical effect, the Mollow triplet splitting of a strongly driven two-level system, to overcome this limitation. We microscopically understand this effect as a pulsed dynamical decoupling protocol and find that it enables sensit…
Quantum coherent control of a quantum system with high-fidelity is rather important in quantum computation and quantum information processing. There are many control techniques to reach these targets, such as resonant excitation, adiabatic passages, shortcuts to adiabaticity, and so on. However, for a single pulse to realize population transfer, the external tiny error has a trivial influence on the final population. The repeated application of the same pulse will greatly amplify the error effect, making it easy to be detected. Here, we propose to measure small control errors in three-level qu…
Nitrogen vacancy (NV) centers in diamond are promising systems for realizing sensitive temperature sensors. Pulsed optically detected magnetic resonance (Pulsed-ODMR) is one of the ways to measure the temperature using NV centers. However, Pulsed-ODMR requires careful calibration and strict time synchronization to control the microwave pulse, which complicates its applicability. Nonetheless, the continuous-wave optically detected magnetic resonance (CW- ODMR) in NV centers is another more advantageous way to measure temperature with NV centers, owing to its simple implementation by applying a …
While quantum devices rely on interactions between constituent subsystems and with their environment to operate, native interactions alone often fail to deliver targeted performance. Coherent pulsed control provides the ability to tailor effective interactions, known as Hamiltonian engineering. We propose a Hamiltonian engineering method that maximizes desired interactions while mitigating deleterious ones by conducting a pulse sequence search using constrained optimization. The optimization formulation incorporates pulse sequence length and cardinality penalties consistent with linear or inte…
Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the relative phase is accumulated quadratically with time, and show that this can be produced by a variety of simple pulse sequences. Interestingly, this scaling has a limited duration, and we show that certain pulse sequences prolong the effect. The performance of these schemes is analyzed and we examine their relevance to state-of-the-art experiments. We analy…
The sensitivity of a practical quantum magnetometer is challenged by both inhomogeneous coupling between sensors and environment and errors in quantum control. Based on the physical criteria of modern quantum sensing, we present a robust and effective composite-pulse for high fidelity operation against inhomogeneous broadening of sensor and control errors via optimized modulation of control field. Such a technique is verified on nitrogen-vacancy (NV) center in diamond to keep almost perfect operation up to a detuning as larger as $110\%$. The sensitivity of the magnetometer with NV center ense…
Being the key resource in quantum physics, the proper quantification of coherence is of utmost importance. Amid complex-looking functionals in quantifying coherence, we set forth a simple and easy-to-evaluate approach: Principal diagonal difference of coherence (C_PDD), which we prove to be non-negative, self-normalized, and monotonic (under any incoherent operation). To validate this theory, we thought of a fictitious two-qubit system (both interacting and non-interacting) and, through the laser pulse-system interaction (semi-classical approach), compare the coherence evolution of C_PDD with …
Defects in solid state materials provide an ideal, robust platform for quantum sensing. To deliver maximum sensitivity, a large ensemble of non-interacting defects hosting coherent quantum states are required. Control of such an ensemble is challenging due to the spatial variation in both the defect energy levels and in any control field across a macroscopic sample. In this work we experimentally demonstrate that we can overcome these challenges using Floquet theory and optimal control optimization methods to efficiently and coherently control a large defect ensemble, suitable for sensing. We …
Magnetometry utilizing a spin qubit in a solid state possesses high sensitivity. In particular, a magnetic sensor with a high spatial resolution can be achieved with the electron-spin states of a nitrogen vacancy (NV) center in diamond. In this study, we demonstrated that NV quantum sensing based on multiple-pulse decoupling sequences can sensitively measure not only the amplitude but also the phase shift of an alternating-current (AC) magnetic field. In the AC magnetometry based on decoupling sequences, the maximum phase accumulation of the NV spin due to an AC field can be generally obtained…
Having accurate gate generation is essential for precise control of a quantum system. The generated gate usually suffers from linear and nonlinear distortion. Previous works have demonstrated how to use a qubit to correct linear frequency distortions but have not commented on how to handle nonlinear distortions. This is an important issue as we show that nonlinear amplitude distortions from the RF electronics can affect Rabi pulses by as much as 10%. We present work that demonstrates how a transmon qubit can be used as a highly sensitive cryogenic detector to characterize these nonlinear ampli…
Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demo…
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 kilohert…
A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree o…
Quantum sensing is one of the key areas which exemplifies the superiority of quantum technologies. Nonetheless, most quantum sensing protocols operate efficiently only when the unknown parameters vary within a very narrow region, i.e., local sensing. Here, we provide a systematic formulation for quantifying the precision of a probe for multi-parameter global sensing when there is no prior information about the parameters. In many-body probes, in which extra tunable parameters exist, our protocol can tune the performance for harnessing the quantum criticality over arbitrarily large sensing inte…
We show that light-pulse atom interferometry with atomic point sources and spatially resolved detection enables multi-axis (two rotation, one acceleration) precision inertial sensing at long interrogation times. Using this method, we demonstrate a light-pulse atom interferometer for Rb-87 with 1.4 cm peak wavepacket separation and a duration of 2T = 2.3 seconds. The inferred acceleration sensitivity of each shot is 6.7 * 10^(-12) g, which improves on previous limits by more than two orders of magnitude. We also measure the Earth's rotation rate with a precision of 200 nrad/s.
We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences [Physical Review Letters 122, 200403 (2019)] can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to $π$ pulse imperfections and spurious responses due to finite-width $π$ pulses. This enhances selectivity of quantum sensors such as those based on NV centers in diamond.
Nitrogen vacancy (NV) centers in diamonds is a promising system for quantum information processing and quantum sensing, and the control of the quantum state is essential for practical applications. In this study, we demonstrate a control of all the three transitions among the ground state sublevels of NV centers by applying external magnetic driving fields. To address the states of a specific NV axis among the four axes, we apply a magnetic field orthogonal to the NV axis. We control two transitions by microwave pulses and the remaining transition by radio frequency pulses. In particular, we i…
A point source atom interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. Unlike a conventional light pulse atom interferometer, the PSI can produce a signal that corresponds to multi-axis rotation only, independent of acceleration. In addition, it can be used to measure acceleration along one direction, independent of rotation. Here, we describe a modified PSI that can be used to measure multi-axis rotation and multi-axis acceleration. Specifi…
We present a protocol for directly detecting time-dependent magnetic field waveforms with a quantum two-level system. Our method is based on a differential refocusing of segments of the waveform using spin echoes. The sequence can be repeated to increase the sensitivity to small signals. The frequency bandwidth is intrinsically limited by the duration of the refocusing pulses. We demonstrate detection of arbitrary waveforms with $\sim 20 {\rm ns}$ time resolution and $\sim 4μ{\rm T}/\sqrt{\rm Hz}$ field sensitivity using the electronic spin of a single nitrogen-vacancy center in diamond.
Sensing the internal dynamics of individual nuclear spins or clusters of nuclear spins has recently become possible by observing the coherence decay of a nearby electronic spin: the weak magnetic noise is amplified by a periodic, multi-pulse decoupling sequence. However, it remains challenging to robustly infer underlying atomic-scale structure from decoherence traces in all but the simplest cases. We introduce Floquet spectroscopy as a versatile paradigm for analysis of these experiments, and argue it offers a number of general advantages. In particular, this technique generalises to more com…
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…
We report on a nanoscale quantum-sensing protocol which tracks a free precession of a single nuclear spin and is capable of estimating an azimuthal angle---a parameter which standard multipulse protocols cannot determine---of the target nucleus. Our protocol combines pulsed dynamic nuclear polarization, a phase-controlled radiofrequency pulse, and a multipulse AC sensing sequence with a modified readout pulse. Using a single nitrogen-vacancy center as a solid-state quantum sensor, we experimentally demonstrate this protocol on a single 13C nuclear spin in diamond and uniquely determine the lat…
Building upon the demonstration of coherent control and single-shot readout of the electron and nuclear spins of individual 31-P atoms in silicon, we present here a systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group. We apply this analysis to the electron and the ionized 31-P nucleus of a single P donor in isotopically purified 28-Si. We find average gate fidelities of 99.95 % for the electron, and 99.99 % for the nuclear spin. These values are above certain error correction thresholds, and demonstrate the potential …
Spin Hamiltonian engineering in solid-state systems plays a key role in a variety of applications ranging from quantum information processing and quantum simulations to novel studies of many-body physics. By analyzing the irreducible form of a general two-body spin-1/2 Hamiltonian, we identify all interchangeable interaction terms using rotation pulses. Based on this identification, we derive novel pulse sequences, defined by an icosahedral symmetry group, providing the most general achievable manipulation of interaction terms. We demonstrate that, compared to conventional Clifford rotations, …
Radical-pair reactions pertinent to biological magnetic field sensing are an ideal system for demonstrating the paradigm of quantum biology, the exploration of quantum coherene effects in complex biological systems. We here provide yet another fundamental connection between this biochemical spin system and quantum information science. We introduce and explore a formal measure quantifying singlet-triplet coherence of radical-pairs using the concept of quantum relative entropy. The ability to quantify singlet-triplet coherence opens up a number of possibilities in the study of magnetic sensing w…
