Article

Measuring Environmental Quantum Noise Exhibiting a Nonmonotonic Spectral Shape

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Abstract

Understanding the physical origin of noise affecting quantum systems is important for nearly every quantum application. Quantum-noise spectroscopy has been used in various quantum systems, such as superconducting qubits, nitrogen-vacancy centers, and trapped ions. Traditional spectroscopy methods are usually efficient in measuring noise spectra with mostly monotonically decaying contributions. However, there are important scenarios in which the noise spectrum is broadband and nonmonotonous, thus posing a challenge to existing noise-spectroscopy schemes. Here we compare several methods for noise spectroscopy: spectral decomposition based on the Carr-Purcell-Meiboom-Gill sequence, the recently presented dynamic sensitivity control (DYSCO) sequence, and a modified DYSCO sequence with a Gaussian envelope (gDYSCO). The performance of the sequences is quantified by analytic and numeric determination of the frequency resolution, bandwidth, and sensitivity, revealing a supremacy of gDYSCO to reconstruct nontrivial features. Using an ensemble of nitrogen-vacancy centers in diamond coupled to a high-density C13-nuclear-spin environment, we experimentally confirm our findings. The combination of the schemes presented offers potential to record high-quality noise spectra as a prerequisite to generate quantum systems unlimited by their spin-bath environment.

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... Noise spectroscopy elucidates the fundamental noise sources in spin systems, which is essential to develop spin qubits with long coherence times for quantum information processing [1], communication [2], and sensing [3]. But noise spectroscopy typically relies on microwave spin control to extract the noise spectrum [4][5][6][7][8][9], which becomes infeasible when high-frequency noise components are stronger than the available microwave power. Here, we demonstrate an alternative all-optical approach to perform noise spectroscopy. ...
... Noise spectroscopy using microwave control sequences has shed light on the fundamental noise processes of various spin systems, such as superconducting qubits [4,5], nitrogen-vacancy centres in diamond [6,7], and gate-defined quantum dots [8,9]. In these systems, pulse sequences are used to control the spin dynamics on timescales faster than the environmental noise. ...
... Our simulations (shown in Fig. 2f and Fig. 2g for B = 1.2 T and B = 2 T, respectively) considering two spectral components of the Overhauser field [13,14] agree with the experimental behaviour. However, to understand the impact of adding π-pulses to the CPMG sequence on the spin dynamics requires a comparison between the rate of application of these pulses with the frequencies of the noise spectra [4,[6][7][8][9][31][32][33]. We can experimentally ex- tract these noise frequencies by the numerical analysis of the measured coherence functions. ...
Preprint
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Noise spectroscopy elucidates the fundamental noise sources in spin systems, which is essential to develop spin qubits with long coherence times for quantum information processing, communication, and sensing. But noise spectroscopy typically relies on microwave spin control to extract the noise spectrum, which becomes infeasible when high-frequency noise components are stronger than the available microwave power. Here, we demonstrate an alternative all-optical approach to perform noise spectroscopy. Our approach utilises coherent control using Raman rotations with controlled timings and phases to implement Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences. Analysing the spin dynamics under these sequences extracts the noise spectrum of a dense ensemble of nuclear spins interacting with a quantum dot, which has thus far only been modelled theoretically. While providing large spectral bandwidths of over 100 MHz, our Raman-based approach could serve as an important tool to study spin dynamics and decoherence mechanisms in a broad range of solid-state spin qubits.
... There exist more intricate strategies, for example, discrete prolate spheroidal sequences (DPSSs) [49] have a filter function that is devoid of additional lobes and higher harmonics resulting in suppression of spectral leakage, while a Gaussian enveloped dynamic sensitivity control sequence (gDYSCO) [50] allows generation of a filter function with minimal spectral leakage at the expense of reduced sensitivity and broader main peak. Though more effective than the basic CPMG approach, these sequences can be challenging to implement in practice and require repeated measurements [49,50], while in contrast our neural-network-based approach is shown to accurately extract underlying noise spectra using only a single measurement of a Hahn-echo decay curve. ...
... There exist more intricate strategies, for example, discrete prolate spheroidal sequences (DPSSs) [49] have a filter function that is devoid of additional lobes and higher harmonics resulting in suppression of spectral leakage, while a Gaussian enveloped dynamic sensitivity control sequence (gDYSCO) [50] allows generation of a filter function with minimal spectral leakage at the expense of reduced sensitivity and broader main peak. Though more effective than the basic CPMG approach, these sequences can be challenging to implement in practice and require repeated measurements [49,50], while in contrast our neural-network-based approach is shown to accurately extract underlying noise spectra using only a single measurement of a Hahn-echo decay curve. Nevertheless, in principle, elements of both techniques could be combined in the pursuit of even better noise-spectrum extraction, while minimizing the increase in experimental complexity. ...
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... There exist more intricate strategies, for example, discrete prolate spheroidal sequences (DPSSs) [50] have a filter function that is devoid of additional lobes and higher harmonics resulting in suppression of spectral leakage, while a Gaussian enveloped dynamic sensitivity control sequence (gDYSCO) [51] allows generation of a filter function with minimal spectral leakage at the expense of reduced sensitivity and broader main peak. Though more effective than the basic CPMG approach, these sequences can be challenging to implement in practice and require repeated measurements [50,51], while in contrast our neural network-based approach has been shown to accurately extract underlying noise spectra using only a single measurement of a Hahn echo decay curve. ...
... There exist more intricate strategies, for example, discrete prolate spheroidal sequences (DPSSs) [50] have a filter function that is devoid of additional lobes and higher harmonics resulting in suppression of spectral leakage, while a Gaussian enveloped dynamic sensitivity control sequence (gDYSCO) [51] allows generation of a filter function with minimal spectral leakage at the expense of reduced sensitivity and broader main peak. Though more effective than the basic CPMG approach, these sequences can be challenging to implement in practice and require repeated measurements [50,51], while in contrast our neural network-based approach has been shown to accurately extract underlying noise spectra using only a single measurement of a Hahn echo decay curve. Nevertheless, in principle, elements of both techniques could be combined in the pursuit of even better noise spectrum extraction, while minimising the increase in experimental complexity. ...
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Full-text available
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... Although the idea is rather simple and appealing, using such a spectrometer to obtain quantitative data on the spatiotemporal spectrum of the noise field requires more caution than when a single qubit is used to reconstruct the spectrum of temporal fluctuations of the local noise affecting it (note that the latter task, while routinely performed in recent years, is not entirely trivial either, especially in case of temporal spectra having peaks at finite frequencies [63,65]). Large part of the paper has been devoted to detailed explanation of methods allowing for reliable extraction of 'spectroscopic' information (spectroscopic formulas defined in section 4.1) from raw measured data. ...
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Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. To evaluate the dephasing time for transverse 1/f noise second-order contributions have to be taken into account. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.
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Enhancing quantum sensing The quantum properties of the nitrogen vacancy (NV) defect in diamond can be used as an atomic compass needle that is sensitive to tiny variations in magnetic field. Schmitt et al. and Boss et al. successfully enhanced this sensitivity by several orders of magnitude (see the Perspective by Jordan). They applied a sequence of pulses to the NV center, the timing of which was set by and compared with a highly stable oscillator. This allowed them to measure the frequency of an oscillating magnetic field (megahertz bandwidth) with submillihertz resolution. Such enhanced precision measurement could be applied, for example, to improve nuclear magnetic resonance-based imaging protocols of single molecules. Science , this issue p. 832 , p. 837 ; see also p. 802
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Enhancing quantum sensing The quantum properties of the nitrogen vacancy (NV) defect in diamond can be used as an atomic compass needle that is sensitive to tiny variations in magnetic field. Schmitt et al. and Boss et al. successfully enhanced this sensitivity by several orders of magnitude (see the Perspective by Jordan). They applied a sequence of pulses to the NV center, the timing of which was set by and compared with a highly stable oscillator. This allowed them to measure the frequency of an oscillating magnetic field (megahertz bandwidth) with submillihertz resolution. Such enhanced precision measurement could be applied, for example, to improve nuclear magnetic resonance-based imaging protocols of single molecules. Science , this issue p. 832 , p. 837 ; see also p. 802
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We demonstrate significant improvements of the spin coherence time of a dense ensemble of nitrogen-vacancy (NV) centers in diamond through optimized dynamical decoupling (DD). Cooling the sample down to 77 K suppresses longitudinal spin relaxation T1T_1 effects and DD microwave pulses are used to increase the transverse coherence time T2T_2 from 0.7\sim 0.7 ms up to 30\sim 30 ms. We extend previous work of single-axis (CPMG) DD towards the preservation of arbitrary spin states. Following a theoretical and experimental characterization of pulse and detuning errors, we compare the performance of various DD protocols. We identify that the optimal control scheme for preserving an arbitrary spin state is a recursive protocol, the concatenated version of the XY8 pulse sequence. The improved spin coherence might have an immediate impact on improvements of the sensitivities of AC magnetometry. Moreover, the protocol can be used on denser diamond samples to increase coherence times up to NV-NV interaction time scales, a major step towards the creation of quantum collective NV spin states.
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The interaction between solid-state qubits and their environmental degrees of freedom produces non-unitary effects like decoherence and dissipation. Uncontrolled decoherence is one of the main obstacles that must be overcome in quantum information processing. We study the dynamically decay of coherences in a solid-state qubit by means of the use of a master equation. We analyse the effects induced by thermal Ohmic environments and low-frequency 1/f noise. We focus on the effect of longitudinal and transversal noise on the superconducting qubit's dynamics. Our results can be used to design experimental future setups when manipulating superconducting qubits.
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In spin resonance experiments random flipping by T1 or T2 processes of nearby, nonresonant spins introduces fluctuations into the precessional frequency of the observed spins. These fluctuations may be described by means of a stochastic model, and for wide classes of both Markoffian and non-Markoffian distributions we make predictions for the line shape, for the free induction decay, and for various spin-echo signals. If the homogeneous broadening of the line is due to a dipolar interaction term, then we find that the conditional distribution for the precessional frequency has the shape of a Lorentzian with a cutoff on the wings, rather than a Gaussian shape as commonly assumed. The causes and consequences of Lorentzian diffusion are analyzed in detail for samples in which T1 processes control the source of local frequency fluctuations and for samples in which T2 processes dominate. Recent two- and three-pulse spin-echo experiments of Mims et al. dramatically confirm the predictions of Lorentzian diffusion for electron paramagnetic resonances in samples with temperature-dependent diffusion, as well as with temperature-independent diffusion. "Instantaneous" diffusion caused by the action of the applied pulses is predicted by our model and explains features of Mims' data. The generality of our principal results still permits the outcome of various resonance experiments to be predicted, even when a simple dipolar interaction is no longer an adequate model.
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The nitrogen-vacancy (NV) colour centre in diamond is an important physical system for emergent quantum technologies, including quantum metrology, information processing and communications, as well as for various nanotechnologies, such as biological and sub-diffraction limit imaging, and for tests of entanglement in quantum mechanics. Given this array of existing and potential applications and the almost 50 years of NV research, one would expect that the physics of the centre is well understood, however, the study of the NV centre has proved challenging, with many early assertions now believed false and many remaining issues yet to be resolved. This review represents the first time that the key empirical and ab initio results have been extracted from the extensive NV literature and assembled into one consistent picture of the current understanding of the centre. As a result, the key unresolved issues concerning the NV centre are identified and the possible avenues for their resolution are examined.
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Application of nuclear magnetic resonance (NMR) spectroscopy to nanoscale samples has remained an elusive goal, achieved only with great experimental effort at subkelvin temperatures. We demonstrated detection of NMR signals from a (5-nanometer)3 voxel of various fluid and solid organic samples under ambient conditions. We used an atomic-size magnetic field sensor, a single nitrogen-vacancy defect center, embedded ~7 nanometers under the surface of a bulk diamond to record NMR spectra of various samples placed on the diamond surface. Its detection volume consisted of only 104 nuclear spins with a net magnetization of only 102 statistically polarized spins.
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Extension of nuclear magnetic resonance (NMR) to nanoscale samples has been a longstanding challenge because of the insensitivity of conventional detection methods. We demonstrated the use of an individual, near-surface nitrogen-vacancy (NV) center in diamond as a sensor to detect proton NMR in an organic sample located external to the diamond. Using a combination of electron spin echoes and proton spin manipulation, we showed that the NV center senses the nanotesla field fluctuations from the protons, enabling both time-domain and spectroscopic NMR measurements on the nanometer scale.
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Multi-qubit systems are crucial for the advancement and application of quantum science. Such systems require maintaining long coherence times while increasing the number of qubits available for coherent manipulation. For solid-state spin systems, qubit coherence is closely related to fundamental questions of many-body spin dynamics. Here we apply a coherent spectroscopic technique to characterize the dynamics of the composite solid-state spin environment of nitrogen-vacancy colour centres in room temperature diamond. We identify a possible new mechanism in diamond for suppression of electronic spin-bath dynamics in the presence of a nuclear spin bath of sufficient concentration. This suppression enhances the efficacy of dynamical decoupling techniques, resulting in increased coherence times for multi-spin-qubit systems, thus paving the way for applications in quantum information, sensing and metrology.
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A spin echo method adapted to the measurement of long nuclear relaxation times (T 2 ) in liquids is described. The pulse sequence is identical to the one proposed by Carr and Purcell, but the rf of the successive pulses is coherent, and a phase shift of 90° is introduced in the first pulse. Very long T 2 values can be measured without appreciable effect of diffusion.
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Losses in superconducting planar resonators are presently assumed to predominantly arise from surface-oxide dissipation, due to experimental losses varying with choice of materials. We model and simulate the magnitude of the loss from interface surfaces in the resonator and investigate the dependence on power, resonator geometry, and dimensions. Surprisingly, the dominant surface loss is found to arise from the metal-substrate and substrate-air interfaces. This result will be useful in guiding device optimization, even with conventional materials.
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We experimentally demonstrate over 2 orders of magnitude increase in the room-temperature coherence time of nitrogen-vacancy centers in diamond by implementing decoupling techniques. We show that equal pulse spacing decoupling performs just as well as nonperiodic Uhrig decoupling and also allows us to take advantage of revivals in the echo to explore the longest coherence times. At short times, we can extend the coherence of particular quantum states out from T2*=2.7  μs out to an effective T2>340  μs. For preserving arbitrary states we show the experimental importance of using pulse sequences that compensate the imperfections of individual pulses for all input states through judicious choice of the phase of the pulses. We use these compensated sequences to enhance the echo revivals and show a coherence time of over 1.6 ms in ultrapure natural abundance 13C diamond.
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Controlling the interaction of a single quantum system with its environment is a fundamental challenge in quantum science and technology. We strongly suppressed the coupling of a single spin in diamond with the surrounding spin bath by using double-axis dynamical decoupling. The coherence was preserved for arbitrary quantum states, as verified by quantum process tomography. The resulting coherence time enhancement followed a general scaling with the number of decoupling pulses. No limit was observed for the decoupling action up to 136 pulses, for which the coherence time was enhanced more than 25 times compared to that obtained with spin echo. These results uncover a new regime for experimental quantum science and allow us to overcome a major hurdle for implementing quantum information protocols.
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Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.
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We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz1/2^{1/2}. Comment: 29 pages, 4 figures
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We theoretically investigate the influence of designed pulse sequences in restoring quantum coherence lost due to background noise in superconducting qubits. We consider both 1/f noise and Random Telegraph Noise, and show that the qubit coherence time can be substantially enhanced by carefully engineered pulse sequences. Conversely, the time dependence of qubit coherence under external pulse sequences could be used as a spectroscopic tool for extracting the noise mechanisms in superconducting qubits, i.e. by using Uhrig's pulse sequence one can obtain information about moments of the spectral density of noise. We also study the effect of pulse sequences on the evolution of the qubit affected by a strongly coupled fluctuator, and show that the non-Gaussian features in decoherence are suppressed by the application of pulses.