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arXiv:2209.10466 · Journal of Magnetic Resonance

Low frequency signal detection via correlated Ramsey measurements

Santiago Oviedo-Casado, Javier Prior, Javier Cerrillo

Published May 7, 2024• 4 citations
arXivHTMLPDF

Abstract

The low frequency region of the spectrum is a challenging regime for quantum probes. We support the idea that, in this regime, performing Ramsey measurements carefully controlling the time at which each measurement is initiated is an excellent signal detection strategy. We use the Fisher information to demonstrate a high quality performance in the low frequency regime, compared to more elaborated measurement sequences, and to optimize the correlated Ramsey sequence according to any given experimental parameters, showing that correlated Ramsey rivals with state-of-the-art protocols, and can even outperform commonly employed sequences such as dynamical decoupling in the detection of low frequency signals. Contrary to typical quantum detection protocols for oscillating signals, which require adjusting the time separation between pulses to match the half period of the target signal, and consequently see their scope limited to signals whose period is shorter than the characteristic decoherence time of the probe, or to those protocols whose target is primarily static signals, the time-tagged correlated Ramsey sequence simultaneously tracks the amplitude and the phase information of the target signal, regardless of its frequency, which crucially permits correlating measurements in post-processing, leading to efficient spectral reconstruction.

DOI
10.1016/j.jmr.2024.107691

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The low frequency region of the spectrum is a challenging regime for quantum probes. We support the idea that, in this regime, performing Ramsey measurements carefully controlling the time at which each measurement is initiated is an excellent signal detection strategy. We use the Fisher information to demonstrate a high quality performance in the low frequency regime, compared to more elaborated measurement sequences, and to optimize the correlated Ramsey sequence according to any given experimental parameters, showing that correlated Ramsey rivals with state-of-the-art protocols, and can even outperform commonly employed sequences such as dynamical decoupling in the detection of low frequency signals. Contrary to typical quantum detection protocols for oscillating signals, which require adjusting the time separation between pulses to match the half period of the target signal, and consequently see their scope limited to signals whose period is shorter than the characteristic decoherence time of the probe, or to those protocols whose target is primarily static signals, the time-tagged correlated Ramsey sequence simultaneously tracks the amplitude and the phase information of the target signal, regardless of its frequency, which crucially permits correlating measurements in post-processing, leading to efficient spectral reconstruction.
Magnetic spectroscopy at the nanoscale provides unique insights into material properties and dynamics, with quantum sensors like nitrogen-vacancy (NV) centers being ideally suited for these scales. However, detecting low-frequency signals remains a challenge due to finite coherence times (T2∗T_2^*T2∗​), as signals oscillating slower than 1/T2∗1/T_2^*1/T2∗​ decay before sufficient phase accumulation occurs. We present RESOLUTE (Ramsey corrElation SpectroscOpy puLse seqUence wiTh phasE cycling), a protocol that overcomes these limitations by combining Ramsey measurements with correlation spectroscopy. By storing accumulated phase as a population imbalance during a correlation period (Tcorr<T1T_\mathrm{corr} < T_1Tcorr​<T1​) between two sensing periods, RESOLUTE generates an effective coherence time T2p>T2∗T_2^p > T_2^*T2p​>T2∗​. This shifts the frequency-matching condition to the correlation time, enabling detection in the previously inaccessible spectral region between 1/T11/T_11/T1​ and 1/T2p1/T_2^p1/T2p​. We experimentally demonstrate an extension of the effective coherence time from T2∗=0.38 μsT_2^* = 0.38\,μsT2∗​=0.38μs to T2p=5.1 μsT_2^p = 5.1\,μsT2p​=5.1μs, surpassing Hahn Echo measurements. The technique successfully detects 13^{13}13C nuclear spin Larmor precession at fields as low as 49 \,G ($\sim505050\,$kHz). We further provide theoretical insight using Fisher information to characterize RESOLUTE's frequency estimation capabilities compared to existing protocols. Finally, by integrating adiabatic pulses and phase cycling, we demonstrate robust spin control and effective DC signal extraction. These advancements provide enhanced sensitivity to weak dipolar interactions, essential for single-molecule imaging and quantum sensing applications.
Achieving high-frequency spectral resolution with quantum sensors, while crucial in fields ranging from physical to biological sciences, is challenging due to their finite coherence time. Here, we introduce a novel protocol that achieves this goal by measuring phase correlations of AC magnetic fields using ensembles of NV centers. Our method extends the sensing dynamic range to frequencies higher than the system's Rabi frequency while achieving arbitrary frequency resolution, limited only by the target field coherence time. Moreover, our approach operates more robustly with respect to the magnetic field's amplitude. Thanks to this robustness, our protocol allows the application of more πππ-pulses in pulse sequences such as CPMG, enabling the decoupling of a broader range of frequency noise. The higher harmonics generated in this process continue to act as a part of the signal, ultimately improving the frequency resolution. This method paves the way for achieving arbitrary frequency resolution with improved performances, making it highly versatile for quantum sensing applications across diverse scientific fields.
High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.
Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for noise spectroscopy are time-consuming, because they require measurements of the noise spectral density at many different frequencies. Here we describe an alternative approach to noise spectroscopy, which requires fewer resources, and relies on direct measurement of arbitrary linear functionals of the noise spectral density. This method uses random pulse sequences with carefully controlled correlations, which are chosen using algorithms for phase retrieval. These measurements allow us to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum, compared to conventional dynamical decoupling approaches.
The dynamics of quantum systems are unavoidably influenced by their environment, but in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.
Time-resolution protocol of quantum sensing aims to measure the fast temporal variation of an external field and demands a high field sensitivity in a short interrogation time $\ensuremath{\tau}$. Since any operation that evolves the quantum state takes time and is counted as part of the interrogation, evaluating the performance of the time-resolution protocol requires a complete end-to-end description of the measurement process. In particular, the initial state has to be one of the quantum sensor's eigenstates in the absence of external fields, and the final projective measurements must be performed in the same eigenstate basis. Building upon prior works which proposed limits for time-resolved sensing using a quantum sensor, we apply optimal control theory to optimize the time-resolution protocol. Our analysis indicates that there exists a critical interrogation time T∗{T}^{*}T∗: When $\ensuremath{\tau}<{T}^{*}$ the optimal protocol is a purely bang-bang strategy; when $\ensuremath{\tau}>{T}^{*}$ the optimal protocol involves a singular control during the interrogation. In the short-$\ensuremath{\tau}$ regime, which is relevant to high time resolution, we propose a detune protocol that involves only smooth control during the entire interrogation. As the discontinuities of control pose the main obstacles to experimental realization, we expect the presented detune protocol to be practically useful. In the long-$\ensuremath{\tau}$ regime, the optimal protocol closely resembles the Ramsey sequence; protocols based on maximizing quantum Fisher information are constructed to highlight the difference between the theoretically optimal and practically implementable measurements. Effective use of the time-resolution protocol requires a setup where the unknown time-domain signal of interest can be identically and repeatedly generated. As a potentially relevant application, we outline the calibration of baseband flux pulse distortion in the control of superconducting qubits.