Reconstruction-Free Quantum Sensing of Arbitrary Waveforms

Abstract

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 ∼ 20 ns time resolution and ∼ 4 µT/ √ Hz field sensitivity using the electronic spin of a single nitrogen-vacancy center in diamond.Well-controlled two-level quantum systems with long coherence times have proven useful for precision sensing [1,2] of various physical quantities including temperature [3], pressure [4], or electric [5] and magnetic fields [6, 7]. By devising suitable coherent control sequences, such as dynamical decoupling [8], quantum sensing has been extended to time-varying signals. In particular, coherent control schemes have allowed the recording of frequency spectra [9-11] and lock-in measurements of harmonic test signals [12].A more general task is the recording of arbitrary waveform signals, in analogy to the oscilloscope in electronic test and measurement. In this case, conventional dynamical decoupling sequences are no longer the method of choice as the sensor output is non-trivially connected to the input waveform signal, requiring alternative sensing approaches. For slowly varying signals, the transition frequency of the sensor can be tracked in real time [13], permitting detection of arbitrary waveforms in a single shot. By using a large ensemble of quantum sensors detection bandwidths of up to ∼ 1 MHz have been demonstrated [14,15], with applications in MRI tomograph stabilization [14], neural signaling [16,17], or magnetoencephalography [18].For rapidly changing signals the waveform can no longer be tracked, and a general waveform cannot be recorded in a single shot. However, if a waveform is repetitive or can be re-triggered, multiple passages of the waveform can be combined to reconstruct the full waveform signal. This method, known as equivalent-time sampling, is routinely implemented in digital oscilloscopes to capture signals at effective sampling rates that are much higher than the rate of analog-to-digital conversion. In quantum sensing, one possibility is to record a series of time-resolved spectra that cover the duration of the waveform [19]. This method, however, is limited to strong signals because the spectral resolution inversely scales with the time resolution. Other approaches include pulsed Ramsey detection [20], Walsh dynamical decoupling [21,22], and Haar wavelet sampling [23], discussed below. These methods use coherent control of the sensor to achieve competitive sensitivities, but require some form of waveform reconstruction.In this Letter we experimentally demonstrate a simple quantum sensing sequence for directly recording timedependent magnetic fields with no need for signal reconstruction. Our method uses a spin echo to differentially ...

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“…Over the past decade, many efforts have been deployed to both improve the sensing capabilities of the NV centres [49][50][51][52][53] and to develop techniques to explore new regimes [54][55][56][57]. These combined advances led to remarkable achievements such as revealing electric fields associated with surface band bending in diamond [58] and probing Johnson noise in metals [59].…”

Heisenberg-Limited Waveform Estimation with Solid-State Spins in Diamond

“…The basic idea is to use a multi-pass scheme [6] to coherently amplify the unknown detection signal, cancel unwanted coherent dynamical evolution and suppress quantum decoherence simultaneously. By combing with periodic dynamical decoupling (PDD) method, both dynamic range and sensitivity for waveform estimation are improved by one order of magnitude [25]. Finally, the scaling law of HQL for waveform estimation is achieved in the experiment with such a PDD-enhanced TDQD protocol, which significantly beats the results of SQL by more than 5 dB and demonstrates the unique characteristic of the quantum version of oscilloscope.…”

“…By employing the inequality of arithmetic and geometric means, the estimation error of arbitrary waveform is bounded by the SQL of δ = O N −q/(2q+1) and the HQL of δ = O N −q/(q+1) [23,37]. For the present case q = 1, the optimal allocation of quantum resource for the best arbitrary waveform estimation can be realized with n 1 = O N 1/3 , n 2 = O N 2/3 for SQL scheme and The accumulation phase as a function of k with the PDD-enhanced (blue circles) and normal [25] (red circles) TDQD protocols. Lines are theoretical results.…”

“…Over the last few decades, lots of experimental systems, such as multi-photon interferometers [4,[14][15][16], trapped ions [17,18], superconducting circuits [19], and solid-spin [7,20,21], exploited quantum entanglement to demonstrate this nonclassical sensitivity. To extend current results for widely high precision metrology applications, it is natural to consider the continuous [22][23][24][25][26] nature of the detected signal, which can be categorized as an arbitrary waveform estimation to further construct a quantum version of oscilloscope. Unlike scalar and vector estimation [1][2][3][4][5][6][7], arbitrary waveform estimation involves infinite degrees of freedom.…”

“…We perform the waveform estimation by employing a PDD-enhanced TDQD protocol which is based on the differential spin-echo detection [25], as shown in Fig. 2(a).…”