Dynamical-Decoupling-Based Quantum Sensing: Floquet Spectroscopy

Abstract

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, multipulse 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 that it offers a number of general advantages. In particular, this technique generalizes to more complex situations, offering physical insight in regimes of many-body dynamics, strong coupling, and pulses of finite duration. As there is no requirement for resonant driving, the proposed spectroscopic approach permits physical interpretation of striking, but overlooked, coherence decay features in terms of the form of the avoided crossings of the underlying quasienergy eigenspectrum. This is exemplified by a set of “diamond-shaped” features arising for transverse-field scans in the case of single-spin sensing by nitrogen-vacancy centers in diamond. We also investigate applications for donors in silicon, showing that the resulting tunable interaction strengths offer highly promising future sensors.

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Plain Language Summary

The development of magnetic resonance imaging revolutionized medical and biological science. Now, recent technical developments offer the comparable prospect of imaging single molecular and biological structures. As in magnetic resonance imaging, single-spin sensing also exploits measurements of the temporal decay of the coherence of quantum spins to infer detailed information. The field of single-spin sensing is at a comparatively early stage, but one day it could have a transformative effect on biological and chemical physics. Here, we show how one can exploit the well-known fact that a quantum system exposed to a periodic potential acquires very different spectral characteristics. We analyze time-periodic sensing protocols using Floquet theory and show it is potentially useful for a wider range of scenarios than standard methods, including many-body interactions and strong quantum entanglement.

In dynamical-decoupling sensing, noise from environmental spins is amplified by a sequence of microwave pulses and detected by a sensor (such as a nitrogen-vacancy color center in diamond). The coherence behavior is often analyzed using signal-processing ideas that rely on the frequency of the pulses becoming resonant with a characteristic frequency in the environment, which leads to a single sharp “dip” in the coherence. We show here that such a restriction is unnecessary. By looking at the nonresonant regime, we identify new information-rich structures that can be interpreted using Floquet spectroscopy but might be overlooked in current experiments since they lie in regimes that do not yield single sharp dips. In particular, we show that transverse magnetic field scans of coherence of nitrogen-vacancy centers in diamond reveal a set of striking diamond-shaped coherence envelopes with sharp boundaries that depend on the interesting frequencies. The power of Floquet theory is that it is applicable to both resonant and nonresonant driving, and it works for a range of coupling strengths.

We expect that our findings will motivate future studies of sensor spins, other than nitrogen-vacancy centers, such as spin-1/2 systems that have long coherence times and allow further control over the Floquet states.