Abstract
Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. However, in common control routines out-of-band spectral leakage complicates interpretation of the sensor’s signal. In this work, we leverage discrete prolate spheroidal sequences (a.k.a. Slepian sequences) to synthesize provably optimal narrowband controls ideally suited to spectral estimation of a qubit’s noisy environment. Experiments with trapped ions demonstrate how spectral leakage may be reduced by orders of magnitude over conventional controls when a near resonant driving field is modulated by Slepians, and how the desired narrowband sensitivity may be tuned using concepts from RF engineering. We demonstrate that classical multitaper techniques for spectral analysis can be ported to the quantum domain and combined with Bayesian estimation tools to experimentally reconstruct complex noise spectra. We then deploy these techniques to identify previously immeasurable frequency-resolved amplitude noise in our qubit’s microwave synthesis chain.
Highlights
Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space
The discrete prolate spheroidal sequences (DPSS) form the basis of the multitaper method of spectral analysis[20], which is employed in estimation problems across a wide range of physical, computational, and biomedical disciplines[21,22]
We introduce the concept of continuously amplitude-modulated control waveforms defined by DPSS functions as effective window functions, and we demonstrate that such controls afford suppression of spectral leakage in the quantum setting
Summary
Essential to the functionality of qubit-based sensors are control protocols, which shape their response in frequency space. Application of modulation which periodically flips the qubit’s state has allowed for a narrowband spectral response[5], which may be tuned by adjusting the interpulse spacing or extending the sequence duration This general approach to “dynamical decoupling noise spectroscopy” has seen broad adoption in quantum information[6,7,8,9,10,11], as well as in nanoscale diamond sensors for biomedical and physics-based applications[12,13,14,15]. DPSS have been suggested in magnetic resonance imaging to avoid out-of-band excitation (so-called Gibbs artifact23) and have recently enabled the design of optimal control algorithms for unitary quantum dynamics, that incorporate bandwidth constraints[24] This strong base of demonstrations motivates our use of DPSS-modulated pulses for quantum sensing. Experiments with trapped atomic ions are used to reconstruct the filter a
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