High-Resolution Quantum Sensing with Shaped Control Pulses

J. Zopes, K. Sasaki, K. S. Cujia, J. M. Boss, K. Chang, T. F. Segawa, K. M. Itoh, and C. L. Degen

Phys. Rev. Lett. 119, 260501 – Published 28 December 2017

Abstract

We investigate the application of amplitude-shaped control pulses for enhancing the time and frequency resolution of multipulse quantum sensing sequences. Using the electronic spin of a single nitrogen-vacancy center in diamond and up to 10 000 coherent microwave pulses with a cosine square envelope, we demonstrate 0.6-ps timing resolution for the interpulse delay. This represents a refinement by over 3 orders of magnitude compared to the 2-ns hardware sampling. We apply the method for the detection of external ac magnetic fields and nuclear magnetic resonance signals of ${}^{13}C$ spins with high spectral resolution. Our method is simple to implement and especially useful for quantum applications that require fast phase gates, many control pulses, and high fidelity.

Received 22 May 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.260501

Physics Subject Headings (PhySH)

Quantum gates Quantum sensing

Electron spin resonance Nuclear magnetic resonance Optically detected magnetic resonance

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Zopes¹, K. Sasaki², K. S. Cujia¹, J. M. Boss¹, K. Chang¹, T. F. Segawa¹, K. M. Itoh², and C. L. Degen^1,*

¹Department of Physics, ETH Zurich, Otto Stern Weg 1, 8093 Zurich, Switzerland
²School of Fundamental Science and Technology, Keio University, Yokohama 223-8522, Japan

^*degenc@ethz.ch

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Vol. 119, Iss. 26 — 29 December 2017

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Images

Figure 1
(a) Dynamical decoupling spectroscopy is based on a periodic pulse modulation of the qubit control field with a precisely timed pulse repetition time $τ$ . (b) Modulation of the microwave signal with square pulses limits the time resolution to multiples of the sampling time $t_{s}$ of the pulse generator hardware. Solid and faint profiles show original and time-shifted pulses. (c) Shaped pulses, here with a cosine-square amplitude profile, enable much finer variations of the pulse timing at the same hardware sampling rate. The minimum interpolated $δ t$ is set by the slope of the pulse envelope and the vertical resolution of the pulse generator (inset). $t_{π}$ is the duration of the $π$ pulse defined by the full width at half maximum of the pulse envelope. In our experiments, the qubit is the solid-state spin of a single nitrogen-vacancy center in diamond.
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Figure 2
Experimental sampling resolution for a sensing sequence with (a) square control pulses and (b) cosine-square control pulses. $t_{s}$ is the hardware sampling time and $δ t$ the interpolated sampling time enabled by the pulse shaping. $N$ is the number of control pulses. $p$ is the probability that the qubit sensor maintains its coherence for different values of the pulse repetition time $τ$ . Solid lines show the theoretical response given by Eqs. (2) and (3) with $B_{ac}$ as the only free parameter, squares and hexagons show the experimental data, and sketches show pulse shapes.
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Figure 3
Sensor response to a dynamical decoupling sequence with (a) $N = 192$ , (b) $N = 672$ , and (c) $N = 10 000$ shaped control pulses. The frequency and amplitude of the ac test signal is $f_{ac} = 9.746 969 MHz$ and $B_{ac} = 0.84 μ T$ for all measurements, respectively. (d) High-resolution plot of the $N = 10 000$ dynamical decoupling sequence showing a timing resolution of $δ t = 0.6 ps$ . Solid lines reflect the theoretical model multiplied by an overall decoherence factor $\exp [- (t / T_{2})^{2}]$ with $T_{2} = 535 μ s$ .
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Figure 4
Applications of the method to high-resolution spectroscopy. (a) Spectrum of two ac test signals separated by 3 kHz. Both signals can be clearly distinguished. (b) NMR spectrum of ${}^{13}C$ nuclei located in close proximity to the NV center sensor spin. Dashed line is the theoretical response to a single ${}^{13}C$ nucleus with hyperfine coupling parameters $a_{∥} = 2 π \times 114 (1) kHz$ and $a_{⊥} = 2 π \times 62 (1) kHz$ . Solid line includes three additional, more weakly coupled ${}^{13}C$ bath spins. Frequency is $1 / (2 τ)$ .
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