Experimental realization of robust dynamical decoupling with bounded controls in a solid-state spin system

F. Wang, C. Zu, L. He, W.-B. Wang, W.-G. Zhang, and L.-M. Duan

Phys. Rev. B 94, 064304 – Published 30 August 2016

Abstract

We experimentally demonstrate a robust dynamical decoupling protocol with bounded controls using long soft pulses, eliminating a challenging requirement of strong control pulses in conventional implementations. This protocol is accomplished by designing the decoupling propagators to go through a Eulerian cycle of the coupler group [Phys. Rev. Lett. 90, 037901 (2003)]. We demonstrate that this Eulerian decoupling scheme increases the coherence time by two orders of magnitude in our experiment under either dephasing or a universal noise environment.

Received 22 January 2016
Revised 12 August 2016

DOI:https://doi.org/10.1103/PhysRevB.94.064304

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum Zeno dynamics Quantum control Quantum error correction Quantum information with solid state qubits

Nitrogen vacancy centers in diamond

Quantum Information, Science & Technology

Authors & Affiliations

F. Wang¹, C. Zu¹, L. He¹, W.-B. Wang¹, W.-G. Zhang¹, and L.-M. Duan^1,2

¹Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

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Vol. 94, Iss. 6 — 1 August 2016

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Images

Figure 1
Dynamical decoupling sequences implemented in our experiments. Each rectangle corresponds to a $π$ rotation of the electron spin. The height and the width of the rectangle correspond to the strength and time duration of the pulse, respectively. The pulse interval $2 τ$ and the pulse duration $τ_{d}$ together make a complete period with $τ_{c} = 2 τ + τ_{d}$ , which is kept the same for different decoupling sequences in our comparison of their performance.
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Figure 2
Coherence decay with the initial states along the $+ Y$ axis under pure dephasing. (a) Free induction decay probed using Ramsey interference. Solid line is a fit to $exp [- {(t / T_{2}^{*})}^{2}]$ with the fitted $T_{2}^{*} = 1.85$ $μ s$ . Panels (b)–(d): Coherence decay under repeated CPMG Y (b), XY4 (c), and XY8 (d) dynamical decoupling sequences compared between fast and slow pulses, where the pulse period is fixed and the pulse number $N$ varies from 8 to 360 along the horizontal axis. Solid lines are fits to $exp [- {(t / T_{2})}^{2}]$ with (b) $T_{2} = 816$ (903) $μ s$ for the fast (slow) CPMG pulses, (c) $T_{2} = 490$ (384) $μ s$ for the fast (slow) XY4 pulses, and (d) $T_{2} = 884$ (896) $μ s$ for the fast (slow) XY8 pulses. The pulse duration $τ_{d}$ and the pulse interval $2 τ$ are taken to be $24 (500)$ ns and $1900 (1424)$ ns, respectively, for the fast (slow) pulses.
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Figure 3
Coherence decay with the initial states along the $+ Y$ axis under weak relaxation environment. (a) Relaxation of spin population in the $| 0 〉$ state. Solid line is a fit to $exp (- t / T_{1}^{*})$ with the fitted $T_{1}^{*} = 1.83$ ms. The inset shows the numerical simulation result of relaxation with the injected microwave noise if there were no dephasing in the environment, for which $T_{1}^{*} = 12.87$ $μ s$ . (b) Free induction decay measured with Ramsey interference. Solid line is a fit to $exp [- {(t / T_{2}^{*})}^{2}]$ with the fitted $T_{2}^{*} = 1.79$ $μ s$ . Panels (c) and (d): Coherence decay under repeated XY4 (c) and XY8 (d) dynamical decoupling sequences compared between fast and slow pulses, where the pulse period is fixed and the pulse number $N$ varies from 8 to 360 along the horizontal axis. Solid lines are numerical simulation results under the injected spin relaxation noise and the natural dephasing environment characterized in Fig. 2 (see the Appendix for the simulation method). The pulse duration $τ_{d}$ and the pulse interval $2 τ$ are taken to be $24 (500)$ ns and 1900 (1424) ns, respectively, for the fast (slow) pulses.
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Figure 4
Same as Fig. 3, but under a strong relaxation environment. Solid lines represent numerical simulation results (see the Appendix for the simulation method). The pulse duration $τ_{d}$ and the pulse interval $2 τ$ are taken to be 24 (100) ns and 240 (164) ns, respectively, for the fast (slow) pulses.
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