Observation of entanglement sudden death and rebirth by controlling a solid-state spin bath

F. Wang, P.-Y. Hou, Y.-Y. Huang, W.-G. Zhang, X.-L. Ouyang, X. Wang, X.-Z. Huang, H.-L. Zhang, L. He, X.-Y. Chang, and L.-M. Duan

Phys. Rev. B 98, 064306 – Published 27 August 2018

Abstract

Quantum entanglement, the essential resource for quantum information processing, has rich dynamics under different environments. Probing different entanglement dynamics typically requires exquisite control of complicated system-environment coupling in real experimental systems. Here, by a simple control of the effective solid-state spin bath in a diamond sample, we observe rich entanglement dynamics, including the conventional asymptotic decay as well as the entanglement sudden death, a term coined for the phenomenon of complete disappearance of entanglement after a short finite time interval. Furthermore, we observe counterintuitive entanglement rebirth after its sudden death in the same diamond sample by tuning an experimental parameter, demonstrating that we can conveniently control the non-Markovianity of the system-environment coupling through a natural experimental knob. Further tuning of this experimental knob can make the entanglement dynamics completely coherent under the same environmental coupling. Probing of entanglement dynamics, apart from its fundamental interest, may find applications in quantum information processing through control of the environmental coupling.

Received 27 January 2018
Revised 21 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064306

Physics Subject Headings (PhySH)

Entanglement manipulation Entanglement production Quantum control Quantum information with solid state qubits

Quantum Information, Science & Technology

Authors & Affiliations

F. Wang¹, P.-Y. Hou¹, Y.-Y. Huang¹, W.-G. Zhang¹, X.-L. Ouyang¹, X. Wang¹, X.-Z. Huang¹, H.-L. Zhang¹, L. He¹, X.-Y. Chang¹, 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

^*Corresponding author: lmduan@umich.edu

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Vol. 98, Iss. 6 — 1 August 2018

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Figure 1
Experimental system. (a) The NV electron spin (red), the host nitrogen nuclear spin (green), and the coupled ${}^{13}C$ spin bath (blue). Entangled state is prepared on the electron-nitrogen pair and is exposed to the spin bath. Hyperfine parameters of distinct carbons are denoted as $A_{i}$ for carbon $i$ . (b) Gate sequence to prepare entanglement in the electron-nitrogen nuclear spin pair. The conditional $π$ rotation is implemented by a 2.928 MHz radio-frequency (rf) signal with two fast $π$ rotations of the electron spin symmetric on both sides to protect the coherence of the electron spin. (c) Entanglement decay as a function of free evolution time with the system subject to the fluctuating spin bath. (d) Entanglement decay as a function of evolution time under the Hahn echo. Solid lines are fits by the function $exp [- {(t / T_{c})}^{2}]$ with $T_{c} = 3.7 μ s$ ( $602 μ s$ ) for (c) [(d)]. The error bars in this and the following figures denote one standard deviation.
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Figure 2
Decay of electron-nuclear spin entanglement under CPMG sequences. (a) Diagram of the CPMG sequence. (b) Asymptotic decay of entanglement as a function of the total evolution time at $τ = 2 μ s$ . Solid line is a fit by the function $exp [- {(t / T_{2})}^{2}]$ with $T_{2} = 1.33$ ms. (c) Observation of entanglement sudden death as a function of the evolution time at $τ = 0.47 μ s$ . (d) and (e) Non-Markovian entanglement dynamics as a function of the total evolution time at $τ = 0.44 μ s$ and $τ = 0.51 μ s$ , which shows entanglement sudden death and rebirth.
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Figure 3
Analysis of the entanglement evolution under CPMG sequences. (a) Upper panel: Decay of electron coherence as a function of half-interpulse duration $τ$ with $N = 16$ . Black dots and solid line are experimental data taken every 10 ns. Red dashed line denotes the simulation result under six identified carbon nuclear spins in the bath with their hyperfine parameters calibrated by the method described in the Supplemental Material [41]. Arrows indicate corresponding $τ$ in Figs. 2–2, respectively. Lower panel: Calculated entanglement concurrence from electron coherence in the upper figure. Inset: Experimental results with the same time range in the blue dashed square. Blue circles are experimental data taken every 50 ns. (b) Upper panel: Noise spectrum constructed from electron spin coherence in (a). Central components correspond to the first order resonance of the nuclear spin bath. Higher order resonance terms are shown as peaks at lower frequencies. Lower panel: Filter function of the CPMG sequences with $N = 16$ . Peaks appear at $ω_{0} / (2 π) = 1 / (4 τ)$ . (c)–(e) Simulation of entanglement decay under the same condition described in Figs. 2–2 respectively. Dashed lines are results corresponds to single identified carbon nuclear spin. Solid line is the result with effects of six carbon nuclear spins combined together.
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Figure 4
Decay of electron coherence and electron-nuclear spin entanglement under the CPMG sequences with interpulse duration $τ$ on resonant with a single carbon. (a) Decay of electron coherence as a function of half-interpulse duration $τ$ under CPMG sequences with $N = 16$ . Black circles are experimental data taken every 10 ns. (b) Entanglement decay as a function of the total evolution time with the half-interpulse duration $τ = 2.253 μ s$ . The sequence is on resonant with carbon 2 [green arrow in (a)]. (c) Entanglement decay as a function of the total evolution time with the half-interpulse duration $τ = 2.579 μ s$ . The sequence is on resonant with carbon 1 [blue arrow in (a)]. Blue (green) solid lines are simulation results with calibrated parameters for carbon 1 (2).
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