Observing Information Backflow from Controllable Non-Markovian Multichannels in Diamond

Ya-Nan Lu, Yu-Ran Zhang, Gang-Qin Liu, Franco Nori, Heng Fan, and Xin-Yu Pan

Phys. Rev. Lett. 124, 210502 – Published 27 May 2020

Abstract

The unavoidable interaction of a quantum open system with its environment leads to the dissipation of quantum coherence and correlations, making its dynamical behavior a key role in many quantum technologies. In this Letter, we demonstrate the engineering of multiple dissipative channels by controlling the adjacent nuclear spins of a nitrogen-vacancy center in diamond. With a controllable non-Markovian dynamics of this open system, we observe that the quantum Fisher information flows to and from the environment using different noisy channels. Our work contributes to the developments of both noisy quantum metrology and quantum open systems from the viewpoints of metrologically useful entanglement.

Received 4 January 2020
Accepted 20 April 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.210502

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum information with solid state qubits Quantum metrology

Nitrogen vacancy centers in diamond

Optically detected magnetic resonance

Quantum Information, Science & Technology

Authors & Affiliations

Ya-Nan Lu ^1,2,*, Yu-Ran Zhang^3,*, Gang-Qin Liu ^1,4,†, Franco Nori ^3,5, Heng Fan^1,4,6,‡, and Xin-Yu Pan^1,4,6,§

¹Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
³Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
⁴Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
⁵Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
⁶CAS Center of Excellence in Topological Quantum Computation, Beijing 100190, China

^*These authors contributed equally to this work.
^†gqliu@iphy.ac.cn
^‡hfan@iphy.ac.cn
^§xypan@aphy.iphy.ac.cn

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Vol. 124, Iss. 21 — 29 May 2020

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Images

Figure 1
Coherent manipulation of multiple spins in diamond. (a) The nitrogen-vacancy (NV) center, its host ${}^{14}N$ nuclear spin, and a nearby ${}^{13}C$ nuclear spin form a three-qubit system. (b) Energy levels of the three-qubit system. At the excited-state level anticrossing (ESLAC), the three spin qubits can be polarized by a short laser pulse and manipulated with resonant radio-frequency (rf) pulses (13.284 MHz for the ${}^{13}C$ nuclear spin and 2.929 MHz for the host ${}^{14}N$ nuclear spin). (c) Rabi oscillations of the ${}^{14}N$ and ${}^{13}C$ nuclear spins under an external magnetic field of $B = 482 G$ along the quantization axis of the NV center (NV electron spin is at the $m_{s} = - 1$ state).
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Figure 2
Physical coding and experimental procedures. The NV electron spin and two strongly coupled nuclear spins play the roles of the open system and controlled dissipative channels, respectively, while the other (weakly coupled) nuclear spins form an uncontrolled dissipative channel. The quantum Fisher information (QFI) is used to characterize the quantum coherence and metrologically useful entanglement of the open system. (a) In the first experiment, the NV electron spin is the open quantum system. The quantum coherence of the system is subject to two controllable dissipative channels formed by the ${}^{14}N$ and ${}^{13}C$ nuclear spins. (b) In the second experiment, the electron spin and the ${}^{13}C$ nuclear spin form the open system, and the entanglement between the two spins is subject to a controllable dissipative channel formed by the ${}^{14}N$ nuclear spin. (c),(d) Quantum circuits and (e),(f) pulse sequences for the experiments. (The controlled gates are implemented by single-spin rotations in the corresponding subspaces.)
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Figure 3
QFI flows of the electron qubit in a controllable non-Markovian environment. Time evolution of the QFI with (a1) the dissipative channel of ${}^{14}N$ open ( $ϕ_{1} = π / 4$ , $π / 2$ ) and the one of ${}^{13}C$ closed ( $ϕ_{2} = 0$ ); (b1) the dissipative channel of ${}^{14}N$ closed ( $ϕ_{1} = 0$ ) and the one of ${}^{13}C$ open ( $ϕ_{2} = π / 4$ , $π / 2$ ); (c1) the dissipative channels of both nuclear spins open ( $ϕ_{1} = ϕ_{2} = π / 2$ ) compared with the one calculated using the results of single channels given in (a1),(b1). QFI flows for the controllable dissipative channels with parameters: (a2) $ϕ_{1} = ϕ_{2} = 0$ ; (a3) $ϕ_{1} = π / 4$ , $ϕ_{2} = 0$ ; (a4) $ϕ_{1} = π / 2$ , $ϕ_{2} = 0$ ; (b2) $ϕ_{1} = 0$ , $ϕ_{2} = π / 4$ ; (b3) $ϕ_{1} = 0$ , $ϕ_{2} = π / 2$ . (c2) When both dissipative channels are open, the total QFI flow is compared with the sum of subflows calculated by results in (a2),(a4),(b3). (c3) The measure of non-Markovianity from the total positive QFI flow in (c2) compared with the measure from the QFI subflows with respect to different dissipative channels [ $N [t, (π / 2), (π / 2)]$ in Eq. (4)], versus the evolution time. The solid curves are for the numerical simulations using experimental parameters.
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Figure 4
(a) Time evolutions of the QFI of the maximally entangled state of the NV electron qubit and the 12.8 MHz ${}^{13}C$ qubit with the controllable dissipative channel of the ${}^{14}N$ qubit. QFI flows of the maximally entangled state with the controllable dissipative channel of ${}^{14}N$ (b) closed ( $ϕ_{1} = 0$ ) and (c) open ( $ϕ_{1} = π / 2$ ). The solid curves are for the numerical simulations using experimental parameters.
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