Preparing multiparticle entangled states of nitrogen-vacancy centers via adiabatic ground-state transitions

Yuan Zhou, Bo Li, Xiao-Xiao Li, Fu-Li Li, and Peng-Bo Li

Phys. Rev. A 98, 052346 – Published 27 November 2018

Abstract

We propose an efficient method to generate multiparticle entangled states of nitrogen-vacancy (NV) centers in a spin-mechanical system, where the spins interact through a collective coupling of the Lipkin-Meshkov-Glick (LMG) type. We show that through adiabatic transitions in the ground state of the LMG Hamiltonian, the Greenberger-Horne-Zeilinger (GHZ)-type or the W-type entangled states of the NV spins can be generated with this hybrid system from an initial product state. Because of adiabaticity, this scheme is robust against practical noise and experimental imperfection, and may be useful for quantum information processing.

Received 2 July 2018
Revised 20 September 2018

DOI:https://doi.org/10.1103/PhysRevA.98.052346

Physics Subject Headings (PhySH)

NV centers Quantum entanglement Quantum information with hybrid systems Quantum information with solid state qubits Quantum phase transitions Quantum state engineering

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuan Zhou, Bo Li, Xiao-Xiao Li, Fu-Li Li, and Peng-Bo Li^*

Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Department of Applied Physics, Xi'an Jiaotong University, Xi'an 710049, China

^*lipengbo@mail.xjtu.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 5 — November 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The scheme diagrams. (a) An array of equidistant sharp magnetic tips are attached near the end of a silicon cantilever NAMR, under which are $N$ distant NV centers with the same distance $d$ . In addition, two microwave fields are applied to drive the NV centers between the state $| m_{s} = 0 〉$ and the state $| m_{s} = - 1 〉$ . (b) Another feasible equivalent setup. An array of NV centers are embedded equidistantly near the end of a diamond NAMR, above which are $N$ magnetic tips with the same distance $d$ . Two microwave fields are also applied to drive the transitions between the state $| m_{s} = 0 〉$ and the state $| m_{s} = - 1 〉$ for the NV centers. (c) Level diagram of the NV center ground triplet state and the feasible transition channels. The blue and red solid arrows indicate the two different microwave driving fields (with frequencies $ω_{1}$ , and $ω_{2}$ , and Rabi frequencies $Ω_{1}$ and $Ω_{2}$ ) applied between state $| m_{s} = 0 〉$ and state $| m_{s} = - 1 〉$ .
Reuse & Permissions
Figure 2
The analysis graphics for the ground state of the isotropy LMG Hamiltonian $H_{isotropy}$ with four different conditions: (a) and (b) are for the negative coefficient $α < 0$ with $ɛ < - N$ and $ɛ > N$ , while (c) and (d) are for the positive coefficient $α > 0$ with $ɛ < - N$ and $ɛ > N$ .
Reuse & Permissions
Figure 3
The diagram for three different adiabatic transition schemes (case I, case II, and case III) between the initial ground states (left) and the final ground states (right) for all of the NV spins. In case I, the transition is $| m_{z} = N / 2 〉 \overset{(I)}{\to} | ϕ_{(I)} 〉$ , with the parameters $α < 0$ and $ɛ > N$ ; in case II, the transition is $| m_{z} = - N / 2 〉 \overset{(II)}{\to} | ϕ_{(II)} 〉$ , with the parameters $α > 0$ , $ɛ > N$ and odd number of NV spins; for case III, the transition is $| m_{z} = - N / 2 〉 \overset{(III)}{\to} | ϕ_{(III)} 〉$ , with the parameters $α > 0$ , $ɛ > N$ and even number of NV spins.
Reuse & Permissions
Figure 4
The dynamical evolution for the population of the target entangled states $| ϕ_{(I)} 〉$ , $| ϕ_{(II)} 〉$ , and $| ϕ_{(III)} 〉$ in the adiabatic transfer scheme for case I, case II, and case III, respectively, with the slowly varying Rabi frequencies $Ω_{1} (t) = 0.3 ν [1 + tanh (ν t / 2000)]$ and $Ω_{2} (t) = 0.3 ν [1 + tanh (ν t / 1500)]$ as illustrated in (g). For case I, (a) $λ = 0.1 ν$ and $| Δ | = 1.1 ν$ , and (b) $λ = 0.05 ν$ and $| Δ | = 1.1 ν$ ; for case II, (c) $λ = 0.1 ν$ and $| Δ | = 1.1 ν$ , and (d) $λ = 0.1 ν$ and $| Δ | = 0.9 ν$ ; for case III, (e) $| Δ | = 1.1 ν$ and $λ = 0.1 ν$ , and (f) $| Δ | = 0.9 ν$ and $λ = 0.1 ν$ .
Reuse & Permissions
Figure 5
The dynamical evolution for the population of the target entangled ground state $| ϕ_{(I)} 〉$ under different disorder distributions, with the parameters $λ = 0.1 ν$ , and $| Δ | = 0.9 ν$ . (a) $| δ λ_{j} | \leq λ \times 5 %$ , disorder-(a)-1: { $- 0.05 λ$ , $0.05 λ$ , $0.04 λ$ , $0.05 λ$ }, disorder-(a)-2: { $- 0.05 λ$ , $0.04 λ$ , $- 0.05 λ$ , $0.05 λ$ }, and disorder-(a)-3: { $0.05 λ$ , $0.04 λ$ , $0.05 λ$ , $0.04 λ$ }. (b) $| δ λ_{j} | \leq λ \times 10 %$ , disorder-(b)-1: { $0.1 λ$ , $- 0.05 λ$ , $0.08 λ$ , $- 0.04 λ$ }, disorder-(b)-2: { $0.05 λ$ , $0.09 λ$ , $0.07 λ$ , $0.01 λ$ }, and disorder-(b)-3: { $- 0.05 λ$ , $- 0.03 λ$ , $- 0.02 λ$ , $0.1 λ$ }. (c) $| δ λ_{j} | \leq λ \times 20 %$ , disorder-(c)-1: { $- 0.2 λ$ , $- 0.01 λ$ , $0.15 λ$ , $0.07 λ$ }, disorder-(c)-2: { $- 0.12 λ$ , $- 0.15 λ$ , $0.2 λ$ , $- 0.1 λ$ }, and disorder-(c)-3: { $0.2 λ$ , $0.05 λ$ , $0.11 λ$ , $- 0.01 λ$ }. (d) $| δ λ_{j} | \leq λ \times 30 %$ , disorder-(d)-1: { $0.3 λ$ , $0.2 λ$ , $0.1 λ$ , $- 0.01 λ$ }, disorder-(d)-2: { $- 0.1 λ$ , $- 0.2 λ$ , $0.3 λ$ , $0.15 λ$ }, and disorder-(d)-3: { $- 0.2 λ$ , $0.3 λ$ , $- 0.1 λ$ , $0.01 λ$ }.
Reuse & Permissions
Figure 6
The dynamical evolution for the population of the target entangled ground state $| ϕ_{(I)} 〉$ under different dispersion distributions of $Ω_{1} (t)$ and $Ω_{2} (t)$ , with the parameters $λ = 0.1 ν$ and $| Δ | = 0.9 ν$ . The different dispersion distributions are respectively no dispersion: { $δ ζ_{1} = 0$ , $δ ζ_{2} = 0$ }, dispersion-1: { $0.05 ζ$ , $0.05 ζ$ }, dispersion-2: { $- 0.05 ζ$ , $0.05 ζ$ }, dispersion-3: { $0.05 ζ$ , $- 0.05 ζ$ }, and dispersion-4: { $0.1 ζ$ , $- 0.1 ζ$ }.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information