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Physical Review A

Generation of Greenberger-Horne-Zeilinger states for silicon-vacancy centers using a decoherence-free subspace

Yi‐Fan Qiao, Jia‐Qiang Chen, Xing‐Liang Dong, Bolong Wang, Xin‐Lei Hei, Cai‐Peng Shen, Yuan Zhou, Fuli Li

Published Mar 7, 2022• 17 citations
Publisher

Abstract

Generating Greenberger-Horne-Zeilinger (GHZ) states of solid-state spins is of great significance for quantum metrology and quantum error correction. We propose here an efficient scheme for generating high fidelity GHZ states in a solid-state setup where multiple silicon-vacancy (SiV) centers are embedded in a quasi-one-dimensional acoustic diamond waveguide. The lattice distortion gives rise to a strong strain coupling between the orbital degree of freedom of SiV centers and the continuum phonon modes. Due to the permutation symmetry, we can take advantage of the decoherence-free subspace to avoid dissipation. Under the quantum Zeno regime, two control fields are used to achieve a ladderlike coupling structure in decoherence-free subspace along with an off-resonant two-photon Raman transition process. We calculate the pulse sequences for $N=4$ and at the same time analyze the effect of different collective decay rates. Moreover, we consider the disorder in the imperfect position of SiV centers and the inhomogeneous strain coupling. This paper may provide a feasible protocol for the generation of GHZ states in a solid-state system.

DOI
10.1103/physreva.105.032415

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Generating Greenberger-Horne-Zeilinger (GHZ) states of solid-state spins is of great significance for quantum metrology and quantum error correction. We propose here an efficient scheme for generating high fidelity GHZ states in a solid-state setup where multiple silicon-vacancy (SiV) centers are embedded in a quasi-one-dimensional acoustic diamond waveguide. The lattice distortion gives rise to a strong strain coupling between the orbital degree of freedom of SiV centers and the continuum phonon modes. Due to the permutation symmetry, we can take advantage of the decoherence-free subspace to avoid dissipation. Under the quantum Zeno regime, two control fields are used to achieve a ladderlike coupling structure in decoherence-free subspace along with an off-resonant two-photon Raman transition process. We calculate the pulse sequences for N=4N=4N=4 and at the same time analyze the effect of different collective decay rates. Moreover, we consider the disorder in the imperfect position of SiV centers and the inhomogeneous strain coupling. This paper may provide a feasible protocol for the generation of GHZ states in a solid-state system.
Multiparticle entanglement is of great significance for quantum metrology and quantum information processing. We present here an efficient scheme for generating stable multiparticle entanglement in a solid-state setup, where an array of silicon-vacancy centers are embedded in a quasi-one-dimensional acoustic diamond waveguide. In this scheme, the continuum of phonon modes induces a controllable dissipative coupling among the SiV centers. We show that, by an appropriate choice of the distance between the SiV centers, the dipole-dipole interactions can be switched off due to destructive interference, thus realizing a Dicke superradiance model. This gives rise to an entangled steady state of SiV centers with high fidelities. The protocol provides a feasible setup for the generation of multiparticle entanglement in a solid-state system.
An alternative scheme is proposed for the generation of an N-qubit Greenberger-Horne-Zeilinger (GHZ) state with distant nitrogen-vacancy (N-V) centers confined in spatially separated photonic crystal (PC) nanocavities via input-output process of photon. The GHZ state is produced by the phase shift brought by the input-output photon. The certain polarized photon transmitted from a PC nanocavity side-coupled a waveguide can obtain different phase shifts due to the different spin states in diamond N-V centers and the optical spin selection rule. Our calculations show that the proposed scheme can work well with a large cavity damping rate which ensures the efficient output of photon.
We propose a scheme to entangle Silicon-Vacancy (SiV) centers embedded in a diamond acoustic waveguide. These SiV centers interact with acoustic modes of the waveguide via strain-induced coupling. Through Morris-Shore transformation, the Hilbert space of this hybrid quantum system can be factorized into a closed subspace in which we can deterministically realize the symmetrical Dicke states between distant SiV centers with high fidelity. In addition, the generation of entangled Dicke states can be controlled by manipulating the strength and frequency of the driving field applied on SiV centers. This protocol provides a promising way to prepare multipartite entanglement in spin-phonon hybrid systems and could have broad applications for future quantum technologies.
In this paper, we propose a system that consists of two acoustic wave resonators (AWRs) coupled to a nitrogen-vacancy-center ensemble (NVE) for constructing Greenberger–Horne–Zeilinger (GHZ) states and controlled-phase (c-phase) gate according to the recent study of surface acoustic waves. The two AWRs are fabricated on a diamond surface in perpendicular way, and the NVE is placed at the center of the crossing. By using the resonant interactions and microwave pulses, we present the protocols of constructing the GHZ states and the c-phase gate in the phonon–spin system. The numerical simulation shows that the fidelities of the two-excitation Bell state, three-excitation Bell state and the c-phase gate can reach 99.19[Formula: see text], 99.46[Formula: see text] and 98.62[Formula: see text], respectively, by considering the decoherence of the system.
We propose a one-step scheme for the generation of Greenberger–Horne–Zeilinger states of multi solid-state qubits and the implementation of quantum phase gates in a system consisting of N spatially separated nitrogen-vacancy centers coupled to the whispering-gallery mode (WGM) of a microsphere cavity. The proposed scheme is based on the effective electronic dipole–dipole interaction between electron spins associated with the NV centers, which is mediated by the WGM and applying external driving laser fields. As the spontaneous emission of the excited states of the NV centers is highly suppressed and the cavity mode is only virtually excited, the scheme is insensitive to decoherence.
Realization of physical systems for quantum information processing fundamentally rests on the ability to generate entanglement among many quantum bits. To this end, solid state quantum systems are often considered a scalable approach due to the relative ease of generating of a large number of individual qubits. However, realizing strong coherent interactions that dominate decoherence processes in the solid state environment is a formidable challenge that has continued to motivate the investigation of new physical systems to store quantum information and new mechanisms to achieve controllable interactions. This thesis takes steps in these directions with diamond color centers, which can store optically accessible quantum information in their electronic spin. We study color center spins as acoustic two level systems, and consider whether their interaction with single phonons in diamond can be engineered to be coherent. Through spectroscopy of color centers in diamond nanomechanical devices and follow-up theoretical work, we identify the negatively charged silicon vacancy (SiV) color center as a promising candidate for phonon-mediated quantum information processing. In the process, an electromechanical device platform capable of tuning the strain environment of color centers is developed. It is used to mitigate thermal decoherence of the SiV spin and demonstrate photon-mediated quantum interference between two SiV centers on a diamond chip, highlighting the utility of nanomechanical devices for photonic quantum networks. Finally, we present high quality factor, wavelength scale acoustic resonators in diamond using phononic crystals towards a coherent interface between SiV centers and single phonons.