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Optics Express

Witnessing quantum entanglement in ensembles of nitrogen–vacancy centers coupled to a superconducting resonator

Yusef Maleki, Aleksei M. Zheltikov

Published Jun 26, 2018• 20 citations
Publisher

Abstract

A hybrid quantum device consisting of three ensembles of nitrogen-vacancy centers (NVEs) whose spins are collectively coupled to a superconducting coplanar waveguide resonator is shown to enable the generation of controllable tripartite macroscopic entangled states. The density matrix of such NVEs can be encoded to recast a three-qubit system state, which can be characterized in terms of the entanglement witnesses in relation to the Greenberger-Horne-Zeilinger (GHZ) states. We identify the parameter space within which the generated entangled states can have an arbitrarily large overlap with GHZ states, indicating an enhanced entanglement in the system.

DOI
10.1364/oe.26.017849

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A hybrid quantum device consisting of three ensembles of nitrogen-vacancy centers (NVEs) whose spins are collectively coupled to a superconducting coplanar waveguide resonator is shown to enable the generation of controllable tripartite macroscopic entangled states. The density matrix of such NVEs can be encoded to recast a three-qubit system state, which can be characterized in terms of the entanglement witnesses in relation to the Greenberger-Horne-Zeilinger (GHZ) states. We identify the parameter space within which the generated entangled states can have an arbitrarily large overlap with GHZ states, indicating an enhanced entanglement in the system.
We show that a hybrid quantum device consisting of three ensembles of nitrogen-vacancy (NV) centers whose spins are collectively coupled to a superconducting coplanar waveguide resonator enables the generation of controllable macroscopic tripartite entangled states. At the instants of time when the waveguide resonator is completely depleted of photons and is thus disentangled from the NV-center ensembles, macroscopic Greenberger–Horne–Zeilinger-type states are generated in NV-diamond memories.
Exploration of macroscopic quantum entanglement is of great interest in both fundamental science and practical application. We investigate a hybrid quantum system that consists of two nitrogen-vacancy centers ensembles (NVE) coupled to a superconducting coplanar waveguide resonator (CPWR). The collective magnetic coupling between the NVE and the CPWR is employed to generate macroscopic entanglement between the NVEs, where the CPWR acts as the quantum bus. We find that, this NVE-CPWR hybrid system behaves as a system of three coupled harmonic oscillators, and the excitation prepared initially in the CPWR can be distributed into these two NVEs. In the nondissipative case, the entanglement of NVEs oscillates periodically and the maximal entanglement always keeps unity if the CPWR is initially prepared in the odd coherent state. Considering the dissipative effect from the CPWR and NVEs, the amount of entanglement between these two NVEs strongly depends on the initial state of the CPWR, and the maximal entanglement can be tuned by adjusting the initial states of the total system. The experimental feasibility and challenge with currently available technology are discussed.
We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.
Quantum entanglement is a kernel of quantum computation and quantum communication. We introduce a theoretical scheme to achieve the entanglement between two separated quantum nodes in a hybrid system. The proposed hybrid system based on diamond nitrogen-vacancy (NV) center spin ensemble is coherently coupled to a superconducting quantum circuit consisting of two quantum nodes and a quantum channel. Each node in our setup is composed of an NV center spin ensemble magnetically coupled to a superconducting coplanar resonator. The NV center spin ensemble composed of N identical and non-interacting NV spins, is placed in the magnetic field antinode of the superconducting coplanar resonator where the coupling is maximized. An array of superconducting quantum interference devices (SQUIDs) is inserted in the central conductor of resonator to make its frequency tunable with the magnetic flux threading through the SQUID loops. This flux is generated by passing current through an on-chip wire, so that the resonator can be brought in resonance with the NV center spins without changing their Zeeman splitting. Quantum qubits encoded into two separate nodes are connected by a vacuum superconducting coplanar resonator that is used as a quantum channel. This setup can potentially take the best elements of each individual system:NV center spin ensemble with longer coherence time capable of preparing, storing and releasing photonic quantum information, and the superconducting quantum circuits are easy to manipulate externally and can perform quantum logic gates to control quantum information rapidly. In order to realize the entanglement between two separated quantum nodes, firstly, we make a canonical transformation and obtain the Hamiltonian of the system that is reduced to two NV center spin ensembles resonantly coupled to a single mode of the superconducting coplanar resonator. Then we put forward the hybrid NV center spin-photon qubit encoding. In this hybrid encoding, the NV center spin and photon degrees of freedom enter on an equal footing into the definition of the qubit, in which case, quantum channel will switch on when three superconducting coplanar resonators are in resonance with each other, and all the manipulations can perform simply by tuning the frequencies of the superconducting coplanar resonators. Under the precise control of the evolution time, high fidelity entanglement between two separated quantum nodes is achieved. We show that this proposal can provide high fidelity quantum entanglement under realistic conditions, both in the resonant and the dispersive interaction cases. This hybrid quantum system will exhibit long coherence time and possess features like easy fabrication, integratability, and potential scalability. Furthermore, the quantum node composed of an NV center spin ensemble magnetically coupled to a superconducting coplanar resonator can be respectively integrated, which has practical applications in the realization of quantum information transmission and quantum entanglement among multiple quantum nodes.
We describe a one-step, deterministic and scalable scheme for creating macroscopic arbitrary entangled coherent states (ECSs) of separate nitrogen-vacancy center ensembles (NVEs) that couple to a superconducting flux qubit. We discuss how to generate the entangled states between the flux qubit and two NVEs by the resonant driving. Then the ECSs of the NVEs can be obtained by projecting the flux qubit, and the entanglement detection can be realized by transferring the quantum state from the NVEs to the flux qubit. Our numerical simulation shows that even under current experimental parameters the concurrence of the ECSs can approach unity. We emphasize that this method is straightforwardly extendable to the case of many NVEs.
We propose a novel scheme for generating N-qubit GHZ entangled state with a hybrid quantum system, which consists of N nitrogen-vacancy centers, N transmission line resonators, a current-biased Josephson junction superconducting qubit, and three kinds of interaction Hamiltonians. The proposal requires no adjustment of the qubit level spacings during the entire operation. Moreover, it is shown that the operation time is independent of the number of qubits. The present proposal is quite useful, and is a promising step to realize the large-sized quantum networks for quantum information processing and quantum computation.