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arXiv:2607.15259

Long-range and steady-state entanglement of nitrogen vacancy centers using microwaves as a drive and synthetic antiferromagnet as a dissipator

Federico Garcia-Gaitan, Branislav K. Nikolić

Published Jul 16, 2026• 0 citations
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Abstract

The search for optimal schemes and dissipative environments that can mediate long-range entanglement between two distant nitrogen-vacancy centers (NVCs) in diamond has been the subject of vigorous efforts over the past decade due to potential applications of such microscopic solid-state qubits in quantum sensing and quantum computing. However, stabilizing entanglement of NVCs into a {\em steady state} poses a significant challenge, typically requiring tuning the environment {\em out of equilibrium}. Here we microscopically and rigorously derive a Lindblad quantum master equation (QME) for a system of two {\em driven-dissipative} NVCs, where the drive is microwave radiation and dissipation is provided by a single magnetic bath that is kept in {\em equilibrium}. The jump operators within the Lindblad QME are expressed in terms of Keldysh Green's functions defined as correlators of dipolar field operators of the bath. This QME makes it possible to predict precise conditions for long-range and steady-state entanglement of two NVCs, while suggesting that a synthetic antiferromagnet could be an {\em optimal} choice for a dissipative environment. By using realistic parameters from available experiments, we estimate steady-state concurrence reaching $\mathcal{C}\simeq 0.28$ for two NVCs separated by $\sim 100 \: \mathrm{nm}$.

DOI
10.48550/arxiv.2607.15259

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The search for optimal schemes and dissipative environments that can mediate long-range entanglement between two distant nitrogen-vacancy centers (NVCs) in diamond has been the subject of vigorous efforts over the past decade due to potential applications of such microscopic solid-state qubits in quantum sensing and quantum computing. However, stabilizing entanglement of NVCs into a {\em steady state} poses a significant challenge, typically requiring tuning the environment {\em out of equilibrium}. Here we microscopically and rigorously derive a Lindblad quantum master equation (QME) for a system of two {\em driven-dissipative} NVCs, where the drive is microwave radiation and dissipation is provided by a single magnetic bath that is kept in {\em equilibrium}. The jump operators within the Lindblad QME are expressed in terms of Keldysh Green's functions defined as correlators of dipolar field operators of the bath. This QME makes it possible to predict precise conditions for long-range and steady-state entanglement of two NVCs, while suggesting that a synthetic antiferromagnet could be an {\em optimal} choice for a dissipative environment. By using realistic parameters from available experiments, we estimate steady-state concurrence reaching C≃0.28\mathcal{C}\simeq 0.28C≃0.28 for two NVCs separated by ∼100 nm\sim 100 \: \mathrm{nm}∼100nm.
Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two-qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Decoherence thermal effects on the entanglement transfer are also discussed. Our results provide evidence that this entanglement transfer by dissipation is feasible, yielding to a steady-state amount of entanglement in the bipartite quantum system which can be optimized for a wide range of realistic physical systems that include state-of-the-art experiments with nitrogen-vacancy centers in diamond, superconducting qubits, or even magnetic molecules embedded in a crystalline matrix.
The solid-state qubits based on diamond nitrogen-vacancy centers (NVC) are promising for future quantum information processing. We investigate the dynamics of entanglement among three NVCs coupled to a microtoroidal cavity supporting two counter-propagating whispering-gallery-modes (WGMs) in the presence of Rayleigh scattering. Our results indicate that the maximal entanglement among all the NVCs could be achieved through adjusting several key parameters, such as the scattering-induced coupling between the WGMs, the distance between the NVCs, and the NVC-WGM coupling strengths, as well as the frequency detuning between the NVC and cavity. We show that entanglement of the NVCs displays a series of damped oscillations under various experimental situations, which reflects the intricate interplay and competition between the Rayleigh scattering and the NVC-WGM coupling. The quantum dynamics of the system is obtained via solutions to the corresponding microscopic master equation, which agrees well with the numerical simulation results using the phenomenological master equation. The feasibility of our proposal is supported by the application of currently available experimental techniques.
We propose a practical implementation of a two-qubit entanglement engine which denotes a scheme to generate quantum correlations through purely dissipative processes. On a diamond platform, the electron spin transitions of two nitrogen-vacancy (NV) centers play the role of artificial atoms (qubits), interacting through a dipole-dipole Hamiltonian. The surrounding carbon-13 nuclear spins act as spin baths playing the role of thermal reservoirs at well-defined temperatures and exchanging heat through the NV center qubits. In our scheme, a key challenge is therefore to create a temperature gradient between two spin baths, for which we propose to exploit the recent progress in dynamical nuclear polarization, combined with microscopy superresolution methods. We discuss how these techniques should allow us to initialize such a long lasting out-of-equilibrium polarization situation between them, effectively leading to suitable conditions to run the entanglement engine successfully. Within a quantum master equation approach, we make theoretical predictions using state-of-the-art values for experimental parameters. We obtain promising values for the concurrence, reaching theoretical maxima.
Nitrogen-vacancy (NV) defect centers in diamond are strong candidates to generate entangled states in solid-state environments even at room temperature. Quantum correlations in spatially separated NV systems, for distances between NVs ranging from a few nanometers to a few kilometers, have been recently reported. In the present paper, we consider the entanglement transfer from two-mode microwave-squeezed (entangled) photons, which are in resonance with the two lowest NV electron spin states, to initially unentangled NV centers. We first demonstrate that the entanglement transfer process from quantum microwaves to isolated NV electron spins is feasible. We then proceed to extend the previous results to more realistic scenarios where 13C^{13}\mathrm{C}13C nuclear spin baths surrounding each NV are included, quantifying the entanglement transfer efficiency and robustness under the effects of dephasing/dissipation noisy nuclear baths. Finally, we address the issue of assessing the possibility of entanglement transfer from the squeezed microwave light to two remote nuclear spins closely linked to different NV centers.
We investigate steady state entanglement (SSE) between two nitrogen-vacancy (NV) center defects in a diamond host on an ultrathin yttrium iron garnet (YIG) strip. We determine the dephasing and dissipative interactions of the qubits with the quanta of spin waves (magnon bath) in the YIG depending on the qubit positions on the strip. We show that the magnon's dephasing effect can be eliminated, and we can transform the bath into a multimode displaced thermal state using external magnetic fields. Entanglement dynamics of the qubits in such a displaced thermal bath have been analyzed by deriving and solving the master equation. An additional electric field is considered to engineer the magnon dispersion relation at the band edge to control the Markovian character of the open system dynamics. We determine the optimum geometrical parameters of the system of distant qubits and the YIG strip to get SSE. Furthermore, parameter regimes for which the shared displaced magnon bath can sustain significant SSE against the local dephasing and decoherence of NV centers to their nuclear spin environments have been determined. Along with SSE, we investigate the steady state coherence (SSC) and explain the physical mechanism of how delayed SSE appears following a rapid generation and sudden death of entanglement using the interplay of decoherence-free subspace states, system geometry, displacement of the thermal bath, and enhancement of the qubit dissipation near the magnon band edge. A nonmonotonic relation between bath coherence and SSE is found, and critical coherence for maximum SSE is determined. Our results illuminate the efficient use of system geometry, band edge in bath spectrum, and reservoir coherence to engineer system-reservoir interactions for robust SSE and SSC.
Abstract We propose and analyze an NV-center implementation of a directed cavity-decay scheme for preparing the ground-state entanglement of two nitrogen-vacancy (NV) centers coupled to a single-mode optical cavity. By combining antisymmetric optical driving with a relative phase difference φ 2 − φ 1 = π , microwave-induced population reshuffling within a triplet subspace, and cavity-assisted dissipation, the system is driven toward a singlet-dominated steady state in the ground-state manifold. Starting from the full Lindblad master equation, we construct a reduced four-state effective description that provides a transparent picture of the dominant pumping and leakage processes responsible for the entanglement-preparation mechanism. Based on this reduced model, we obtain analytical expressions for the steady-state fidelity and the effective population-subspace dissipative gap. Within the ideal weak-driving model, the preparation fidelity is mainly limited by the cavity cooperativity C , and in the strong-microwave regime the steady-state infidelity scales as 1 − F ∼ 1 / C . In contrast, the convergence speed is governed by the effective population-subspace gap, revealing the distinct physical roles of cavity-assisted pumping and microwave-induced reshuffling. Direct numerical simulations of the full Lindblad dynamics show quantitative agreement with the reduced description in the weak-driving regime. Deviations become visible at Ω / γ = 0.3 and quantitatively significant by Ω / γ ≃ 0.5 , where higher-excitation corrections can no longer be neglected. Along the specific control path Ω MW = Ω / 3 , the full dynamics confirm a path-dependent speed–fidelity trade-off: increasing the optical drive accelerates the preparation but lowers the steady-state fidelity. Our results provide a useful route toward preparing entanglement between NV spins in hybrid quantum systems.