Entanglement of mechanical oscillators mediated by a Rydberg tweezer chain

TL;DR

This work presents a hybrid system where two GHz mechanical oscillators at opposite ends of a Rydberg-atom tweezer chain become entangled through both coherent transport and engineered dissipation. By modeling $H_{osc}$, $H_{chain}$, and $H_{couple}$ with resonant coupling ($\omega=\Delta$) and applying a Schrieffer–Wolff reduction for $J\ll V$, the authors derive an effective direct oscillator–oscillator coupling $J^2/V$ and identify higher-order pair-exchange processes, demonstrating deterministic entanglement generation. They also develop a dissipative scheme using quantum-jump trajectories, where carefully chosen decay channels ($\gamma_\downarrow$ vs $\gamma_\uparrow$) and post-selection yield probabilistic but enhanced entanglement, revealing a nontrivial interplay between coherence and dissipation. The findings highlight the tunability and flexibility of Rydberg chains for creating nonclassical correlations between distant macroscopic objects, with implications for quantum acoustics and tests of quantum-classical boundaries.

Abstract

Mechanical systems provide a unique test bed for studying quantum phenomena at macroscopic length scales. However, realizing quantum states that feature quantum correlations among macroscopic mechanical objects remains an experimental challenge. Here, we propose a quantum system in which two micro-electromechanical oscillators interact through a chain of Rydberg atoms confined in optical tweezers. We demonstrate that the coherent dynamics of the system generate entanglement between the oscillators. Furthermore, we utilize the tunability of the radiative decay of the Rydberg atoms for dissipative entanglement generation. Our results highlight the potential to exploit the flexibility and tunability of Rydberg atom chains to generate nonclassical correlations between distant mechanical oscillators.

Figures (3)

• Figure 1: Mechanical oscillators linked by a Rydberg atom chain.(a): Schematic of the oscillator-atom system illustrating the levels, coupling strengths and decay rates introduced in the main text. Excitations in the Rydberg spin chain and the oscillators are depicted as violet filled circles, while white filled circles indicate the absence of excitations. (b,c): Coherent evolution of the number of excitations in the oscillators $\ev{a^\dagger a}$, $\ev{b^\dagger b}$ and oscillator entanglement quantified by the negativity $\mathcal{N}$. The results correspond to the system presented in (a) with $N=2$ atoms and $V = 10J$. In panel (b) the system is initialized in $\ket{\psi_1}$ and in panel (c) in $\ket{\psi_2}$ (see text). Dark lines are obtained from the effective Hamiltonian \ref{['eq:eff-hamiltonian']}, while lighter, semi-transparent lines show the exact dynamics under the full Hamiltonian \ref{['eq:total-hamiltonian']}. In panel (c), $\ev{b^\dagger b}$ is shown as a dashed curve to improve visibility.
• Figure 2: Entanglement generation through atom chain dissipation.(a): Time evolution of excitations in the sites of the spin chain $\ev*{\mathcal{P}_\uparrow^{(i)}}$ and the number of excitations in the oscillators $\ev*{a^\dagger a},\,\ev*{b^\dagger b}$ for a selected single trajectory and system parameter $V = 3J$, $\gamma_\downarrow = \gamma_\uparrow = 0.2J$ and $\kappa=0$. The system is initially prepared in the state $\ket{\psi_\mathrm{init}} = \ket{0}_a \otimes \ket{\uparrow\uparrow\uparrow\uparrow\uparrow} \otimes \ket{0}_b$. Atom decay is marked with the corresponding jump operator, with $\sqrt{\gamma_\downarrow}$ omitted. Atoms that have decayed to the ground state are colored gray. (b): Time evolution of the oscillator negativity $\mathcal{N}$ for the trajectory shown in (a) (blue) in comparison to the purely coherent evolution (red) for the same parameters. (c): Probability distributions $P(\mathcal{N})$ of final-state negativities $\mathcal{N}$ for $2000$ trajectories using the parameters from (a) with $\gamma_\uparrow=0.2J$ (blue) and $\gamma_\uparrow=0$ (green). The averages of the negativity distributions $\mathcal{N}_\mathrm{avg}$ are depicted by vertical dashed lines.
• Figure 3: Parameter dependence of average final-state negativity.(a): The average final-state negativity $\mathcal{N}_\mathrm{avg}$ as a function of $\gamma_\downarrow$ for different atom numbers $N$ and fixed parameters $V = 2J$, $\kappa = 0$, and $\gamma_\uparrow = 0.001J$. Averages are taken over 1000 trajectories for $N = 3$ and $N = 7$, and over 100 trajectories for $N = 11$. (b):$\mathcal{N}_\mathrm{avg}$ as a function of $\gamma_\downarrow$ for different coupling strengths $V$ with $N = 5$, $\kappa = 0$, and $\gamma_\uparrow = 0.001J$. Each data point is averaged over $1000$ trajectories. (c): Comparison of two cases, with ($\kappa=0.001J$) and without oscillator decay. Parameters are $V = 2J$, $N = 5$, and $\gamma_\uparrow = 0.001J$. For the case with oscillator decay, we also show results after post-selecting trajectories that complete within a cutoff time of $0.3/\kappa$. For $\gamma_\downarrow = 0.001J$ the data point is missing because no trajectory satisfied the post-selection criterion. Averages are taken over $10^4$ trajectories. In all panels, log-normal curves are fitted to the data.