Stationary two-qubit entanglement mediated by one-dimensional plasmonic nanoarrays

TL;DR

This work analyzes stationary two-qubit entanglement between quantum-dot qubits mediated by a one-dimensional plasmonic nanoparticle array. Using an effective cavity-QED approach in the weak-driving limit, it derives how the array mediates both coherent and dissipative qubit-qubit interactions and reveals a striking even-odd parity effect: even-$n$ arrays leverage coherent coupling while odd-$n$ arrays exploit resonant dissipative coupling at the single-particle LSPR to sustain entanglement over micron-scale separations. The authors show that odd-$n$ arrays can outperform even-$n$ arrays in maintaining entanglement at long distances, despite strong plasmonic losses, and validate the analytical model against numerical simulations. These results offer a pathway to robust plasmonic quantum networks by tuning array parity and driving conditions to control stationary two-qubit entanglement.

Abstract

Entanglement is one of the key measures of quantum correlations present in nanophotonic systems, with promising applications in quantum optics and beyond. Previous studies have shown that the degree of entanglement between two quantum dot qubits is preserved when a metal nanoparticle is used to mediate the interactions between the qubits. In this work, we investigate long-range plasmonic mediation of qubit--qubit entanglement by studying the impact of the number of mediating metal nanoparticles on stationary concurrence. Collinear and periodically spaced metal nanoparticles that satisfy the weak-coupling approximation are considered. An effective model that enables the derivation of the mediated interactions within the framework of cavity quantum electrodynamics is employed. Under weak driving at the single particle resonance frequency, the model shows that odd-number arrays are more robust to entanglement decay. We attribute this to strong inter-qubit dissipative coupling as a result of a hybridized dipole plasmon resonating with the driving frequency in odd-number arrays. These arrays can sustain non-vanishing stationary entanglement beyond an inter-qubit spacing of one micron, opening up the possibility of independent spatial optical probing of each quantum dot.

Figures (8)

• Figure 1: (Color online) Geometry of the QD-NA-QD system. A one-dimensional MNP array is sandwiched by two QD qubits, with dipole moments $\bm{\mu}_{1}$ and $\bm{\mu}_{2}$, respectively. The center-to-center distance between each QD and the nearest MNP is $d_{qn}$. The MNPs in the array are spaced periodically with a center-to-center distance denoted as $d_{nn}$. As the number $n$ of MNPs in the array increases, the qubit--qubit separation, $d_{qq}$, increases. Nearest-neighbor couplings are represented by the QD-MNP dipole--dipole coupling rate $g$ and the MNP-MNP dipole--dipole coupling rate $\kappa$. Each QD qubit has ground and excited states denoted as $|g_{i}\rangle$ and $|e_{i}\rangle$ ($i=1,2$), respectively.
• Figure 2: (Color online) Dependence of the coherent coupling, $\tilde{G}_{ij}$ and the dissipative coupling, $\tilde{\Gamma}_{ij}$ ($i = 1, j = 2$), on the inter-qubit separation $d_{qq}-2r_{0}$ for (a) even-$n$ arrays: $\tilde{G}_{ij} \neq 0$, $\tilde{\Gamma}_{ij} = 0$ and (b) odd-$n$ arrays: $\tilde{G}_{ij} = 0$, $\tilde{\Gamma}_{ij} \neq 0$ , at $\omega = \omega_{0} \approx 2\pi c/(480$ nm). Dashed curves: polynomial fits. Solid points: data.
• Figure 3: (Color online) Energy-level diagrams showing the transition rates at the driving frequency $\omega = \omega_{0}$ between the Dicke states of the two NA-coupled qubits for the (a) even-$n$ array with symmetric excitation rate, $\Omega_{s}$, (b) odd-$n$ array with symmetric excitation rate, $\Omega_{s}$, and (c) odd-$n$ array with antisymmetric excitation rate, $\Omega_{a}$.
• Figure 4: (Color online) Symmetric and antisymmetric decay rates, $\gamma_{s}$ and $\gamma_{a}$, as a function of the driving frequency $\omega$ for even-$n$ arrays: $n = 2, 4, 6, 8$ and odd-$n$ arrays: $n = 3, 5, 7, 9$. The dashed vertical line in each panel represents the position of the single particle LSPR, $\omega_{0}$.
• Figure 5: (Color online) Dependence of the stationary concurrence on the driving field intensity and the normalized detuning rate, $\Delta/\gamma_{i}$, of each qubit, for the even-$n$ arrays (a) $n = 2$ and (b) $n = 4$.