Antibunching dynamics of plasmonically mediated entanglement generation

Dissipative entanglement-generation protocols embrace environmental interactions to generate long-lived entangled states. In this paper, we report on the antibunching dynamics for a pair of actively driven quantum emitters coupled to a shared dissipative plasmonic reservoir. We find that antibunching is a universal signature for entangled states generated by dissipative means and examine its use as an entanglement diagnostic. We discuss the experimental validation of plasmonically mediated entanglement generation by Hanbury Brown-Twiss interferometry with picosecond timing resolution determined by an effective two-qubit Rabi frequency, and we analyze the robustness of entanglement generation with respect to perturbations in local detunings, couplings, and driving fields.

Figure 1

(a) Schematic diagram of the setup described by Eq. (1). (b) Solid (dashed) lines show the numerical (effective analytic) populations of the ground ($G$), symmetric ($S$), and antisymmetric ($A$) states for a system with Hamiltonian parameters (and their effective counterparts without dissipation): ${\mathrm{\Delta }}_0=-{\mathrm{\Delta }}_1=0.02, g_0=g_1=0.02, {\eta }_0={\eta }_1=0.02$, and ${\gamma }_d=2{\gamma }_r={10}^{-8}$. Hamiltonian parameters in all figures are expressed as ratios with respect to the dominant energy scale set by ${\gamma }_a=50\text{THz}$.

Figure 2

Heat map of steady-state concurrence $C_{ss}$ as a function of (left) qubit detunings ${\mathrm{\Delta }}_{0,1}$ with equal qubit drivings ${\eta }_0={\eta }_1=0.05$ and (right) qubit driving amplitudes ${\eta }_{0,1}$ with asymmetric qubit detunings ${\mathrm{\Delta }}_0=-{\mathrm{\Delta }}_1=0.01$. Symmetric drivings and couplings with antisymmetric detunings yields near unity concurrence steady states ${\rho }_{ss}\approx |A\rangle \langle A|$. Parameters common to both panels are coupling strengths $g_0=g_1=0.05$ and plasmon detuning and driving ${\mathrm{\Delta }}_a={\eta }_a=0$.

Figure 3

The steady-state $g^{\left(2\right)}\left(\tau \right)$ correlation function as driving amplitudes ${\eta }_1=0.05$ and ${\eta }_0$ varies across $\left[0.04,0.06\right]$. The blue traces in panel (a) correspond to statistical mixtures of $|gg\rangle$ and $|eg\left(ge\right)\rangle$ depending on the circle endpoints. These states showing a $g^{\left(2\right)}\left(0\right)=0.5$ and correspond to general mixed states. Over this range the concurrence evolves (see color bar labeled by $C$) from 0, where $g^{\left(2\right)}\left(0\right)=1/2$, to 1, where $g^{\left(2\right)}\left(0\right)=0$. Other Hamiltonian parameters, as ratios of ${\gamma }_a$, are ${\mathrm{\Delta }}_0=-{\mathrm{\Delta }}_1=0.02, g_0=g_1=0.05$, and ${\eta }_1=0.05$. $\tau$ is presented in units of $1/(\pi *{\gamma }_a)\approx 6$ fs.

Figure 4

Zero-delay correlations $g^{\left(2\right)}\left(0\right)$ as a function of (left) qubit detunings ${\mathrm{\Delta }}_{0,1}$ and (right) qubit drive amplitudes ${\eta }_{0,1}$ using parameters reported in Fig. 2. Dark bands, which overlap strongly with the high concurrence regions, denote parameter regimes for which antibunching is present.

Figure 5

Oscillation time scales for antibunching signal as a function of (left) qubit detunings ${\mathrm{\Delta }}_{0,1}$ and (right) qubit drive amplitudes ${\eta }_{0,1}$. Time scales reported are in units of $T=1/(\pi *{\gamma }_a)\approx 6\text{fs}$ with remaining parameters as in Fig. 2. Entangled region around ${\eta }_0={\eta }_1=0.03$ displays a characteristic bunching time scale $T_{AB}\sim 10\text{ps}$.