Dynamical correlations and chimera-like states of nanoemitters coupled to plasmon-polaritons in a lattice of conducting nanorings

TL;DR

This work analyzes a hybrid system where a 2D lattice of dispersive nanorings hosts plasmon-polaritons and contains quantum nanoemitters. By solving time-dependent Maxwell equations coupled to semi-classical four-level NE rate equations via FDTD, it reveals a critical transition at a NR plasma frequency $\omega_c$ (about $4.9\times10^{11}$ Hz) where PP-NE coupling becomes strong, driving NE cross-correlations and inducing chimera-like synchronization patterns. The study shows that, in the critical regime, small changes in $\omega_p$ dramatically alter NE correlations, with chaotic or non-smooth dynamics and localized desynchronization coexisting with synchronization. These findings highlight a tunable mechanism for controlling light-matter dynamics in dispersive nanolattices, with potential applications in compact optical devices and tunable light sources.

Abstract

We systematically investigate semiclassical dynamics of the optical field produced by quantum nanoemitters (NEs) embedded in a periodic lattice of conducting nanorings (NRs), in which plasmon polaritons (PPs) are excited. The coupling between PPs and NEs through the radiated optical field leads to establishment of a significant cross-correlation between NEs, so that their internal dynamics (photocurrent affected by the laser irradiation) depends on the NR's plasma frequency $ω_{p}$. The transition to this regime,combined with the nonlinearity of the system, leads to a steep increase of the photocurrent in the NEs, as well as to non-smooth (chimera-like or chaotic) behavior in the critical (transition) region, where small variations of $ω_{p}$ lead to significant changes in the level of the NE pairwise cross-correlations. The chimera-like state is realized as coexistence of locally synchronized and desynchronized NE dynamical states. A fit of the dependence of the critical current on $ω_{p}$ is found, being in agreement with results of numerical simulations. The critical effect may help to design new optical devices, using dispersive nanolattices which are made available by modern nanoelectronics.

Figures (10)

• Figure 1: The system is built as the lattice of size $7\times 7$. composed of conducting NRs with embedded quantum NEs (solid circles) emitting the optical field. In the present setup, four NEs form two clusters shown by red and blue colors. PPs are excited in the NRs and interact with the NEs. The NEs are connected by straight lines that correspond to the optimized path calculated by means of TSP (traveling salesman problem) method (with a traveling photon passing each NE without visiting the same NE twice) and Fermat's principleBurlak:2015BURLAK:2023b.
• Figure 2: The schematic representation of NE as a four-level system, see Eqs. (\ref{['EqForN_03']})-(\ref{['M_rateEq']}). The external pump lifts electrons from the ground level (with population $N_{0}$) to the third level (with population $N_{3}$). After a short lifetime $\tau _{32}$, the electrons perform the nonradiative transfer to the second level (with population $N_{2}$). The second level and the first level (with population $N_{1}$) are defined as the upper and lower lasing levels. Electrons are transferred from the upper level to the lower one by both spontaneous and stimulated emission. At last, electrons can perform the nonradiative transfer from the first level back to the ground one.
• Figure 3: The temporal dynamics (FDTD) of spatial distribution of the PP field generated by NEs in the ${7}\times{7}$ lattice of conducting NRs (see Fig. \ref{['Fig_Latt_Emitts']}) at $\omega _{p}=2.3$ THz at different simulating times $t_{f}$: (a) $20$, (b) $40$, (c) $60$, (d) $80$. The color coding represents values of the field amplitude.) At long times $t_f > 60$, the PP field, generated in the NR lattice by NEs, gradually covers nearly the entire NR lattice. The local field (shown by the red color) in the vicinity of NEs (see panel (a)) is the largest. The optical field is concentrated in gaps of the NR lattice and practically does not penetrate into the NRs.
• Figure 4: Dependencies $\omega _{\parallel }/\omega _{p}$ (a) and $\omega _{\perp }/\omega _{p}$ (b) on parameter $x=L_{n}/R$ in the interval $[0,10]$, see Eqs.(\ref{['w_parall']}) and (\ref{['T_dir']}) respectively. Dotted lines ((d) and (e)) show the approximate solutions. It is seen that such an approximation is correct only for $L_{n}/R<0.9$. At $x\approx 1.75$ the values of $\omega _{\parallel }$ and $\omega _{\perp }$ are close. The yellow dashed line (c) displays the function $y(x)$ from Eq.(\ref{['L_dir']}), and the black line (f) displays the asymptotic value $1/\sqrt{2}$ of the normalized surface plasmon frequency for $x \gg 1$.
• Figure 5: The temporal dynamics produced by the numerical solution of the system of Eq.(\ref{['MaxwellEqs']})-(\ref{['M_rateEq']}) for the $7\times 7$ NR lattice with two different plasma frequencies: $\omega _{p}=2.3\times 10^{-2}~$THz (the left) and $2.3$ THz (the left and right columns, respectively). Here (a) and (b) show the dynamics of populations $N_{1}$ and $N_{2}$ of the NE lasing levels, respectively (see Eq. ( \ref{['EqForN_12']}); the dynamics of populations $N_{0,3}$, see Eq. ( \ref{['EqForN_03']}), is not displayed here). (c,d) The average quantum polarization ${\mathbf{|P|}}$ and photocurrent $i_{ph}={\partial \mathbf{|P|}}/{\partial t}$. Panels (e) and (f) exhibit a drastic difference in the average current $\left\langle J\right\rangle$ (see Eq. (\ref{['averJ']})) in NRs at $\omega _{p}<\omega _{c}$ (the left) and $\omega _{p}>\omega _{c}$ ((e) and (f), respectively).