Fast and High Excitation Transport in Waveguide Quantum Electrodynamics

TL;DR

The paper investigates fast and high excitation transport in waveguide QED using two spatially separated chirally-coupled atomic arrays. By analyzing the singly-excited subspace and the non-Hermitian matrix $\mathcal{M}$ with complex eigenenergies $\mathcal{E}_n=\omega_n-i\gamma_n$, it shows that transport is governed by a few spectrally isolated right eigenstates localized in the destination array, enabling rapid convergence to a steady state. Importantly, finite nonreciprocal decay characterized by $D=(\gamma_R-\gamma_L)/(\gamma_R+\gamma_L)$ is essential to realize this enhanced transport, rather than relying on purely cascaded unidirectional schemes. The study reveals trade-offs between transport magnitude and speed as functions of $D$, $N$, and interatomic spacings $\xi_L,\xi_D,\xi_R$, and identifies a design principle based on spectral isolation of subradiant modes to achieve fast, directional energy transfer in wQED with potential quantum information applications.

Abstract

Waveguide quantum electrodynamics (wQED) with underlying collective and long-range atom-atom interactions has led to many distinct dynamical phenomena, including modified collective radiations and intriguing quantum correlations. It stands out as a unique platform to illustrate correlated photon transport, as well as to promise applications in quantum information processing. Here we manifest a fast and high atomic excitation transport by employing two separated chirally-coupled atomic arrays. This enhanced waveguide-mediated transport of excitations emerges due to the dominance of few subradiant right eigenstates that are spectrally isolated and spatially localized in the system's dynamics. Contrary to the instinct of applying the cascaded systems with unidirectional couplings to expedite direct and high excitation transport, the optimal system configurations in open wQED systems demand slight or finite nonreciprocal decay channels to facilitate energy transport by exploiting waveguide-mediated couplings. We also investigate the effect of the couplings' directionality and the scaling of atom number on the transport properties. Our results showcase the wide applicability in wQED platforms and provide insights into quantum engineering and quantum information applications.

Figures (11)

• Figure 1: Schematic of the system. A two-level atomic array coupled to a waveguide with asymmetric decay rates, $\gamma_L \ne \gamma_R$, corresponding to the left- and right-propagating modes. The atoms are divided into two spatially separated groups with a distance $x_D$ between them, each with interparticle spaces $x_L$ and $x_R$, respectively. A coherent drive with a Rabi frequency $\Omega$ is applied only to the atoms in the left group and the detuning of atoms in the rotating frame of the driving frequency is $\delta$. The coupling to the guided modes induces infinite-range or all-to-all dipole-dipole interactions among atoms, including coherent exchange and collective dissipation. This setting provides a minimal model for studying excitation transport between driven and undriven atomic arrays in the low-energetic excitation regime, where the spatial arrangement plays a key role in shaping the steady-state population distributions.
• Figure 2: Excitation transport $T_p$ and characteristic time $\tau$. (a) The dependence of $T_p$ on $\xi_L$ and $\xi_R$ at $\xi_D=1.5\pi$ and $D=0.5$. A total of $N=20$ atoms with $N_L=N_R$. (b) A cross-sectional cut in (a) with $\xi_L=1.8\pi$ (the light green line), where $T_p$ (black solid line) is plotted with the associated $\tau$ (orange dashed line) versus $\xi_R$. We observe that relatively high $T_p$ values coincide with relatively short $\tau$ values, indicating the optimal conditions of $\xi_R$ for efficient excitation transport from the driven group to the undriven one.
• Figure 3: Characterization of the steady states with high excitation transport. The parameters are chosen as $N = 20$, $D = 0.5$ for (a, b, c) $\xi_L = 1.8\pi$, $\xi_D = 1.5\pi$, $\xi_R = 1.158\pi$, and (d, e, f) $\xi_L = 1.96\pi$, $\xi_D = \xi_R=1.158\pi$, where we observe an optimal $T_p$ and $\tau$. (a) Site-resolved excitation profile $\tilde{P}_\mu$ of the steady state (gray bars) compared with that of the right eigenstate (orange bars) with the smallest eigenenergy magnitude, $|\mathcal{E}_0|$. This also corresponds to the mode with the minimal frequency shift $\omega_0$ of the interaction matrix $M$ as shown in (c), where most of the excitations are localized in the right group. (b) Spectrum of the steady-state population decomposed onto the normalized right eigenspace of $M$, ordered by ascending values of $|\omega_n|$. The dominant contribution results from the mode whose weight $\mathcal{E}_n^{-1}$ significantly exceeds all other components. (c) Complex eigenenergies $\mathcal{E}_n=\omega_n-i\gamma_n$ plotted in logarithmic scales in the complex plan. The orange dot marks the mode with minimal eigenenergy shift $|\omega_0|$, which lies closest to the origin compared to the rest of the modes (blue dots), showing a long-lived and spectrally isolated behavior. Similarly, (d) excitation profile $\tilde{P}_\mu$ and two right eigenstates (orange and green bars) with their spectral decomposition in (e) and complex energies in (f).
• Figure 4: The effect of directionality factor $D$ and scaling of atom number $N$. With the atoms equally partitioned ($N_L=N_R$), we find the optimal interatomic spacing configuration that indicates fast and high excitation transport and plot the associated $T_p$ and $\tau$ versus $D$ in (a) for $N=20$ and versus even total atom number $N$ in (b) for $D=0.5$. (c) The corresponding complex eigenenergy plots for $D=0.2$ (Blue dots) and $0.8$ (orange dots) in (a). (d) The corresponding spectrally-isolated modes for $N=30$ in (b).
• Figure 5: Phase diagrams of $T_p$ with respect to $\xi_L$ and $\xi_R$ in the range $[\pi, 2\pi]$, at fixed $\xi_D = 1.5\pi$ and $N_L = N_R = 5$, for different values of directionality $D$ (indicated at the top of each panel). As $D$ increases toward the unidirectional limit, the high-$T_p$ regions become broader but the values of $T_p$ decrease.