Exotic collective behaviors of giant quantum emitters in two-dimensional baths

TL;DR

This work investigates nonlocal light-matter interactions of giant atoms embedded in high-dimensional photonic reservoirs, focusing on a $2$D bath and extending insights to a $3$D environment. A nonperturbative resolvent framework yields exact two-atom dynamics, revealing geometry-dependent non-Markovian decay, bound states in the continuum, and excitation beats. Phase engineering of the nonlocal couplings enables highly directional (chiral) emission and robust decoherence-free dipole-dipole interactions in 3D, offering design principles for 2D quantum memories and high-dimensional quantum networks. Together, these results establish a versatile platform for manipulating light-matter interactions beyond the dipole approximation, with feasible experimental implementations in ultracold-atom lattices and superconducting circuits.

Abstract

Nonlocal light-matter interactions with giant atoms in high-dimensional environments are not only fundamentally intriguing for testing quantum electrodynamics beyond the dipole approximation but also crucial for building high-dimensional quantum networks and engineering multipartite entangled states. Given the enigmatic and largely uncharted collective signatures exhibited by multiple giant atoms within two-dimensional optical baths, we delve into their nonperturbative collective dynamics within the single-excitation subspace, focusing on the case where they are coupled to a common two-dimensional photonic reservoir and employing a resolvent operator approach. We demonstrate that precisely engineered atomic arrangements lead to unconventional quantum dynamics, featuring non-Markovianity-induced beats and long-lived bound states in the continuum, thereby providing a versatile platform for implementing two-dimensional quantum memory. Phenomenologically, we observe the emergence of exotic photon emission patterns in both two- and three-dimensional (3D) baths. The emission directions are shown to be precisely controllable on demand through exact phase engineering of the coupling parameters, enabling a highly efficient chiral light-matter interface. Moreover, our generalization to a 3D bath reveals that coherent dipole-dipole interactions can survive despite the coupling to a continuum of modes, a finding that challenges conventional wisdom regarding decoherence.

Figures (9)

• Figure 1: (a) Schematic representation: A pair of two-level GAs coupled to a photonic lattice with nearest-neighbor hopping $J$. We plot the Markovian (black solid lines) and non-Markovian (triangles) decay rates, along with the corresponding frequency shift $\delta\omega_{e}$ (red solid lines), as a function of detuning $\Delta$. The simulations in panels (b-c) [(d-e)] are performed by considering two coupled SGAs (DGAs), with the physical parameters specified in the legend. All panels share the identical coupling $g=0.2J$.
• Figure 2: (a)-(b) The antisymmetric population $|c_{-}(t)|^{2}$ for a pair of DGAs (SGAs) with different atomic size $n_{\blacklozenge}=1,3,5,7,9\, (n_{\hbox{$\blacksquare$}}=1,3,5,7)$. The latter is plotted in logarithmic scale. Panel (c) plots the integrated non-Markovian measure $\mathcal{I}(\Lambda,\rho_{1},\rho_{2})$ as a function of $Jt$ for SGAs with $n_{\hbox{$\blacksquare$}}\!=\!1$ by performing time evolution initiated from 10000 random initial state pairs $(\rho_{1},\rho_{2})$. The evolutionary trajectories maximizing the non-Markovianity $\mathcal{N}(\Lambda)$ are explicitly identified. Panels (a)-(c) share the same detuning $\Delta=0$, while the coupling strength is set to $g=0.01J$ in panel (a) and $g=0.25J$ in panels (b) and (c). We also plot the bath population $|C_{\boldsymbol{n}}^{\pm}(t)|$ in real space [(d)-(g)] at time $tJ=100$ with $g=0.2J$, where the performed physical parameters are specified in the legend.
• Figure 3: The functions$\max\limits_{\mu=\pm,\nu=\pm}[\mathcal{B}_{\mu,\nu}(t)]$ versus coupling phases $\varphi_{1},\varphi_{2},\varphi_{3}$ for a pair of (a) SGAs and (b) DGAs. Panels (c) and (d) are the bath population $|C_{\boldsymbol{n}}^{\pm}(t)|$ in real space at time $tJ=100$ with $g=0.2J$, utilizing the optimal parameters $\varphi_{p}$ obtained respectively from panels (a) and (b). Other physical parameters are specified in the legend.
• Figure 4: The bath population $|C_{\boldsymbol{n}}^{\pm}(t)|$ in 3D real space at time $tJ=50$ with $g=0.2J$ and $\ket{\psi(0)}=\ket{+}$ for three detuning regimes: $\Delta = 0$ (a), $\Delta = J$ (b), $\Delta = 2J$ (c). An overhead view in the inset of (a) is given. The analytical (markers) and numerical (solid lines) atomic population dynamics $\left|C_{1,2}(t)\right|^{2}$ are shown in panel (c) for the initial $\ket{eg}$ state using parameters $g=0.1J$, $\Delta = 0$, and $n=1$.
• Figure 5: (a) An integration contour (horizontal dark blue line) to calculate Eq. (\ref{['B1']}). One needs to close the contour of integration in the lower half of the complex plane (dashed and vertical dark blue line) to evaluate the integration. Here, the information includes bound-state energies, branch cuts detour, unstable poles, and band regions, within the lower half of the complex plane. Near the band edges, the integration contour transitions from the first Riemann sheet ($1^{{\rm st}}$ RS) to the second or third Riemann sheet ($2^{{\rm st}}$ RS and $3^{{\rm st}}$ RS, represented by the brown and cyan regions) when evaluating the integrand in Eq. (\ref{['B1']}). Notably, this transition occurs specifically at the band center when moving between the second and third Riemann sheets. Panels (b) and (c) describe the self-energies $\Sigma^{{\rm I}}_{\pm}(E)$ for a pair of DGAs and SGAs, respectively, with $n_{\blacklozenge}=1, n_{\hbox{$\blacksquare$}}=1,\Delta=0$, and $g=J$. Roots of the poles equation $z-\Delta-\Sigma^{{\rm I}}_{\pm}(z)=0$ are obtained from the intersection points between $E-\Delta$ (blue solid line) and $\Sigma^{{\rm I}}_{\pm}(E)$ (red/cyan solid lines).