Exotic Cooperative Quantum Optics of Moire Exciton Superlattices

Abstract

The unique properties of two-dimensional moire systems have been widely studied from many perspectives. However, relatively little work has explored how the real space structure of the moire systems can directly engender novel properties and functionalities. In this work, we exploit the feature that moire excitons naturally form an ordered superlattice with a lattice constant comparable to the wavelength of the resonant light, which enables intriguing cooperative optical responses. Particularly, we show that the collective moire exciton states can have either strongly enhanced (superradiant) or suppressed (subradiant) radiative decay rate, depending on their in-plane wavevector. These super- and subradiant states can be efficiently switched by a gate-induced electric field gradient. Moreover, the cooperative transmittance $T$ of the nanometer-thick moire system can be switched from $T \approx 0$ (opaque) to $T \approx 1$ (transparent) with less than $2~\%$ heterostrain or a $1^{\circ}$ adjustment in the twist angle $θ$. These features are robust against non-radiative losses and inhomogeneity, making the moire system a highly versatile platform for cooperative quantum optics with potential applications in e.g., single photon storage and switching.

Figures (4)

• Figure 1: (a) moiré potential and exciton lattice in real space. Upper panels shows a two-dimensional moiré potential landscape. Lower panel shows multiple localized moiré exciton states in each potential minimum, labeled by $\alpha$. In this work, we focus on the lowest energy $\alpha=1$ state. (b) Illustration of the electronic band structure of the moiré system in the unfolded Brillouin zone. The electron acquires an wave vecotr $q_i$ relevant to $K_T$ after vertical optical transition from $K_B$. (c, d) Real space wavefunction $\vert \langle r\vert \chi_{\alpha} \rangle \vert$ of (a) $\alpha=1$ and (b) $\alpha=2$ exciton with $\theta=0.2^{\circ}$. Blue (red) color denotes small (large) wavefunction amplitude.
• Figure 2: An ordered moiré superlattice. Each lattice site $R_n$ is modeled by a two-level system $\vert R_n \rangle$ and $\vert G_n \rangle$. The red arrow indicates the interactions among moiré excitons, characterized by the Green's function $G_{ij}$.
• Figure 3: (a) Collective radiative decay rate $\Gamma_{\nu}$ as a function of in-plane wavevector $k_{\parallel}$ for a finite lattice with approximately $50\times 50$ excitons. The dashed circle denotes the light cone with $\vert k_{\parallel} \vert = k_0$. (b, c) Real part of the wavefunction of the collective exciton in real space, i.e., $\mathrm{Re}[\langle R_n \vert \nu(k_{\parallel})\rangle]$. (b) and (c) correspond to two states with $\vert k_{\parallel}\vert > k_0$ and $\vert k_{\parallel}\vert < k_0$. Each pixel corresponds to moiré lattice site $R_n$. Blue (purple) color indicate positive (negative) values of the wavefunction. (d) A collective exciton state can be switched between super- to sub-radiant states by an electric field gradient $\beta$. The electric field is along out-of-plane $z$ direction, while the gradient is along the in-plane $x$ or $y$ direction.
• Figure 4: (a) Transmittance $T(\omega)$ as a function of frequency detuning $\omega-\omega_0$ with $\theta = 0.2^{\circ}$. (b) The electric field profile $\vert E(r) \vert^2$ at $\omega-\omega_0\approx 161~\rm GHz$, where $T(\omega)$ reaches the minimum at $\theta = 0.2^{\circ}$. Light is incident from left, and the fields $\vert E(r) \vert^2$ are normalized by $E_0^2$ with $E_0$ the incident field strength. (c) Minimum of $T$ as a function of inhomogeneous linewidth with $\theta=0.2^{\circ}$. (d) $T$ as a function of $\omega-\omega_0$ for varied $\theta$. The non-radiative linewidth is taken as $\gamma_{\rm nr} = 100~\rm GHz$ in these plots.