Moiré-Induced Optical Nonlinearities: Single- and Multiphoton Resonances

Moiré excitons promise a new platform with which to generate and manipulate hybrid quantum phases of light and matter in unprecedented regimes of interaction strength. We explore the properties in this regime, through studies of a Bose-Hubbard model of excitons coupled to cavity photons. We show that the steady states exhibit a rich phase diagram with pronounced bistabilities governed by multiphoton resonances reflecting the strong interexciton interactions. In the presence of an incoherent pumping of excitons we find that the system can realize single- and multiphoton lasers.

Figure 1

(a) Band configuration of the intralayer and interlayer excitons. (b) Schematic representation of spatially localized hybrid excitons in a microcavity. (c) Enlargement of typical polariton, photon, and exciton dispersions, for $a_M=5\mathrm{nm}$, $\mathrm{\Omega }=15\mathrm{meV}$ and $m_c=5\times {10}^{-5}{m}_e$, with $m_e$ the electron mass.

Figure 2

(a) Stability phase diagram: black (grey) regions correspond to low (high-density) phases, separated by a bistability region (orange). Exciton number as a function of $f/U_X$ and $\mathrm{\Delta }{\omega }_X/U_X$, at $\mathrm{\Delta }{\omega }_c/U_X=-1$, showing hysteresis for: (b) increasing $f/U_X$; and (c) decreasing $f/U_X$. (d) Purity of the steady state at $\mathrm{\Delta }{\omega }_X/U_X=1.2$, for the two hysteretic branches, of increasing (decreasing) $f/U_X$ [black (orange)]. (e) Stability phase diagram showing the effects of saturation, with ${\mathrm{\Omega }}_{\mathrm{sat}}=\mathrm{\Omega }/4$.

Figure 3

Exciton amplitude $|⟨\widehat{x}⟩|$ for $\mathrm{\Delta }{\omega }_X/U_X=1.2$, and $\mathrm{\Delta }{\omega }_c/U_X=1$. We show the EGP (black dotted line), self-consistent on-site diagonalization (red dashed line), and noninteracting excitons (solid green line).

Figure 4

Photon amplitude $n_{\alpha }=|\alpha {|}^2$ as a function of $\delta$ for $\mathrm{\Omega }/U_X=1/12$ (red dashed line), $\mathrm{\Omega }/U_X=1/8$ (green dash-dotted line), $\mathrm{\Omega }/U_X=1/6$ (black dash-dotted line), we fix ${\mathrm{\Gamma }}_x/U=1/10{\mathrm{\Gamma }}_x/{\gamma }_X=6$, ${\mathrm{\Gamma }}_x/{\gamma }_c=3$. (inset, left) Photon amplitude as a function of $2{\mathrm{\Omega }}^2/(U_X{\gamma }_c)$ for varying $\mathrm{\Omega }$. Single-particle transitions $\delta /U_X=0$ (red dashed line) and $\delta /U_X=-1$ (black dash-dotted line) and $\delta /U_X=-1/2$ (blue dash-dotted line). (Inset, right) Sketch of the exciton level scheme and the photon transitions, the wavy red arrow illustrates the one-photon resonance $|2⟩\to |1⟩$, while the green wavy arrows depict a two-photon process.