Nonlinear Polariton Fluids in a Flatband Reveal Discrete Gap Solitons

Phase frustration in periodic lattices is responsible for the formation of dispersionless flatbands. The absence of any kinetic energy scale makes flatband physics critically sensitive to perturbations and interactions. We report on the experimental investigation of the nonlinear response of cavity polaritons in the gapped flatband of a one-dimensional Lieb lattice. We observe the formation of gap solitons with quantized size and abrupt edges, a signature of the frozen propagation of switching fronts. This type of gap soliton belongs to the class of truncated Bloch waves, and has only been observed in closed systems up to now. Here, the driven-dissipative character of the system gives rise to a complex multistability of the flatband nonlinear domains. These results open up an interesting perspective regarding more complex 2D lattices and the generation of correlated photon phases.

Figure 1

(a) Schematic representation of the 1D Lieb lattice. Filled circles: localized eigenstate with relative phase indicated with signs. (b) Scanning electron microscopy image of a micropillar lattice. Inset: Schematic representation of a single pillar with embedded layers. (c) Energy resolved photoluminescence measured in momentum space under nonresonant pumping, for linear polarization parallel ($H$) and orthogonal ($V$) to the lattice. Solid lines: calculated dispersion solving a tight-binding Hamiltonian. For $H$ polarization, $E_A=E_C=1468.9\mathrm{meV}$, $E_B=E_C-0.30\mathrm{meV}$, and $t=t^{\prime }=0.30\mathrm{meV}$; for V polarization, $E_A=E_C+0.18\mathrm{meV}$, $E_B=E_C-0.30\mathrm{meV}$, and $E_C=1468.6\mathrm{meV}$, with the same $t$, $t^{\prime }$. Arrows indicate the energy $\hslash {\omega }_{H,V}$ and wave vector of the resonant pump.

Figure 2

(a),(b) Total emission intensity (a) measured and (b) calculated under resonant excitation tuned to energy $\hslash {\omega }_H$ as a function of power. (c) 2D real-space image of the excitation spot. Black line: spatial profile integrated over the transverse direction. (d)–(g) Real-space emission intensity measured at pumping powers indicated in (a). Highly excited micropillars are indicated by circles. (h),(i) Size of the nonlinear domains (h) measured and (i) calculated as a function of (h) excitation power, (i) $F^2$.

Figure 3

Total intensity measured under resonant excitation of the flatband (same excitation parameters as in Fig. 2) when scanning the excitation power up and down as indicated by arrows. (b)–(e) Real-space emission patterns measured for $P=10.2\mathrm{mW}$ on different branches as indicated in (a).

Figure 4

(a) Total intensity measured as a function of excitation power under $V$ polarized excitation tuned to an energy $\hslash {\omega }_V$. (b) Corresponding calculated intensity as a function of $F^2$. In (a) and (b), blue (red) color corresponds to increasing (decreasing) excitation power. (c),(d) Spatially resolved emission represented in logarithmic color scale measured for $P=19\mathrm{mW}$ (c) in the dispersive ($V$ polarized pump) and (d) in the flatband ($H$ polarized pump). (e),(f) Measured integrated intensity on $C$ sites extracted from (c),(d). Black lines, pump spot profile; red line, exponential fit of the emission intensity spatial decay. (g),(h) Calculated intensity on $C$ sites for (g) a dispersive band ($E_A=6\gamma$) and (h) a flatband ($E_A=0$) considering (g) $\mathrm{\Delta }=3\gamma$, $F^2=300$ and (h) $\mathrm{\Delta }=2\gamma$, $F^2=30$.