Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from $S$ and $P_{x,y}$ photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Figure 1

(a) Scanning electron microscope image of a section of the 2D Lieb lattice. The enlarged image shows a schematic diagram of 1 unit cell and the 3 sublattices. (b) Lattice emission in energy-momentum space measured under low-power nonresonant excitation. White dotted lines correspond to bands calculated from the tight-binding model. (c)–(e) Emission in real space at the energies of the $S$ flat band (c), the AB band maxima (d) and the $P$ flat band (e). The white squares correspond to one unit cell as shown in (a) and the corresponding energies are shown by arrows in (b).

Figure 2

(a) Peak intensity and (b) full width at half maximum of the three lattice modes as a function of the sample irradiance in the vicinity of the condensation thresholds. (c)–(g) The far-field emission with increasing irradiance, with condensation occurring in (f) and (g). The sample irradiances are 620 (c), 1360 (d), 2180 (e), 4030 (f), and $5630\mathrm{kW}{\mathrm{cm}}^{-2}$ (g). The color scale is the same as that of Fig. 1. (h)–(j) Real space images of the lattice condensates. a.u. refers to arbitrary units.

Figure 3

(a) Color maps showing spatial energy variation of the $S$ flat band (a), AB band (b), and $P$ flat band (c) condensate emission constructed from experimental data above threshold.

Figure 4

$S_1$ linear Stokes parameter of the real space emission at the energies of the $S$ (a) and $P$ (b) flat band. The color scale is linear with red (blue) representing $H$ ($V$) polarization, depicted by arrows on either side of the color bar. (c),(d) Schematic of the nearest neighbor hopping processes for $S$, $P_x$, and $P_y$ orbitals, in the case of polarization-dependent hopping probabilities.