Polarized edge state emission from topological spin phases of trapped Rydberg excitons in ${\mathrm{Cu}}_2\mathrm{O}$

In one-dimensional chains of trapped Rydberg excitons in cuprous oxide semiconductor the topological spin phase has been recently predicted [Phys. Rev. Lett. 123, 126801 (2019)]. This phase is characterized by the diluted antiferromagnetic order of $p$-shell exciton angular momenta-1 and the edge states behaving akin to spin-$1/2$ fermions. Here we study the properties of the ground state in the finite chains and its fine structure resulting from the effective interaction of the edge spins. We demonstrate that these edge states can be detected optically via the enhancement of the circular polarization of the edge emission as compared with the emission from the bulk. We calculate the distribution of the exciton angular momentum vs. trap number in the chain numerically and analytically based on the variational ansatz.

Figure 1

(a) Schematics of the circularly polarized emission from the diluted antiferromagnetic state of $p$-shell Rydberg excitons in an array of traps. (b) Representation of diluted antiferromagnetic order by a chain of spins-1/2 with singlet coupling.

Figure 2

Energy spectrum of the chain with open boundary conditions as function of the number of excitons $N$. For each $N$ we show only seven lowest states, energies are counted from the lowest one. Four states converging to the degenerate ground state in the limit of infinite chain are shown by red squares and circles. Three lowest energy magnon excitations with $S_z=0$ and $S_z=\pm 1$ are shown by blue triangles.

Figure 3

(a) Spatial distribution of the angular momentum $\langle L_j^z\rangle$ for two lowest states (downward-pointing triangle) and two second-lowest states (upward-pointing triangle). Inset shows the dependence $\langle L_j^z\rangle$ for the lowest state. Red curve shows the fit to Eq. (6). Blue circles show the decay of the Néel correlator squared $|C_{\text{Néel}}{\left(j\right)|}^2$, Eq. (13), calculated for the infinite chain via ITEBD approach, see text for details. Chain length is $N=16$. (b) Spatial distribution of the angular momentum ${\langle L_j^z\rangle }^2$ for the third state depending on the number of excitons in a chain.