Fig. 1. Two-dimensional quantum walk in non-Hermitian synthetic lattice.
a Example of photonic quantum walk in a 2D synthetic lattice. The blue and red curved arrows show the direction-dependent loss and gain. b Winding of effective eigenenergies ϵup/down(kx, ky) in the complex energy plane for a single bulk non-Hermitian lattice with periodic boundary condition, showing line-gapped topology (indicated by the green line). Here we choose five different values ky ≡ 0, ± π/4, ± 3π/8. c Four bulk lattices with different gain-loss patterns are glued along their edges to form a corner. Note that δx > 0 implies gain for a step towards −X and loss for a step toward +X. For δx < 0 the gain-loss is inverted. A similar rule applies for δy. d Averaged spatial profile of corner skin modes formed in the system shown in c, by taking non-Hermitian parameters δx = δy = 0.175. The lattice size is 30 × 30. e The time-multiplexed experimental scheme, with which the lattice parameters can be (dynamically) controlled by the intensity modulators. EDFA: Erbium-doped fiber amplifier. PD: Photodiode.