Non-Hermitian invisibility in tight-binding lattices

Abstract

A flexible control of wave scattering in complex media is of relevance in different areas of classical and quantum physics. Recently, great interest has been devoted to scattering engineering in non-Hermitian systems, with the prediction and demonstration of new classes of non-Hermitian potentials with unique scattering properties, such as transparent and invisible potentials or one-way reflectionless potentials. Such potentials have been found for both continuous and discrete (lattice) systems. However, wave scattering in lattice systems displays some distinct features arising from the discrete (rather than continuous) translational invariance of the system, characterized by a finite band of allowed energies and a finite speed of wave propagation on the lattice. Such distinct features can be exploited to realize invisibility on a lattice with methods that fail when applied to continuous systems. Here we show that a wide class of time-dependent non-Hermitian scattering potentials or defects with arbitrary spatial shape can be synthesized in an Hermitian single-band tight-binding lattice, which are fully invisible owing to the limited energy bandwidth of the lattice.

Anomalous non-Hermitian dynamical phenomenon on the quantum circuit

“…The degeneracy splitting. This figure shows that the NHSE, [1] the dynamical chiral phenomenon [27] and other non-Hermitian dynamical phenomena with the global space-transitional-symmetry break [28,[30][31][32]36] originate from the (periodic-boundary spectral) degeneracy splitting. [32] <xφ> 2…”

“…[14][15][16][17][18][19][20][21][22][23][24][25] It is regarded as the non-perturbative breakdown of Bloch theorem, [26] which leads to new physical phenomena. Recently, people theoretically predicted some anomalous non-Hermitian dynamical phenomena in the NHSE system, [27][28][29][30][31][32][33][34][35] for example, the edge burst phenomenon in a lossy quantum walk, [28] the invisibility phenomenon in tight-binding lattices. [30] In experiment, people implement part of non-Hermitian dynamical phenomena, [14,18,36] for example, the funneling phenomenon in the optic system.…”

“…Recently, people theoretically predicted some anomalous non-Hermitian dynamical phenomena in the NHSE system, [27][28][29][30][31][32][33][34][35] for example, the edge burst phenomenon in a lossy quantum walk, [28] the invisibility phenomenon in tight-binding lattices. [30] In experiment, people implement part of non-Hermitian dynamical phenomena, [14,18,36] for example, the funneling phenomenon in the optic system. [36] Generally, those NHSE experiments are constructed in the topolectrical circuits, [15,16,22] the photonic system [14,36] and the acoustics system, [24,25] which mostly are the classical system.…”