Demonstration of a two-dimensional PT-symmetric crystal: Bulk dynamics, topology, and edge states
arXiv:1809.00041
Abstract
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time (PT) symmetry transformations likewise can exhibit real eigenvalue spectra. These findings had a particularly profound impact in the field of photonics, where PT-symmetric potential landscapes can be implemented by appropriately distributing gain and loss. Following this approach, several hallmark features of PT symmetry were shown, such as the existence of non-orthogonal eigenmodes, non-reciprocal light evolution, diffusive coherent transport, and to study their implications in settings including PT-symmetric lasers and topological phase transitions. Similarly, PT-symmetry has enriched other research fields ranging from PT-symmetric atomic diffusion, superconducting wires, and PT-symmetric electronic circuits. Nevertheless, to this date, all experimental implementations of PT-symmetric systems have been restricted to one dimension, which is mostly due to limitations in the technologies at hand for realizing appropriate non-Hermitian potential landscapes. In this work, we report on the experimental realization and characterization of a two-dimensional PT-symmetric system by means of photonic waveguide lattices with judiciously designed refractive index landscape with alternating loss. A key result of our work is the demonstration of a non-Hermitian two-dimensional topological phase transition that coincides with the emergence of mid-gap edge states. Our findings pave the grounds for future investigations exploring the full potential of PT-symmetric photonics in higher dimensions. Moreover, our approach may even hold the key for realizing two-dimensional PT-symmetry also in other systems beyond photonics, such as matter waves and electronics.
References in corpus (10)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Complex Extension of Quantum Mechanics
- Experimental Study of Active LRC Circuits with PT-Symmetries
- Spawning rings of exceptional points out of Dirac cones
- Probing topological invariants in the bulk of a non-Hermitian optical system
- Edge states and topological phases in non-Hermitian systems
- Simulation and detection of Dirac fermions with cold atoms in an optical lattice
- PT-symmetry in honeycomb photonic lattices
- Bifurcation diagram and pattern formation in superconducting wires with electric currents
- Zero modes and the edge states of the honeycomb lattice