Reconfiguration of quantum states in $\mathcal PT$-symmetric quasi-one dimensional lattices

TL;DR

This paper explores how quantum states in quasi-one-dimensional lattices with parity-time symmetry can be reconfigured through energy gain and loss, revealing phase transitions and transport properties in non-Hermitian systems.

Contribution

It demonstrates control of quantum transport in $ ext{PT}$-symmetric lattices and maps the phase diagram including exceptional points and symmetry-breaking transitions.

Findings

Transport occurs only in unbroken $ ext{PT}$ phases.

Broken phases exhibit symmetry-broken states with degenerate eigenstates.

Degeneracies are lifted in the complex energy plane due to non-Hermiticity.

Abstract

We demonstrate mesoscopic transport through quantum states in quasi-1D lattices maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss. We investigate the phase diagram of the non-Hermitian system where transitions take place between unbroken and broken $\mathcal{PT}$-symmetric phases via exceptional points. Quantum transport in the lattice is measured only in the unbroken phases in the energy band-but not in the broken phases. The broken phase allows for spontaneous symmetry-broken states where the cross-stitch lattice is separated into two identical single lattices corresponding to conditionally degenerate eigenstates. These degeneracies show a lift-up in the complex energy plane, caused by the non-Hermiticity with $\mathcal{PT}$-symmetry.