Experimentally-realizable $\mathcal{PT}$ phase transitions in reflectionless quantum scattering

TL;DR

This paper demonstrates experimentally accessible $ ext{PT}$ phase transitions in reflectionless quantum scattering with real, inverted potentials, revealing symmetry-breaking phenomena and exceptional points observable in cold-atom experiments.

Contribution

It introduces a new class of real, inverted potentials exhibiting $ ext{PT}$ symmetry breaking, including a mixed phase and exceptional points, with measurable effects in cold-atom setups.

Findings

Existence of reflectionless states in unbroken $ ext{PT}$ phase

Disappearance of reflectionless states in broken $ ext{PT}$ phase

Identification of exceptional points with quartic dip in reflectivity

Abstract

A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{PT}$-symmetric Schr\"odinger equations that exhibit spontaneous $\mathcal{PT}$ symmetry breaking despite having purely real potentials. These potentials are one-dimensional, inverted, and unstable and have the form $V(x) = - \lvert x\rvert^p$ ($p>0$), terminated at a finite length or energy to a constant value as $x\to \pm\infty$. The signature of unbroken $\mathcal{PT}$ symmetry is the existence of reflectionless propagating states at discrete real energies up to arbitrarily high energy. In the $\mathcal{PT}$-broken phase, there are no such solutions. In addition, there exists an intermediate mixed phase, where reflectionless states exist at low energy but disappear at a fixed finite energy, independent of termination length. In the mixed phase exceptional points (EPs) occur at specific $p$ and energy values, with a quartic dip in the reflectivity in contrast to the quadratic behavior away from EPs. $\mathcal{PT}$-symmetry-breaking phenomena have not been previously predicted in a quantum system with a real potential and no reservoir coupling. The effects predicted here are measurable in standard cold-atom experiments with programmable optical traps. The physical origin of the symmetry-breaking transition is elucidated using a WKB force analysis that identifies the spatial location of the above-barrier scattering.