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

Abstract

A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{P}\mathcal{T}$-symmetric Schrödinger equations that exhibit spontaneous $\mathcal{P}\mathcal{T}$ symmetry breaking despite having purely real potentials. These potentials are one-dimensional, inverted, and unstable and have the form $V(x)=-|x{|}^p$ ($p>0$), terminated at a finite length or energy to a constant value as $x\to \pm \infty$. The signature of unbroken $\mathcal{P}\mathcal{T}$ symmetry is the existence of reflectionless propagating states at discrete real energies up to arbitrarily high energy. In the $\mathcal{P}\mathcal{T}$-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. $\mathcal{P}\mathcal{T}$-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.

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Observation of parity-time symmetry breaking in a single spin system
• Quantum Gases in Optical Boxes
• A high-accuracy algorithm for designing arbitrary holographic atom traps
• Reflectionless excitation of arbitrary photonic structures: A general theory

Cited by in corpus (4)

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• Computation and Verification of Spectra for Non-Hermitian Systems
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