Experimentally Realizable PT Phase Transitions in Reflectionless Quantum Scattering

Above-barrier quantum scattering with truncated real potentials V(x)=-|x|^{p} provides an experimentally accessible platform that exhibits spontaneous parity-time symmetry breaking as p is varied. The unbroken phase has reflectionless states that correspond to bound states in the continuum of the nontruncated potentials at arbitrarily high discrete real energies. In the fully broken phase there are no bound states. There is a mixed phase in which exceptional points occur at specific energies and values of p. These effects should be observable in cold-atom scattering experiments.