Experimentally-realizable PT phase transitions in reflectionless quantum systems

Although parity-time (PT) reversal symmetry has been measured in classical wave equations, the fundamental physical symmetry has yet to be measured in lossless fundamental quantum mechanics, where PT-symmetry theory was originally developed. We show theoretically that standard cold-atom experiments with programmable traps could be used to observe both eigenstates of PT-symmetric systems and PT-symmetry breaking behavior in fundamental quantum scattering systems. We demonstrate that weakly bound states predicted for the upside-down PT-symmetric potentials V(x)=-x^4, -x^6, -x^8 can be measured to arbitrarily high accuracy as reflectionless states in the truncated purely real potential V(x)=-|x|^p for positive parameter p. Quantum scattering calculations indicate the measurements are robust to experimental error. In addition, spontaneous PT-symmetry-breaking can be measured as a function of p. In the unbroken phase, there exist an infinite number of reflectionless states at real energies; in the broken phase, there are no real-eigenenergy solutions; and in the mixed phase, exceptional points are measurable with their signature quartic dips in the reflection coefficient. The findings invite a hunt for PT-symmetry behaviors in near-threshold atomic scattering systems.