Perpetual emulation threshold of PT-symmetric Hamiltonians
We describe a technique to emulate the dynamics of two-level PT-symmetric spin Hamiltonians, replete with gain and loss, using the unitary dynamics of a larger quantum system. The two-level system in question is embedded in a subspace of a four-level Hamiltonian, with the exterior levels acting as reservoirs. The emulation time is normally finite, limited by the depletion of the reservoirs. We show that it is possible to emulate the desired behaviour of the PT-symmetric Hamiltonian without depleting the reservoir levels, by including an additional coupling between them. This extends the emulation time indefinitely, when in the unbroken symmetry phase of the non-unitary PT dynamics. We propose a realistic experimental implementation using dynamically decoupled magnetic sublevels of ultracold atoms.
Perpetual emulation threshold of PT-symmetric Hamiltonians; D. Trypogeorgos, A. Valdés-Curiel, I. B. Spielman, and C. Emary; Journal of Physics A: Mathematical and Theoretical 51 325302 (2018). doi:10.1088/1751-8121/aacc5e