Emergence of the exceptional surface of a two level system coupled with 1D energy continuum

Yujin Dunham (Osaka Prefecture U.)

Exceptional points have been associated with many intriguing phenomena in non-Hermitian physics, such as enhanced sensing [1].  Recently, Zhou, et alhave reported the appearance of a multi-dimensional surface of exceptional points (an exceptional surface) appearing in the parameter space of a non-Hermitian Hamiltonian exhibiting parity-time (PT) symmetry [2].  However, in their model the dissipation has been introduced in a phenomenological manner that ignores the underlying microscopic structure of a true quantum reservoir.  By contrast, in our work we apply complex spectral analysis to a variation of the Friedrichs Hamiltonian, which describes the interaction of a discrete state with a continuum that represents a 1D microscopic reservoir.  We generalize the Friedrichs model by incorporating the spin degree of freedom, which can be flipped by a local magnetic field that acts on the discrete site.  By applying a projection operator method, we obtain a non-Hermitian effective Hamiltonian exhibiting explicit eigenvalue dependence without introducing any phenomenological approximation.  The explicit eigenvalue dependence of the Hamiltonian results in a non-linear eigenvalue problem, which we show is related to the appearance of an exceptional surface in the parameter space of our exact model.
[1] J. Wiersig, Phys. Rev. Lett. 112, 203901 (2014)
[2] H. Zhou et al, Optica 6, 020190 (2019)