A non-Hermitian symmetric Bose–Hubbard model: eigenvalue rings from unfolding higher-order exceptional points

By Eva-Maria Graefe, U. Günther, H. Korsch, A. Niederle. 2008

205 citations recorded by the source corpus.

We study a non-Hermitian symmetric generalization of an N-particle, two-mode Bose–Hubbard system, modeling for example a Bose–Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analyzed drawing special attention to the occurrence and unfolding of exceptional points (EPs). We find that for vanishing particle interaction there are only two EPs of order N + 1 which under perturbation unfold either into [(N + 1)/2] eigenvalue pairs (and in the case of N + 1 odd, into an additional zero-eigenvalue) or into eigenvalue triplets (third-order eigenvalue rings) and (N + 1) mod 3 single eigenvalues, depending on the direction of the perturbation in parameter space. This behavior is described analytically using perturbational techniques. More general EP unfoldings into eigenvalue rings up to (N + 1)th order are indicated.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bae09e6eaa9a1c6ee774ab6c345d5c4801f20c3f

Citations in the corpus

• Nonlinear waves in PT -symmetric systems (2016, unknown): “…of PT -symmetric BEC models can be developed from a nonHermitian Bose-Hubbard model, where the gain-loss coefficient γ is introduced explicitly (Graefe et al., 2008; Graefe and Liverani, 2013; Graefe, Korsch, and Niederle, 2008): H = iγ(a†2a2 − a†1a1) + v(a†1a2 + a†2a1) + c(a†1a1 − a†2a2)2.”