Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
Dipartimento di Fisica, Politecnico di Milano - Piazza L. da Vinci 32, I-20133 Milano, Italy and Istituto di Fotonica e Nanotecnlogie del Consiglio Nazionale delle Ricerche, sezione di Milano Piazza L. da Vinci 32, I-20133 Milano, Italy
Received: 3 March 2014
Accepted: 14 April 2014
The spectral and transport properties of a non-Hermitian tight-binding lattice with unidirectional hopping are theoretically investigated in three different geometrical settings. It is shown that, while for the infinitely-extended (open) and for the ring lattice geometries the spectrum is complex, lattice truncation makes the spectrum real. However, an exceptional point of order equal to the number of lattice sites emerges. When a homogeneous dc force is applied to the lattice, in all cases an equally-spaced real Wannier-Stark ladder spectrum is obtained, corresponding to periodic oscillatory dynamics in real space. Possible physical realizations of non-Hermitian lattices with unidirectional hopping are briefly discussed.
PACS: 42.82.Et – Waveguides, couplers, and arrays / 03.65.-w – Quantum mechanics / 11.30.Er – Charge conjugation, parity, time reversal, and other discrete symmetries
© EPLA, 2014