Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping

Abstract

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.

arXiv comment6 pages, 3 figure, to appear in EPL

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• Wave emission and absorption at spectral singularities
• Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures
• Quantum decay in a topological continuum
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• New perspective on chiral exceptional points with application to discrete photonics
• Super Bloch Oscillation in a PT symmetric system
• Quantum decay and amplification in a non-Hermitian unstable continuum
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
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• Topological states at exceptional points
• Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
• Noisy Stark probes as quantum-enhanced sensors