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.

6 pages, 3 figure, to appear in EPL

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• Exponentially Fragile PT-Symmetry in Lattices with Localized Eigenmodes
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
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Cited by in corpus (11)

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• Wave emission and absorption at spectral singularities
• Quantum Phase Transition in a Quantum Ising Chain at Nonzero Temperatures
• New perspective on chiral exceptional points with application to discrete photonics
• Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity
• Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain
• Probing the superfluid-insulator phase transition by a non-Hermitian external field
• 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