Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems

• URL: http://arxiv.org/abs/2404.02399v1
• Date: Wed, 3 Apr 2024 02:06:50 GMT
• Title: Extended Wannier-Stark ladder and particle-pair Bloch oscillations in dimerized non-Hermitian systems
• Authors: H. P. Zhang, Z. Song,
• Abstract summary: We show that although the energy levels can be complex, they are still equally spaced by a real Bloch frequency. We propose two types of dimerized non-Hermitian systems to demonstrate our results.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the Hermitian regime, the Wannier-Stark ladder characterizes the eigenstates of an electron in a periodic potential with an applied static electric field. In this work, we extend this concept to the complex regime for a periodic non-Hermitian system under a linear potential. We show that although the energy levels can be complex, they are still equally spaced by a real Bloch frequency. This ensures single-particle Bloch oscillations with a damping (or growing) rate. The system can also support standard two-particle Bloch oscillations under certain conditions. We propose two types of dimerized non-Hermitian systems to demonstrate our results. In addition, we also propose a scheme to demonstrate the results of electron-pair dynamics in a single-particle 2D $\mathcal{PT}$-symmetric square lattice.

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