Formations of generalized Wannier-Stark ladders: Theorem and applications
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| Format: | Preprint |
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2024
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| _version_ | 1866912201875390464 |
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| author | Zhang, H. P. Song, Z. |
| author_facet | Zhang, H. P. Song, Z. |
| contents | The Wannier-Stark ladder (WSL) is a basic concept, supporting periodic oscillation, widely used in many areas of physics. In this paper, we investigate the formations of WSL in generalized systems, including strongly correlated and non-Hermitian systems. We present a theorem on the existence of WSL for a set of general systems that are translationally symmetric before the addition of a linear potential. For a non-Hermitian system, the WSL becomes complex but maintains a real energy level spacing. We illustrate the theorem using 1D extended Bose-Hubbard models with both real and imaginary hopping strengths. It is shown that the Bloch-Zener oscillations of correlated bosons are particularly remarkable under resonant conditions. Numerical simulations for cases with boson numbers $n=2$, $3$, and $4$ are presented. Analytical and numerical results for the time evolution of the $n$-boson-occupied initial state indicate that all evolved states exhibit quasi periodic oscillations, but with different profiles, depending on the Hermiticity and interaction strength. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formations of generalized Wannier-Stark ladders: Theorem and applications Zhang, H. P. Song, Z. Strongly Correlated Electrons Quantum Gases Quantum Physics The Wannier-Stark ladder (WSL) is a basic concept, supporting periodic oscillation, widely used in many areas of physics. In this paper, we investigate the formations of WSL in generalized systems, including strongly correlated and non-Hermitian systems. We present a theorem on the existence of WSL for a set of general systems that are translationally symmetric before the addition of a linear potential. For a non-Hermitian system, the WSL becomes complex but maintains a real energy level spacing. We illustrate the theorem using 1D extended Bose-Hubbard models with both real and imaginary hopping strengths. It is shown that the Bloch-Zener oscillations of correlated bosons are particularly remarkable under resonant conditions. Numerical simulations for cases with boson numbers $n=2$, $3$, and $4$ are presented. Analytical and numerical results for the time evolution of the $n$-boson-occupied initial state indicate that all evolved states exhibit quasi periodic oscillations, but with different profiles, depending on the Hermiticity and interaction strength. |
| title | Formations of generalized Wannier-Stark ladders: Theorem and applications |
| topic | Strongly Correlated Electrons Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2411.11897 |