Tight-binding tunneling amplitude of an optical lattice
| Autor: | Bo Liu, Maksims Arzamasovs |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Physics
Optical lattice 010102 general mathematics Scanning tunneling spectroscopy General Physics and Astronomy Semiclassical physics 01 natural sciences Particle in a one-dimensional lattice Amplitude Tight binding Linear combination of atomic orbitals Quantum mechanics 0103 physical sciences 0101 mathematics 010306 general physics Quantum tunnelling |
| Zdroj: | European Journal of Physics. 38:065405 |
| ISSN: | 1361-6404 0143-0807 |
| DOI: | 10.1088/1361-6404/aa8d2c |
| Popis: | The particle in a periodic potential is an important topic in an undergraduate quantum mechanics curriculum and a stepping stone on the way to more advanced topics, such as courses on interacting electrons in crystalline solids, and graduate-level research in solid-state and condensed matter physics. The interacting many-body phenomena are usually described in terms of the second quantized lattice Hamiltonians which treat single-particle physics on the level of tight-binding approximation and add interactions on top of it. The aim of this paper is to show how the tight-binding tunneling amplitude can be related to the strength of the periodic potential for the case of a cosine potential used in the burgeoning field of ultracold atoms. We show how to approach the problem of computing the tunneling amplitude of a deep lattice using the JWKB (Jeffreys–Wentzel–Kramers–Brillouin, also known as semiclassical) approximation. We also point out that care should be taken when applying the method of the linear combination of atomic orbitals (LCAO) in an optical lattice context. A summary of the exact solution in terms of Mathieu functions is also given. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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