Lesson 3. Double-well BJJ oscillation dynamics (OL 0-step)

This study is a preparation step for the understanding of the many-body physics in optical lattices (OL) with MCTDHB. The main physical goal of this study is to show that in a relatively deep double-well system the tunnelling time can be approximatively described by a single parameter J=<φL h φR>. We study the following scenario: Initially system is prepared in a left well, then we let it evolve and monitor its oscillations.

Period of the one-particle oscillations can be computed:

  1. Exactly, i.e., defined by the energy difference between ground and first excited states T=2π/(E1-E0)

  2. Approximately,  T=π/J=π/L h φR>

 Here we deal with  a non-interacting system, i.e., it is described at MCTDHB(1), as a result you will create this picture and understand the dynamics behind:

 


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1) Define a new quantum system in terms of the many-body physics.