Looped Bloch Bands and Nonlinear Landau-Zener Tunneling of Bose-Einstein Liquid Droplets in Optical Lattices
Yu-Wen Wang1,3, Szu-Cheng Cheng2, Wen-Hsuan Kuan3*
1Graduate Institute of Photonics and Optoelectronics, National Taiwan University, Taipei, Taiwan
2Department of Optoelectric Physics, Chinese Culture University, Taipei, Taiwan
3Department of Applied Physics and Chemistry, University of Taipei, Taipei, Taiwan
* Presenter:Wen-Hsuan Kuan, email:wenhsuan.kuan@gmail.com
By solving the Lee-Huang-Yang amended time-dependent Gross-Pitaevskii equation, this work theoretically investigates the Bloch oscillations and the formation of discrete solitons of the dilute Bose-Einstein liquid droplets in the deep optical lattices. Employing the temporal super-Gaussian envelope function with the localized Wannier wavefunction basis establishes the energy functional for determining the stationary properties of the droplets. The long-term evolution of the characteristic parameters and the breathing and self-trapping of the droplets are observed by solving Euler-Lagrange equations. The derivation of the group velocity and the effective mass from the effective Hamiltonian under the effective mass approximation helps position the soliton's center of mass by solving a force-driven and damped spring-mass second-order differential equation.
We further investigate the Landau-Zener tunneling of droplets in accelerating shallow optical lattices. The dynamics of the droplet is described by a coupled nonlinear Schrödinger equation in the two-level plane-wave approximation. The analytical solutions of the eigenvalue equation are the roots of a quartic equation, from which the looped Bloch bands can be formed in the near adiabatic regime as the nonlinear effects present. It is found that the Lee-Huang-Yang interaction depresses the nonlinear Landau-Zener tunneling in the nonadiabatic regimes that preserve the Bloch oscillations and the system's stability.


Keywords: Bose-Einstein liquid droplet, Optical lattice, Lee-Huang-Yang effect, Bloch oscillation, Nonlinear Landau-Zener tunneling