Significantly stable mode of the ultracold atomic wave packet in amplitude-modulated parabolic optical lattices

We show that a conspicuous wave packet of ultracold noninteracting bosonic atoms emerges in a one-dimensional parabolic optical lattice as in the setup of the Aarhus experiment [P. L. Pedersen, M. Gajdacz, N. Winter, A. J. Hilliard, J. F. Sherson, and J. Arlt, Phys. Rev. A 88, 023620 (2013)], given the lattice height is harmonically modulated with a particular amplitude at a resonant frequency. We show that this four-band periodic wave packet (4B PWP) executes stable timewise periodic motion for an infinitely long time. We apply the Floquet theory to analyze the parameter dependence of the 4B PWP in detail. Our analysis shows that it consists mainly of two principal Floquet eigenstates of the periodically driven Hamiltonian. The informative Husimi representation yields temporal slices of the phase space of the 4B PWP, visually identifying moments where the interband transitions take place. The provided data should aid the experiment in locating the 4B PWP.