A semiclassical theory of quasienergies and floquet wave functions

Tak‐San Ho, Shih‐I Chu, James V. Tietz

Xiaobing Luo, Qiongtao Xie, Biao Wu

We investigate the quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasienergies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasienergy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second-quantized model, we find also a triangular structure in the quantum quasienergy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasienergies is further explored by a semiclassical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasienergies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.

H. J. Korsch

Christophe De Beule, Steven Gassner, Spenser Talkington +1 more

We develop the Floquet-Bloch theory of noninteracting fermions on a periodic lattice in the presence of a constant electric field. As long as the field lies along a reciprocal-lattice vector, time periodicity of the Bloch Hamiltonian is inherited from the evolution of momentum in the Brillouin zone. The corresponding Floquet quasienergies yield the Wannier-Stark ladder with interband couplings included to all orders. These results are compared to perturbative results where the lowest-order interband correction gives the field-induced polarization shift in terms of the electric susceptibility. Additionally, we investigate electronic transport by coupling the system to a bath within the Floquet-Keldysh formalism. We then study the breakdown of the band-projected theory from the onset of interband contributions and Landau-Zener resonances in the band-resolved currents. In particular, we consider the transverse quantum-geometric response in two spatial dimensions due to the Berry curvature. In the strong-field regime, the semiclassical theory predicts a plateau of the geometric response as a function of field strength. Here, we scrutinize the conditions under which the semiclassical results continue to hold in the quantum theory.

Dmitry A. Telnov, Shih‐I Chu

In the framework of the Floquet formulation of time-dependent density functional theory we present several exact relations involving different parts of the quasienergy functional. These relations hold when the exact densities and exchange-correlation energy functional are employed. They can be used as useful constraints and tests when searching for the approximate forms of the time-dependent exchange-correlation functionals. The general results are illustrated on an exactly soluble model, Hooke's atom in a linearly polarized monochromatic laser field.

Maurice A. de Gosson