Floquet Physics
Floquet Physics
With more than 35 years of experience of Martin Holthaus in this area, the physics of periodically driven quantum systems is a hallmark of the Condensed Matter Theory group. A common thread connecting a substantial part of our research concerns particles evolving in spatially periodic lattice potentials while being subjected to a time-periodic driving force: In such systems the Floquet states constitute spatio-temporal Bloch waves with a quasienergy dispersion relation which can be controlled and deliberately engineered by varying, e.g., the strength or the frequency of the drive.
A particularly simple example occurs in periodically driven single-band tight binding systems for which the width of the quasienergy band varies in accordance with a Bessel function of order zero, evaluated at the dimensionless scaled driving amplitude, as already reported in Phys. Rev. Lett. 69, 351 (1992). Our group has elaborated on the ramifications of this observation with particular emphasis on ultracold atoms in periodically modulated optical lattices, similar to the earlier prediction of a metal-insulator transition undergone by driven ultracold atoms in incomensurate optical lattices made in Phys. Rev. Lett 78, 2932 (1997).
For instance, it is known that the celebrated superfluid-to-insulator transition exhibited by ultracold atoms in optical lattices is controlled by the ratio of the interparticle interaction strength and the nearest-neighbor hopping matrix element; since the latter is effectively renormalized by a time-periodic driving force one can switch from the superfluid to the insulating phase and back by ramping the drive up and down again in an adiabatic manner. The following figure, presented in Phys. Rev. Lett. 95, 260404 (2005), illustrates this finding by depicting the time evolution of the momentum distribution for such a process. Our prediction was later confirmed experimentally by the Arimondo group in Pisa.
At the single-particle level the collapse of the quasienergy band at the zeros of the Bessel function, as realized in driven optical lattices, leads to a phenomenon termed dynamic localization, which we have discussed in a review article published as chapter 12 of the book "Dynamical Tunneling - Theory and Experiment" (Taylor and Francis CRC, 2011). Here we also have compared the anticipated ideal variation of the quasienergy band width with measurements made by the Arimondo group, even confirming the expected reversal of the sign of the renormalized hopping matrix element as shown below.
However, for large driving amplitudes the idealized Bessel function-like deformation of the lowest band is disrupted by the unavoidable couplings to higher bands, as is demonstrated in the following figure and explained in more detail in J. Phys. B: At. Mol. Opt. Phys. 49, 013001 (2016). In a laboratory experiment such a disruption will correspond to enhanced heating, and ultimately to the escape of the atoms from the lattice.