Directed transport and Floquet analysis for a periodically kicked wave packet at a quantum resonance

The dynamics of a kicked quantum mechanical wave packet at a quantum resonance is studied in the framework of Floquet analysis. It is seen how a directed current can be created out of a homogeneous initial state at certain resonances in an asymmetric potential. The almost periodic parameter dependence of the current is found to be connected with level crossings in the Floquet spectrum.

Figure 1

Rate of momentum increase on an initially homogeneous wave function for $a=0.3$, as a function of potential strength $U_0$, assuming the form of Eq. (36) for the potential. (b)–(e) are close-ups of the full curve shown in (a).

Figure 2

Floquet eigenvalues ${\omega }_{x_0}^{\mu }$ as functions of $x_0$ for four choices of potential strength $U_0$. There appears a level crossing at $x_0\approx 0.4$ for $U_0=3.3$ which disappears again for larger $U_0$; this signals a sharp feature in the curve for the force $F$ in Fig. 1. Because of periodicity, only the range $0<x<\pi ∕2$ is displayed.

Figure 3

Floquet eigenvalues ${\omega }_{x_0}^{\mu }$ as functions of $x_0$ for four choices of potential strength $U_0$. The level crossing coincides with the sharp minima of the force curve in Fig. 1.

Figure 4

Floquet eigenvalues ${\omega }_{x_0}^{\mu }$ as functions of $x_0$ for four choices of potential strength $U_0$.

Figure 5

A selection of eigenvector components ${\alpha }_{x_{0}l}^{\mu }$ as functions of $x_0$, for a few choices of $U_0$.