Experimental Observation of Dynamical Localization in Laser-Kicked Molecular Rotors

The periodically kicked rotor is a paradigm system for studying quantum effects on classically chaotic dynamics. The wave function of the quantum rotor localizes in angular momentum space, similarly to Anderson localization of the electronic wave function in disordered solids. Here, we observe dynamical localization in a system of true quantum rotors by subjecting nitrogen molecules to periodic sequences of femtosecond pulses. Exponential distribution of the molecular angular momentum—the hallmark of dynamical localization—is measured directly by means of coherent Raman scattering. We demonstrate the suppressed rotational energy growth with the number of laser kicks and study the dependence of the localization length on the kick strength. Because of its quantum coherent nature, both timing and amplitude noise are shown to destroy the localization and revive the diffusive growth of energy.

Figure 1

Rotational Raman spectrum of nitrogen molecules excited with a train of $N=24$ pulses at a kick strength of $P=2.3$ for 20 different periodic (a) and nonperiodic (b) sequences. (c) The average experimental distributions (solid lines) are compared to the numerical simulations (dashed lines) for both the periodic (middle red lines) and the nonperiodic (upper black lines) pulse trains. The initial distribution is shown by the lower gray lines. (d) The exact calculated populations (dashed lines) and the approximate populations (solid lines), retrieved from the experimental Raman signal as discussed in the text. The retrieved populations are fitted with an exponential or Gaussian function (thick green lines). The dotted vertical line represents the excitation limit due to the finite pulse duration.

Figure 2

Evolution of the molecular angular momentum distribution with the number of kicks $N$ (each of strength $P=2.3$) for a periodic (a) and nonperiodic (b) excitation. Respective exponential and Gaussian fits, shown individually in the lower plots, indicate the changes of the distributions at $N=8$, 16, and 24 (thick green lines, see text for distribution widths). The dotted vertical line represents the excitation limit due to the finite pulse duration.

Figure 3

Angular momentum distributions after 24 pulses of a periodic (a) and nonperiodic (b) train for three kick strengths: $P=1$ (dotted line), $P=2$ (solid line), and $P=3$ (dashed line). The dotted vertical line represents the excitation limit due to the finite pulse duration.

Figure 4

Rotational energy as a function of the number of kicks $N$ with a mean strength of $P=2.3$. Compared are the experimentally retrieved energies (connected symbols) with the numerically calculated ones (lines), for a periodic sequence (red squares, dashed line), and the same sequence after the introduction of amplitude noise (blue triangles, dash-dotted line) or timing noise (black circles, dotted line).