Anderson Localization in Periodically Kicked Molecules

The periodically kicked rotor is a text book example for deterministic chaos: Although an extremely simple system, the dynamics of a periodically kicked classical rotor can easily become chaotic. It was natural to use this model system in search for signs of chaos in a quantized systems. However, the discrete levels of a quantum rotor prevent chaotic dynamics. Instead, the periodically kicked quantum rotor exhibits new phenomena, like the quantum resonance or dynamical localization.

We investigate signs of quantum chaos in one of the simplest natural systems for a kicked rotor: A linear molecule interacting with a periodic train of short laser pulses.

The effect of quantum resonance occurs when the molecules are kicked with a period that equals the rotational period of the molecule, which is a few pico seconds for small diatomic molecules like nitrogen. Under this condition, the absorption of energy is strongly enhanced.

Equally interesting is the kicking with a period far detuned from the rotational period. Under this condition, the molecules become transparent to the laser kicks: No matter how much one kicks the molecules, they will not absorb any energy. Instead, the population distribution of the angular momentum states become exponentially localized, as shown in the picture. This effect is due to a mechanism closely related to Anderson localization. We are devising possible experiments in order to experimentally observe the Anderson-like localization in periodically kicked molecules.

Interesting new opportunities arise when one considers both regimes – quantum resonance and dynamical localization – at the same time. For example, consider two molecules with different moments of inertia and therefore different rotational periods, like 14N2 and 15N2¬. Due to the different time-scales it is possible to devise a pulse train which strongly excites one molecular species under the condition of quantum resonance, but leaves the other species unchanged under the condition of Anderson-like localization. Thereby, one can selective excite rotations in just one molecular species in a mixture. As seen in the picture, when kicking with a period of 8.4 ps, only for 14N2 higher rotational levels are excited, and vice versa for a period of 9.0 ps, only for 15N2 higher rotational levels are excited. The experiments were done by the group of Valery Milner from UBC, Canada.

References:

  1. S. Zhdanovich, C. Bloomquist, J. Floß, I. Sh. Averbukh, J. W. Hepburn, and V. Milner, "Quantum Resonances in Selective Rotational Excitation of Molecules with a Sequence of Ultrashort Laser Pulses", Phys. Rev. Lett. 109, 043003 (2012).
  2. J. Floß and I. Sh. Averbukh, "Quantum resonance, Anderson localization, and selective manipulations in molecular mixtures by ultrashort laser pulses", Phys. Rev. A 86, 021401(R) (2012).
  3. J. Floß, S. Fishman, and I. Sh. Averbukh, "Anderson localization in laser-kicked molecules", Phys. Rev. A 88, 023426 (2013).