Unified parameter for localization in isotope-selective rotational excitation of diatomic molecules using a train of optical pulses

Abstract

We obtained a simple theoretical unified parameter for the characterization of rotational population propagation of diatomic molecules in a periodic train of resonant optical pulses.The parameter comprises the peak intensity and interval between the pulses, and the level energies of the initial and final rotational states of the molecule. Using the unified parameter, we can predict the upper and lower boundaries of probability localization on the rotational level network, including the effect of centrifugal distortion. The unified parameter was tentatively derived from an analytical expression obtained by performing rotating-wave approximation and spectral decomposition of the time-dependent Schrödinger equation under an assumption of time-order invariance. The validity of the parameter was confirmed by comparison with numerical simulations for isotope-selective rotational excitation of KCl molecules.

Resonant Quantum Kicked Rotor as A Continuous-Time Quantum Walk

“…The experimental implementation of such momentum quantum walks was largely discussed in [18,19]. Similar observations on the interference patterns in the resonant quantum kicked rotor and possible analogies with quantum walks were reported in, e.g., [20][21][22][23][24][25][26][27]. Here, we discuss their equivalence from a general viewpoint first, showing a direct connection between the Hamiltonians describing the two processes and then by studying the probability distributions explicitly for exemplary initial states.…”

Localization in Rotational Excitation of Diatomic Molecules Induced by a Train of Optical Pulses

“…The correctness of the rotating-wave approximation was validated in J JM . 5 by numerical calculations in the previous report [10]. By dividing all the frequency parameters by B f , we obtain the model equation system as:…”

“…The mathematical modeling of molecular rotational excitation has been described in our previous report [10]. In the previous work, we assumed a constant transition probability between neighboring states for simplicity.…”

“…Localizations 1 and 2 depend on the amplitude, and localizations 3 and 4 are independent of it. We have already derived the unified parameter for the combination effect of localizations 1 and 2 [10]. The unified parameter comprises the peak amplitude and interval between the pulses as well as the level energies of the initial (J ¼ r) and final (J ¼ s) rotational states of the molecule.…”

“…We regard the molecular excitation as an extended class of CTQWs, and try to apply some mathematical methods developed for quantum walks to the present system. In a previous report, we proposed a mathematical model of molecular rotational excitation and derived a unified parameter to predict localization behavior and its dependence on the pulse amplitude under some simplifying assumptions [10]. In this paper, we introduce further general model equations and classify the types of localization from the viewpoint of physics.…”