Method and stability to control the quantum state with wave-shape manipulation of chirped laser pulse

The method to control quantum states by using a time-periodic external field is called Floquet engineering [1,2]. The standard Floquet theory is applicable to ideal systems irradiated by a continuous wave. It has succeeded in revealing various characteristics of Floquet engineerings. However, in experiments, pulse lasers have been often used rather than continuous waves. 

Recently, Ikeda, et al (2022), revealed that the time evolution of systems driven by a pulse laser can be well described by the combination of the adiabatic time evolution of Floquet states and the Landau-Zener (LZ) transition between neighboring Floquet states.

Based on these backgrounds, in this research [3], we propose a stable ultrafast method to control quantum states by laser application with chirping [4] and changing pulse length. Chirping is the established technique of gradually changing laser frequency. We focus on a simple two-level system with up and down spin states as the target of laser. As in previous research, we show that the chirped pulse driven two-level system can be well described by combining Floquet theory and LZ tunneling. Using this method, we show that chirped laser makes the transition probability from up (down) to down (up) states approach to unity with high accuracy. We also show that the high transition probability (almost unity) is preserved in a wide parameter space: Namely, the chirped laser provides a stable way of controlling the transition probability rather than non-chirped pulses.