Two-level systems with periodic $N$-step driving fields: Exact dynamics and quantum state manipulations

TL;DR

This paper derives exact solutions for two-level quantum systems driven by periodic N-step fields, revealing diverse phenomena and providing a general formula for transition probabilities applicable across parameter regimes, with applications in quantum state control.

Contribution

It introduces an exact analytical approach for N-step driven two-level systems, enabling precise description of dynamics and transition probabilities across various parameters.

Findings

Transition probability expressed by cosine functions with discrete frequencies

Few main frequencies suffice to describe system dynamics

Beating phenomena occur when main frequencies are similar

Abstract

In this work, we derive exact solutions of a dynamical equation, which can represent all two-level Hermitian systems driven by periodic $N$-step driving fields. For different physical parameters, this dynamical equation displays various phenomena for periodic $N$-step driven systems. The time-dependent transition probability can be expressed by a general formula that consists of cosine functions with discrete frequencies, and, remarkably, this formula is suitable for arbitrary parameter regimes. Moreover, only a few cosine functions (i.e., one to three main frequencies) are sufficient to describe the actual dynamics of the periodic $N$-step driven system. {Furthermore}, we find that a beating in the transition probability emerges when two (or three) main frequencies are similar. Some applications are also demonstrated in quantum state manipulations by periodic $N$-step driving fields.