Periodically Driven Three-Level Systems

TL;DR

This paper investigates the dynamics of a three-level quantum system driven periodically, analyzing both adiabatic and non-adiabatic regimes, and applies the findings to nitrogen vacancy centers in diamond.

Contribution

It introduces a comprehensive analytical and numerical framework for understanding driven three-level systems with uniaxial anisotropy, including the effects of cascaded SU(3) LZSM interferometers.

Findings

Analytical results match numerical probabilities in weak and strong driving limits.

Derived a general theory for adiabatic passages in forbidden transition scenarios.

Observed multiple LZSM interference patterns in the system.

Abstract

We study the dynamics of a three-level system (ThLS) sinusoidally driven in both longitudinal and transverse directions and in the presence of a uniaxial anisotropy $D$ entering the generic Hamiltonian through the zero-energy splitting term $D(S^{z})^{2}$ where $S^{z}$ is the projection of the spin vector along the quantization direction. As a consequence of the addition of this term, the order of the symmetry group of the Hamiltonian is increased by a unit and we observe a sequence of cascaded $SU(3)$ Landau-Zener-St\"uckelberg-Majorana (LZSM) interferometers. The study is carried out by analytically and numerically calculating the probabilities of non-adiabatic and adiabatic evolutions. For non-adiabatic evolutions, two main approximations based on the weak and strong driving limits are discussed by comparing the characteristic frequency of the longitudinal drive with the amplitudes of driven fields. For each of the cases discussed, our analytical results quite well reproduce the gross temporal profile of the exact numerical probabilities. This allows us to check the range of validity of analytical results and confirm our assumptions. For adiabatic evolutions, a general theory is constructed allowing for the description of adiabatic passages in arbitrary ThLSs in which direct transitions between states with extremal spin projections are forbidden. A compact formula for adiabatic evolutions is derived and numerically tested for some illustrative cases. Interference patterns demonstrating multiple LZSM transitions are reported. Applications of our results to the Nitrogen Vacancy Center (NVC) in diamond are discussed.