The investigation of Landau – Zener transition in coupled three-particle systems

Sahel Ashhab

Mehdi Hosseini, Farrokh Sarreshtedari

Transition dynamics of a coupled two-particle quantum system is numerically investigated in a laser controlled Landau–Zener process. The effect of the laser parameters as well as the coupling strength of the particles on the Landau–Zener transition dynamics are investigated and discussed. It is shown that the coupling strength between the particles, which describes the ferromagnetic or antiferromagnetic behavior of the system, interestingly changes the uncoupled system transitions and introduces new intermediate states. The obtained results provide the required controlling parameters for optimal engineering of the quantum states.

Artur Mikhailovich Ishkhanyan

Sahel Ashhab

We consider the Landau-Zener problem for a multilevel quantum system that is coupled to an external environment. In particular, we consider a number of cases of three-level systems coupled to a harmonic oscillator that represents the external environment. We find that, similar to the case of the Landau-Zener problem with a two-level system, when the quantum system and the environment are both initially in their ground states the probability that the system remains in the same quantum state is not affected by the coupling to the environment. The final occupation probabilities of the other states are well described by a common general principle: the coupling to the environment turns each Landau-Zener transition process in the closed system into a sequence of smaller transitions in the combined Hilbert space of the system and environment, and this sequence of transitions lasts a total duration that increases with increasing system-environment coupling strength. These results provide an intuitive understanding of Landau-Zener transitions in open multilevel quantum systems.

Fu-Quan Dou, Sheng-Chang Li, Hui Cao

Honghua Zhong, Qiongtao Xie, Jiahao Huang +4 more

We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the Rabi regime, where the system is dominated by the intermode coupling, the system can be looked as an ensemble of identical noninteracting single-particle LZ systems and the photon-induced sideband transitions are similar to the ones in single-particle LZ systems. In the Fock regime, where the system is dominated by the interparticle interaction, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different ``photon'' numbers.