Geometric phase and non-adiabatic resonance of the Rabi model
- URL: http://arxiv.org/abs/2110.01158v1
- Date: Mon, 4 Oct 2021 02:31:08 GMT
- Title: Geometric phase and non-adiabatic resonance of the Rabi model
- Authors: Sijiang Liu, Zhiguo L\"u and Hang Zheng
- Abstract summary: We investigate the effects of counterrotating terms on geometric phase and its relation to the resonance of the Rabi model.
We find it is the higher-order harmonic terms that play an important role on the cyclic state.
- Score: 1.8047694351309205
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We investigate the effects of counterrotating terms on geometric phase and
its relation to the resonance of the Rabi model. We apply the unitary
transformation with a single parameter to the Rabi model and obtain the
transformed Hamiltonian involving multiple harmonic terms. By combining the
counter-rotating-hybridized rotating-wave method with time-dependent
perturbation theory, we solve systematically time evolution operator and then
obtain the geometric phase of the two-level system. Our results are beyond
adiabatic approximation and rotating-wave approximation (RWA). Higher-order
harmonic resonance happens when driving frequency is equal to higher-order
subharmonic of the Rabi frequency. In comparison with numerically exact
results, our calculated results are accurate over a wide range of parameters
space, especially in higher-order harmonic resonance regimes. In these regimes
we demonstrate geometric phases change dramatically while those of the RWA are
smooth. The RWA is thoroughly invalid even if the driving strength is extremely
weak. We find it is the higher-order harmonic terms that play an important role
on the cyclic state and demonstrate the characters of geometric phase in
higher-order harmonic resonance regime. We also present analytical formalism of
the change rate of geometric phase and quasienergies, which agree well with
numerically exact ones even in the strong driving case. The developed method
can be applied to explore the dynamics of strongly driven qubits and physical
properties of higher-order harmonic processes.
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