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Chemical Physics Letters

Gaussian wavepacket dynamics and the Landau—Zener model for non-adiabatic transitions

Niels E. Henriksen

Published Sep 1, 1992• 11 citations
Publisher
DOI
10.1016/0009-2614(92)85825-u

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In the non-Hermitian Landau-Zener models, we investigate the dynamical transition both in parity-time symmetric and symmetry-broken regimes. Taking into account the complex nature of the energy of the non-Hermitian systems, the absolute value of the gap was used to determine the relaxation rate of the system. To show the dynamics of the phase transitions, the relative population is used to estimate the topological defect density in nonequilibrium phase transitions, rather than the excitations in the corresponding Hermitian systems. The result shows that the adiabatic-impulse approximation, which is fundamental to the Kibble-Zurek mechanism, may be adapted to the parity-time symmetric non-Hermitian Landau-Zener models to examine the dynamics near the critical point. The most basic non-Hermitian two-level models with an exact solution exhibiting the Kibble-Zurek mechanism are presented. It would be interesting to extend this scenario to quantum many-body models, such as the quantum phase transition in the Ising model.
Quantum adiabatic dynamics is the crucial element of adiabatic quantum computing and quantum annealing. Shortcuts to adiabaticity enable acceleration of the computational time by suppressing unwanted non-adiabatic processes with designed classical fields. Here, we consider quantum state transfer in the Landau-Zener model, which exemplifies the key elements of quantum adiabatic dynamics. We argue that non-adiabatic transitions can be suppressed by autonomous quantum dynamics, which involves coupling the Landau-Zener qubit to a second quantum system. By tuning the coupling strength, the composite quantum dynamics can reduce the probability of unwanted processes by more than two orders of magnitude. This is a prime example of control where the quantum properties of the control fields are key for implementing shortcuts to adiabaticity.
A complete adiabatic transport of Bose-Einstein condensate in a double-well trap is investigated within the Landau-Zener (LZ), and Gaussian Landau-Zener (GLZ) schemes for the case of a small non-linearity, when the atomic interaction is weaker than the coupling. The schemes use the constant (LZ) and time-dependent Gaussian (GLZ) couplings. The mean field calculations show that LZ and GLZ suggest essentially different transport dynamics. Significant deviations from the case of a strong coupling are discussed.