Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models

Abstract

We consider the simplest non-integrable model of multistate Landau-Zener transition. In this model two pairs of levels in two tunnel coupled quantum dots are swept passed each other by the gate voltage. Although this 2 × 2 model is non-integrable, it can be solved analytically in the limit when the inter-level energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar 2 × 1 model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In 2 × 1 model, the probability for a particle, residing at time t → −∞ in one dot, to remain in the same dot at t → ∞ falls off exponentially with tunnel coupling. By contrast, in 2 × 2 model, this probability grows exponentially with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as manifestation of the Dicke effect. PACS numbers: v 2 v 2 J J J J arXiv:1706.09503v1 [cond-mat.mes-hall] 28 Jun 2017 0 J 0 ∆ − vt 2 J J J vt 2 −∆ − vt 2 0 J J 0 ∆ − vt 2 J J J J −∆ + vt 2

Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

“…where all parameters are real. The symmetric model has emerged previously in discussions of nonadiabatic behavior in MLZ systems in the large coupling limit [30]. Physically, both models, ( 17) and ( 18), can describe a single electron that jumps between discrete levels of two quantum dots.…”

Generalized Adiabatic Impulse Approximation

“…The LZ grid model has applications in various fields, including atomic physics [26,27], quantum information science [29,58], and open quantum physics [59][60][61][62][63]. No general method, however, is known to analyze the transition probabilities in the LZ grid model.…”

“…Approximate methods have been developed for the case where the separation of parallel levels in a band is very small [64]. Besides, there are several arguments against the validity of transition probabilities in the LZ grid model [58,[65][66][67].…”

“…This system has been experimentally realized and its dynamics has drawn much attention [44,68]. Various methods have been proposed to derive an approximate solution for the dynamics [58,64,67].…”

Adiabaticity in nonreciprocal Landau-Zener tunneling

“…LZT model has many extensions by taking diverse physical conditions into account, such as in multi-level systems [28][29][30][31][32][33][34][35][36], in a nonlinear interacting system with level energies depend on the occupation of the levels [10][11][12], and in a time-dependent sweeping scheme [37,38], and so on. All the above studies are focusing on the Hermitian systems, which is under the assumption of being conservative and obeying time-reversal symmetry, and obviously exhibiting real-valued eigenvalues.…”