Abstract
We study the dynamics of a quantum two-state system driven through an avoided crossing under the influence of a super-Ohmic environment. We determine the Landau–Zener probability employing the numerical exact quasi-adiabatic path integral and a Markovian weak coupling approach. Increasing the driving time in the numerical protocol, we find converged results which shows that super-Ohmic environments only influence the Landau Zener probability within a finite crossing time window. This crossing time is qualitatively determined by the environmental cut-off energy. At weak coupling, we show that the Markovian weak coupling approach provides an accurate description. Since pure dephasing of a super-Ohmic bath is non-Markovian, this highlights that pure dephasing hardly influences the Landau–Zener probability. The finite crossing time window, thus, results from the suppression of relaxation once the energy splitting exceeds the environmental cut-off energy.Graphical abstract
Highlights
The transition dynamics of a driven quantum system in the vicinity of avoided crossings of its energy levels [1–4] is at the heart of various very different physical problems
We studied the Landau–Zener dynamics, i.e., the Landau–Zener probability and the excited-statesurvival probability, under the influence of an superOhmic environment to reveal whether its influence is restricted to a crossing time window around the avoided crossing and, if so, what determines this crossing time window
For a longitudinal Ohmic bath, this crossing time window is determined by the driven quantum system, i.e., the tunnel coupling between the driven states and the driving speed
Summary
The transition dynamics of a driven quantum system in the vicinity of avoided crossings of its energy levels [1–4] is at the heart of various very different physical problems. The driving protocol of the Landau–Zener model runs for an infinite time, but the tunnel coupling between the two states influences the dynamics only, while it exceeds their energy splitting restricting the dynamics to a Landau–Zener crossing time window during which the avoided crossing takes place This allows to employ the theoretical results from the simplified Landau–Zener model for the description of real systems where driving is always finite. A transversal Ohmic bath, in contrast, influences the dynamics in the much wider time window around the avoided crossing [30] determined roughly by the regime where the energy splitting does not exceed the maximal excitation energy of the environment Both cases can be understood within a Markovian weak coupling approach [35,36] where time-dependent effective relaxation rates can be determined. Pure dephasing rates for the longitudinal Ohmic environment are not suppressed, but seem not to affect the studied Landau– Zener probability PLZ nor the excited-state survival probability PES
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
