Quantum system driven by incoherent a.c fields: Multi-crossing Landau Zener dynamics

Quantum Interferometry for Different Energy Landscapes in a Tuneable Josephson Junction Circuit

“…When the system is driven slowly, it follows an adiabatic scenario; the resulting level crossing system is resumed by a three-state Landau-Zener problem. The investigation of the tunneling probability is done via dynamic matrix approach [52] [75]. In order to find the transition probability, we use the Hamiltonian (17).…”

“…From the field vector (or transition matrix) above it is seen that the probable occupation varies with the initial occupied state; therefore, if the initial occupation is 1 − , then the survival probability is given by the quantities When the system is prepared in such a way that the initial occupation is 0 , the survival probability is given by the quantities   operate separately. Therefore, the system behaves at each of these points as if they where an anti-crossing (avoided crossing); the fictitious crossing are expected and the probability changes drastically [52] [75].…”

“…The Landau-Zener tunneling is at the basis of several quantum mechanical processes, and it was recently discovered in periodic structures, with applications in driven superlattices [40], current driven Josephson junction [41] and bosonic systems [42] [43] [44]. The Landau-Zener tunneling occurs at the crossing of two energy levels which move away due to a weak interaction [35], and it has largely been investigated for particular configurations such as external field influence, periodic modulation [45] [46], non-linear models [42] [43] [47] [48], multi-state models [37] [49] and multi-crossing model in its multiple configurations (real or fictitious crossing) [50] [51] [52] and it still gains a lot of attention due to its prominent uses.…”