Classes of Exactly Solvable Generalized Semi‐Classical Rabi Systems

Abstract

The exact quantum dynamics of a single spin-1/2 in a generic time-dependent classical magnetic field are investigated and compared with the quantum motion of a spin-1/2 studied by Rabi and Schwinger. The possibility of regarding the scenario studied here as a generalization of that considered by Rabi and Schwinger is discussed and the notion of a time-dependent resonance condition is introduced and carefully legitimated and analyzed. Several examples help to disclose analogies and departures of the quantum motion induced in a generalized Rabi system with respect to that exhibited by the spin-1/2 in a magnetic field precessing around the z-axis. It is found that, under a generalized resonance condition, the time evolution of the transition probability P − + (t) between the two eigenstates ofŜ z may be dominated by a regime of distorted oscillations, or may even exhibit a monotonic behavior. At the same time, the authors succeed in predicting asymptotic behaviors with no oscillations in the time-dependence of P − + (t) under general conditions. New scenarios of experimental interest originating a Landau-Zener transition are brought to light.

Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems

“…(A11) is the static version of Eq. (23). For further details on the quantum mechanical motion in two-level quantum systems described by time-dependent Hamiltonians, we refer to Ref.…”

“…In this section, we introduce our driving strategies in terms of classes of exactly solvable generalized semi-classical Rabi systems [22,23].…”

“…Unlike the original Rabi scenario, in the so-called generalized Rabi scenario proposed by Messina and collaborators in Refs. [22,23], B , B ⊥ , and φ ω are arbitrary time-dependent dynamical variables. In particular, assuming the so-called generalized Rabi condition,φ…”

“…In any quantum driving scheme considered in this paper, following Refs. [22,23], we assume the success probability p 0 (θ) and the failure probability p 1 (θ) can be recast as…”

Continuous-time quantum search and time-dependent two-level quantum systems

“…First, we extend the application of recently introduced mathematical techniques in Refs. [30,31] to quantum search problems. Second, we were able to give a physical interpretation of the schedule function in terms of control magnetic fields.…”