Solvable multistate model of Landau-Zener transitions in cavity QED

Abstract

We consider the model of a single optical cavity mode interacting with two-level systems (spins) driven by a linearly time-dependent field. When this field passes through values at which spin energy level splittings become comparable to spin coupling to the optical mode, a cascade of Landau-Zener (LZ) transitions leads to co-flips of spins in exchange for photons of the cavity. We derive exact transition probabilities between different diabatic states induced by such a sweep of the field.

Multistate Landau-Zener models with all levels crossing at one point

“…For example, for N = 4 we have then five parameters forα and only three independent HCs. In the case of the driven TavisCummings model, however, we have additional information because all transition probabilities from the extremal slope levels are known when N is arbitrary [3]. In any case, HCs are highly nonlinear, so it is not obvious that they can be disentangled to reconstruct elements of the scattering matrix.…”

“…General solution of the DTCM is currently known only in the form of an algorithm that allows derivation of transition probabilities in any invariant sector of this model recursively from solutions for lower dimensional sectors [3]. Complexity of this procedure is growing very quickly.…”

“…This article continues the series of publications [1][2][3][4][5] about exact results in the MLZ theory [6]. This theory deals with explicitly time-dependent Schrödinger equations of the form…”

“…The same models have been used previously to explain experiments with molecular nanomagnets [13], although analytical solutions of these models had not been known. Similarly, the DTCM [3], which belongs to the class (1), had been extensively studied by variety of approximate and numerical methods before its solution was found [14]. Originally, this model attracted attention due to applications to experiments with molecular Bose condensates [15].…”

“…Recent discovery of integrability conditions [2] has led to numerous fully solvable models of this type. Complexity of these models varies from the elementary two-state case [7,8] and few-state models [2] to systems of spins and fermions with nonlinear interactions and combinatorially large phase space [3,4].…”