Three-level Landau-Zener dynamics

Abstract

We compute Landau-Zener probabilities for 3-level systems with a linear sweep of the uncoupled energy levels of the 3×3 Hamiltonian matrix H(t). Two symmetry classes of Hamiltonians are studied: For H(t) ∈ su(2) (expressible as a linear combination of the three spin 1 matrices), an analytic solution to the dynamical problem is obtained in terms of the parabolic cylinder D functions. For H(t) ∈ su(3) (expressible as a linear combination of the eight Gell-Mann matrices), numerical solutions are calculated. In the adiabatic regime, full population transfer is obtained asymptotically at large times, but at intermediate times, all three levels are populated, and Stückelberg oscillations can manifest from the occurrence of two avoided crossings. For the open system, (wherein interaction with a reservoir occurs), we numerically solve a Markovian quantum master equation for the density matrix with Lindblad operators that models interaction with isotropic white Gaussian noise. We find that Stückelberg oscillations are suppressed and that the decoherence cannot be modeled in terms of simple a exponential.

Landau-Zener transitions and adiabatic impulse approximation in an array of two Rydberg atoms with time-dependent detuning

“…In the limit V 0 → 0, the three avoided level crossings merge at the point of zero detuning [see Fig. 4(a)], and we get a spin-1 SU(2) model [8]. The presence of RRI makes the model in Eq.…”

“…In the three-level LZ model, the detuning varies linearly in time [3,7,8] and the Hamiltonian in the diabatic basis {|gg , |s , |rr } is given by,…”

“…The paradigmatic example being the LZ model in which the diabatic energy levels cross each other linearly in time [1,2]. The latter had been generalized to both multi-level systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and many-body setups [19][20][21][22][23][24][25][26][27]. If driven periodically across an avoided level crossing, the separate LZTs interfere, leading to Landau-Zener-Stückelberg (LZS) interferometry [28].…”

Master-equation approach to the three-state open Majorana model

“…Ellinas has considered an Hamiltonian with a phenomenological non-Hermitian term proportional to the longitudinal component of the angular momentum [48], while other Authors such as Kenmoe et al [49] have considered the effects of a classical colored noise due to fluctuations of the parameters of the classical fields. Very recently, Band and Avishai have considered a phenomenological master equation to describe the effects of a white Gaussian isotropic noise [50]. An analysis of the quantum noise based on a microscopic model has been developed almost two decades ago by Saito and Kayanuma [51], but essentially limited, for the spin-1 case, to interaction operators which are diagonal in the basis of the diabatic states, and to colored or strong white noise.…”

Adiabatic spin-dependent momentum transfer in an SU(N) degenerate Fermi gas

“…3 is not perfectly respected. Unlike, e.g., [34], the LZ problem in our SOC mechanism remains inherently three-level, and the exact timescales depend on the relative values of Ω 1 , Ω 2 , ∆ [35][36][37]. We first introduce the usual two-level LZ transfer probability:…”