Adiabatic-Markovian bath dynamics at avoided crossings

Abstract

We investigate the dissipative influence of environmental fluctuations on the dynamics of driven quantum systems at an avoided crossing. We derive two simple approximative equations valid for weak system-bath coupling and compare results for the dissipative Landau-Zener problem with numerically exact results. Very good agreement is found for slow, i.e., adiabatic, driving. Specifically, the minimum in the Landau-Zener probability resulting from the competition of driving and dissipation is well described. For system-bath couplings and temperatures, where this minimum is observed in the adiabatic driving regime, good agreement is also observed for fast driving when the dynamics tends toward nonadiabatic behavior. Otherwise, however, for large temperatures and fast driving our approximation fails even for weak system-bath couplings, for which an undriven system is still accurately described by weak-coupling approximations.

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

“…Although not straightforward to justify, especially in the non-adiabatic large-v regime, we will assume it here, following the literature 26 , and refer to Ref. 36 for a detailed discussion of the different time-scales involved in the dynamics.…”

“…Following Ref. 37, we perform a time-dependent rotation in spin space around the y-axis,R t = exp[iφ tσ y /2], with φ t = arctan( (t)/∆), such thatR † tĤQ (t)R t = −E tσ x /2, with E t ≡ Λ t ≡ ∆ 2 + 2 (t). This leads to an effective qubit Hamiltonian of the form:…”

“…In order to make a more direct contact with the well known weak-coupling QME for an unbiased spin-boson problem ( = 0), we choose to perform, following Ref. 37, a time-dependent rotation in spin space around the y-axis,…”

“…Couplings of this kind have already been considered in the literature, precisely in the present dissipative LZ context [23][24][25][26][27] . A number of results are known on this problem, both exact 23,24 at zero temperature and numerical at finite temperature [25][26][27] , obtained by means of a perturbative quantum master equation (QME) approach and by the so-called quasi-adiabatic path integral (QUAPI) 28,29 . Let P gs (v, T ) denote the probability that the system remains in the ground state ofĤ Q (t) when evolving from the ground state at t = −∞ up to t = +∞ in presence of a thermal bath at temperature T .…”

Suppression of the Landau-Zener transition probability by weak classical noise

“…Refs. [12][13][14][15][16][17][18][19][20][21][22][23][24][25], the drive is assumed to be strictly linear. The subject of study is the effect of coupling of the qubit levels to the environment on the probability of the LandauZener transition.…”