Landau-Zener Transitions in a Dissipative Environment: Numerically Exact Results

We study Landau-Zener transitions in a dissipative environment by means of the numerically exact quasiadiabatic propagator path integral. It allows to cover the full range of the involved parameters. We discover a nonmonotonic dependence of the transition probability on the sweep velocity which is explained in terms of a simple phenomenological model. This feature, not captured by perturbative approaches, results from a nontrivial competition between relaxation and the external sweep.

Figure 1

The LZ probability $P$ for various temperatures $T$ is shown for a weak system-bath coupling $\alpha =0.0016$. The dotted lines are guides to the eye. The solid line marks the coherent LZ probability $P_0$, while the dashed line indicates the high-temperature limit $P_{\mathrm{SD}}$ (see text). Inset: comparison with perturbative approaches for $T=4{\Delta }_0$ (see text).

Figure 2

Same as Fig. 1 for larger system-bath coupling $\alpha =0.02$ (a) and $\alpha =0.2$ (b).

Figure 3

LZ probability $P$ for different $\alpha$ for $T=4{\Delta }_0$. Inset: linear dependence of $v_{\min }$ on $\alpha$.

Figure 4

LZ probability $P$ for various cutoff frequencies ${\omega }_c$ for $T=4{\Delta }_0$ and $\alpha =0.00985$. Inset: $P(v_{\min })$ (bottom) and $v_{\min }$ (top) versus ${\omega }_c$. Solid lines: predictions from our simple model.

Figure 5

(a) Onset temperature $T_o$ and (b) maximal slope versus sweep velocity for $\alpha =0.02$, 0.0016. (c) LZ probability at the minimum sweep velocity (left axis, ○) and minimum sweep velocity (right axis, □) versus temperature, inferred from Fig. 1.