Anti-Kibble-Zurek Behavior in Crossing the Quantum Critical Point of a Thermally Isolated System Driven by a Noisy Control Field

We show that a thermally isolated system driven across a quantum phase transition by a noisy control field exhibits anti-Kibble-Zurek behavior, whereby slower driving results in higher excitations. We characterize the density of excitations as a function of the ramping rate and the noise strength. The optimal driving time to minimize excitations is shown to scale as a universal power law of the noise strength. Our findings reveal the limitations of adiabatic protocols such as quantum annealing and demonstrate the universality of the optimal ramping rate.

Figure 1

Schematic driving through a QCP with a noisy control field. Under an idealized smooth control field $g(t)$, diabatic transitions are suppressed as the ramp time $\tau$ is increased, as dictated by the KZM. The presence of noise in the control field $g(t)$ gives rise to anti-KZ behavior, limiting the performance of adiabatic protocols.

Figure 2

Anti-Kibble-Zurek behavior induced by a noisy control field. (a) The density of excitations upon completion of the annealing schedule for different values of $W$ as a function of ramp time $\tau$. The numerically exact value surpasses the power-law scaling predicted by the KZM when $W^2>0$. (b) A similar dependence is observed in the residual energy density $Q$. (c) Noise-induced effects are more pronounced in the energy spread $\mathrm{\Delta }E$ and already manifested for short ramp times. (d) The difference between the density of excitations generated in the presence and absence of noise scales linearly as a function of ramp time $\tau$ for fast ramps with $W^2\tau <1$, at a characteristic heating rate. Deviations are noticeable for long ramps.

Figure 3

Universal scaling of the optimal annealing time. The scaling of the optimal annealing time ${\tau }_{\text{opt}}$ that minimizes the density of excitations as a function of heating rate $r$, verifies the universal prediction in Eq. (2). Inset: The heating rate $r$ is shown to scale linearly as a function of square of the strength of noise $W^2$.