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arXiv:1605.01062 · Physical Review Letters

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

Anirban Dutta, Armin Rahmani, Adolfo del Campo

Published Aug 17, 2016• 90 citations
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Abstract

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.

DOI
10.1103/physrevlett.117.080402

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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.
In this paper we show that if we impose noise to the time varying coupling parameter of a closed system, then the system exhibits anti-Kibble-Zurek behavior leading to growth of excitations. Furthermore, our finding indicates that to minimize excitations, there is optimal ramp time, which is proportional to the noise strength but the exponent does not show agreement with the results of previous works. It is demonstrated there are restrictions of adiabatic protocols, like quantum annealing, and the rate of optimal ramp time is universal.
We propose an optimized adiabatic-impulse (OAI) protocol that substantially reduces the evolution time for crossing a quantum phase transition while preserving Kibble-Zurek (KZ) scaling. Near criticality, the control parameter is ramped linearly across the critical point at a rate characterized by a quench time τQτ_QτQ​. Away from criticality, the evolution remains adiabatic and is tuned close to the threshold of adiabatic breakdown, as quantified by an adiabatic coefficient ζζζ that scales as τQατ_Q^ατQα​. As a consequence, the total evolution time exhibits a sublinear power-law dependence on τQτ_QτQ​, and the conventional linear quench is recovered in the limit α→∞α\rightarrow\inftyα→∞. We apply the OAI protocol to the transverse Ising chain and numerically determine the minimal ζζζ required for KZ scaling. We further investigate the nonequilibrium dynamics in the presence of a noisy field that can induce anti-Kibble-Zurek (AKZ) behavior. Within the OAI protocol, noise-induced defects is significantly attenuated due to the shorter evolution time. The optimal quench time at which the defect density is minimized obeys an altered universal power-law scaling with the noise strength. Finally, we generalize the OAI protocol to the nonlinear quenches and numerically demonstrate a marked reduction in noise-induced defects.
The Kibble-Zurek (KZ) mechanism is a universal framework that can in principle describe nonequilibrium phase transition phenomena in any system with the required symmetry properties. However, a conflicting phenomenon termed anti-KZ behavior has been reported in the study of ferroelectric phase transitions, in which slower driving results in more topological defects [S. M. Griffin et al., Phys. Rev. X 2, 041022 (2012)]. Although this finding is significant, related experimental work remains scarce. In this work, we experimentally demonstrate anti-KZ behavior under a noisy control field in three different quantum phase transition protocols using a single trapped 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ ion. The density of defects is studied as a function of the quench time and the noise intensity. We experimentally verify that the optimal quench time to minimize excitations scales as a universal power law of the noise intensity. Our work provides an experimental verification of anti-KZ behavior in a two-level system.
We analyze mechanisms for universal out-of-equilibrium dynamics near criticality by exploring the effect of randomized quantum resetting (QR) under a finite-time quench across a quantum phase transition. Using the transverse-field Ising chain as a generic model and exploiting its exact solution, QR is found to cause a crossover of the scaling of the topological defect density with the time scale τττ of the quench, from Kibble-Zurek to anti-Kibble-Zurek scaling as τττ increases. This reflects a competition between non-adiabatic quench-driven excitations and QR, giving rise to local minima of the defect densities at optimal annealing times. These times and the corresponding local minima are shown to scale as universal power laws with the rate of QR. Additional results for the scaling of the mean excess energy suggest that a system driven across a quantum critical point exhibits the same scaling behavior under a linear quench with QR as with uncorrelated noise.
We investigate the quench dynamics of an open quantum system involving a quantum phase transition. In the isolated case, the quench dynamics involving the phase transition exhibits a number of scaling relations with the quench rate as predicted by the celebrated Kibble-Zurek mechanism. In contact with an environment however, these scaling laws break down and one may observe an anti-Kibble-Zurek behavior: slower ramps lead to less adiabatic dynamics, increasing thus nonadiabatic effects with the quench time. In contrast to previous works, we show here that such anti-Kibble-Zurek scaling can acquire a universal form in the sense that it is determined by the equilibrium critical exponents of the phase transition, provided the excited states of the system exhibit singular behavior, as observed in fully connected models. This demonstrates novel universal scaling laws granted by a system-environment interaction in a critical system. We illustrate these findings in two fully connected models, namely, the quantum Rabi and the Lipkin-Meshkov-Glick models. In addition, we discuss the impact of nonlinear ramps and finite-size systems.
When a system is swept through a quantum critical point (QCP), the Kibble-Zurek mechanism predicts that the average number of topological defects follows a universal power-law scaling with the ramp time scale. This scaling behavior is determined by the equilibrium critical exponents of the underlying phase transition. We show that the correspondence between Kibble-Zurek scaling and quantum criticality does not hold generally. In particular, the defect density can exhibit a suppression faster than the Kibble-Zurek prediction even when the quench crosses a critical point, while conventional Kibble-Zurek scaling may persist for quenches through a non-critical point. Our results, based on models representative of a broad class of quasi-one-dimensional Fermi systems, identify the dynamical conditions under which universal defect scaling emerges and clarify the relation between defect generation and equilibrium criticality.