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arXiv:2008.00885 · Physical Review A

Experimental verification of anti–Kibble-Zurek behavior in a quantum system under a noisy control field

Ming-Zhong Ai, Jin‐Ming Cui, Ran He, Zhong-Hua Qian, Xin-Xia Gao, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo

Published Jan 26, 2021• 26 citations
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Abstract

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 ${}^{171}{\mathrm{Yb}}^{+}$ 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.

DOI
10.1103/physreva.103.012608

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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 study the dynamics of a transverse-field XY\mathrm{XY}XY chain driven across quantum critical points by noisy control fields. We characterize the defect density as a function of the quench time and the noise strength and demonstrate that the defect productions for three quench protocols with different scaling exponents exhibit the anti-Kibble-Zurek behavior, whereby slower driving results in more defects. The protocols are quenching through the boundary line between paramagnetic and ferromagnetic phases, quenching across the isolated multicritical point, and quenching along the gapless line, respectively. We also show that the optimal quench time to minimize defects scales as a universal power law of the noise strength in all three cases. Furthermore, by using quantum simulation of the quench dynamics in the spin system with well-designed Landau-Zener crossings in pseudomomentum space, we propose an experimentally feasible scheme to test the predicted anti-Kibble-Zurek behavior of this noisy transverse-field XY\mathrm{XY}XY chain with two-level systems under controllable fluctuations.
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.
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.
The Kibble-Zurek (KZ) hypothesis identifies the relevant time scales in out-of-equilibrium dynamics of critical systems employing concepts valid at equilibrium: It predicts the scaling of the defect formation immediately after quenches across classical and quantum phase transitions as a function of the quench speed. Here, we study the crossover between the scaling dictated by a slow quench, which is ruled by the critical properties of the quantum phase transition, and the excitations due to a faster quench, where the dynamics is often well described by the classical model. We estimate the value of the quench rate that separates the two regimes and support our argument using numerical simulations of the out-of-equilibrium many-body dynamics. For the specific case of a ϕ^{4} model we demonstrate that the two regimes exhibit two different power-law scalings, which are in agreement with the KZ theory when applied to the quantum and classical cases. This result contributes to extending the prediction power of the Kibble-Zurek mechanism and to providing insight into recent experimental observations in systems of cold atoms and ions.
In the nonadiabatic dynamics across a quantum phase transition, the Kibble-Zurek paradigm describes that the average number of topological defects is suppressed as a universal power law with the quench time scale. A conflicting observation, termed anti-Kibble-Zurek dynamics, has been reported in several studies, specifically in the driven systems with an uncorrelated stochastic (white) noise. Here, we study the defect generation in the driven transverse field/anisotropy quantum XY model in the presence of a correlated (colored) Gaussian noise. We propose a generic conjecture that properly captures the noise-induced excitation features, which shows good agreement with the numerical simulations. We show that the dynamical features of defect density are modified by varying the noise correlation time. Our numerical simulations confirm that, for fast noises, the dynamics of the defect density is the same as that of the uncorrelated (white) noise, as is expected. However, the larger ratio of noise correlation time to the annealing time results in larger defect density formation and reforms the universal dynamical features. Our finding reveals that the noise-induced defects scale linearly with the annealing time for fast noises, while in the presence of slow noises the noise-induced defects scale linearly with the square of the annealing time. The numerical simulations confirm that the optimal annealing time, at which the defect density is minimum, scales linearly in logarithmic scale with the total noise power having different exponents for fast and slow noises.
The Kibble-Zurek mechanism (KZM) predicts that when a system is driven through a continuous phase transition, the density of topological defects scales universally with the quench rate. Recent theoretical work [H.-B. Zeng \textit{et al.}, \textit{Phys. Rev. Lett.} \textbf{130}, 060402 (2023)] has challenged this picture, showing that under sufficiently fast quenches, both the defect density and freezing time become independent of the quench rate and instead scale universally with the quench range. Here, we experimentally test this prediction using a single trapped-ion qubit to simulate fast quantum quenches in the Landau-Zener and 1D Rice-Mele models. We identify a critical quench rate vc v_c vc​ that scales with the quench range δmax⁡ δ_{\max} δmax​, separating two distinct dynamical regimes. In the Rice-Mele model, for v<vc v < v_c v<vc​, the defect density follows the KZM scaling ∼v1/2 \sim v^{1/2} ∼v1/2; for v>vc v > v_c v>vc​, it exhibits a universal scaling ∼δmax⁡ \sim δ_{\max} ∼δmax​, independent of the quench rate. Our results provide direct experimental evidence of the predicted breakdown of KZM universality under fast quenches.