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arXiv:1612.06902 · Physical Review Letters

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

Petar Jurcevic, Heng Shen, Philipp Hauke, Christine Maier, Tiff Brydges, Cornelius Hempel, B. P. Lanyon, Markus Heyl, R. Blatt, Christian F. Roos

Published Aug 21, 2017• 536 citations
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Abstract

The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.

DOI
10.1103/physrevlett.119.080501

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The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
The theory of phase transitions represents a central concept for the characterization of equilibrium matter.In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs).We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models.During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time.Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
We investigate the nonequilibrium quench dynamics of the one-dimensional transverse-field Ising model in both integrable and nonintegrable regimes. In particular, we report on a novel type of dynamical quantum phase transition (DQPT) that is characterized by a singular multipartite entanglement signature occurring at critical times in the post-quench dynamics. We show that this behavior is fundamentally distinct from previously studied DQPTs characterized by a nonanalytic rate function. We quantify the multipartite entanglement of the state by the quantum Fisher information and demonstrate that the DQPT belongs to a different universality class than the ground-state phase transition. Furthermore, we perform a spectral analysis of the DQPT and demonstrate that it is a genuine nonequilibrium transition arising from the constructive interference of excited states of the system during the many-body dynamics. Finally, we discuss potential experimental realizations in Rydberg platforms as well as applications in the context of quantum metrology.
Quantum many-body systems in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, there still exist a lot of questions regarding how to understand the nonequilibrium dynamical behavior of quantum many-body systems, which are not accessible with the thermodynamic description. Experiments in quantum simulators are opening up a route toward the generation of quantum states beyond the equilibrium paradigm. As an example, in closed quantum many-body systems, dynamical quantum phase transitions act as phase transitions in time, with physical quantities becoming nonanalytic at a critical time, extending important principles such as universality to the nonequilibrium realm. Here, in a solid-state quantum simulator, we report the experimental detection of out-of-time-order correlators in the presence of nonequilibrium phase transitions with the transverse field Ising model, which are a central concept to quantify quantum information scrambling and quantum chaos. Through measuring the multiple quantum spectra, we eventually observe the buildup of quantum correlation. Further applications of this protocol could potentially enable studies of other exotic phenomena such as many-body localization and tests of the holographic duality between quantum and gravitational systems.
Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
In the context of closed quantum systems, when a system prepared in its ground state undergoes a sudden quench, the resulting Loschmidt echo can exhibit zeros, resembling the Fisher zeros in the theory of classical equilibrium phase transitions. These zeros lead to nonanalytical behavior of the corresponding rate function, which is referred to as the dynamical quantum phase transition (DQPT). In this paper, we investigate DQPTs in the context of open quantum systems that are coupled to both Markovian and non-Markovian dephasing baths via a conserved quantity. The general framework is corroborated by studying the nonequilibrium dynamics of a transverse-field Ising ring. Our paper might shed light on theoretical developments of DQPTs in the strong system-bath coupling regime.
Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite that DQPTs are defined and signaled by the nonanalyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the noninteracting case, and upon the addition of repulsive intracell interactions. On the other hand, the intercell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in nonequilibrium quantum many-body systems.