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arXiv:2410.15389 · Science Advances

Observation of quantum superposition of topological defects in a trapped-ion quantum simulator

Zhi-Wen Cheng, Yukai Wu, Shi-Jiao Li, Q.-X. Mei, B.-W. Li, Gangxi Wang, Yue Jiang, B. Qi, Z.-C. Zhou, Pan‐Yu Hou, Luming Duan

Published Oct 18, 2024• 6 citations
arXivHTMLPDF

Abstract

Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a "Schrodinger kink" that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics.

DOI
10.1126/sciadv.adr9527

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Topological defects are discontinuities of a system protected by global properties, with wide applications in mathematics and physics. While previous experimental studies mostly focused on their classical properties, it has been predicted that topological defects can exhibit quantum superposition. Despite the fundamental interest and potential applications in understanding symmetry-breaking dynamics of quantum phase transitions, its experimental realization still remains a challenge. Here, we report the observation of quantum superposition of topological defects in a trapped-ion quantum simulator. By engineering long-range spin-spin interactions, we observe a spin kink splitting into a superposition of kinks at different positions, creating a "Schrodinger kink" that manifests nonlocality and quantum interference. Furthermore, by preparing superposition states of neighboring kinks with different phases, we observe the propagation of the wave packet in different directions, thus unambiguously verifying the quantum coherence in the superposition states. Our work provides useful tools for nonequilibrium dynamics in quantum Kibble-Zurek physics.
It is now widely accepted that quenches through the critical region of quantum phase transitions result in post-transition states populated with topological defects-analogs of the classical topological defects. However, consequences of the very nonclassical fact that the state after a quench is a superposition of distinct, broken-symmetry vacua with different numbers and locations of defects have remained largely unexplored. We identify coherent quantum oscillations induced by such superpositions in observables complementary to the one involved in symmetry breaking. These oscillations satisfy Kibble-Zurek dynamical scaling laws with the quench rate, with an instantaneous oscillation frequency set primarily by the gap of the system. In addition to the obvious fundamental significance of a superposition of different broken symmetry states, quantum coherent oscillations can be used to verify unitarity and test for imperfections of the experimental implementations of quantum simulators.
Abstract The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one-dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects.
The Kibble Zurek mechanism describes the universal formation of topological defects during continuous symmetry breaking phase transitions. It has been confirmed in a wide variety of systems and is of interest within theoretical high energy physics and cosmology. While during high temperature phase transitions classical methods can be used to study topological defect formation, in zero temperature quantum phase transitions, quantum effects can dominate dynamics such that classical approximations fail. This is problematic in quantum field theory because topological defect formation constitutes a non-perturbative non-equilibrium phenomenon, yet there are at present no well-developed non-perturbative non-equilibrium methods available for calculations. Nonetheless, due to its generality and confirmation in other cases, the Kibble-Zurek mechanism is expected to hold. This means that in addition to being of physical interest in its own right, the Kibble-Zurek mechanism is also an excellent test for any potential non-perturbative non-equilibrium techniques. In this thesis, tensor network techniques are applied to the problem of confirming the Kibble Zurek mechanism in the phi^4 quantum field theory in D = (1 + 1) spacetime dimensions. Such techniques have already been highly successful in condensed matter and to some extent in quantum field theory. The kink defects of the theory are studied both in equilibrium and in the non-equilibrium scenario of their formation. Results consistent with the Kibble-Zurek mechanism are found, which provides evidence that the mechanism holds in this case and confirms tensor networks as a promising non-perturbative non-equilibrium method for quantum field theory. As tensor network methods are developed further to higher dimensions and more sophisticated theories, they could one day provide a powerful method for the non-perturbative study of non-equilibrium high energy physics and cosmology, an area of physics which remains essentially unexplored yet important for our understanding of nature.
Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.
Quantum simulation with controllable many-body platforms offers a powerful route to exploring complex phases and dynamics that are difficult to access in natural materials. Among these, topological spin textures such as skyrmions are central to modern condensed-matter physics and play a key role in chiral quantum many-body systems. Their controlled realisation in large, programmable quantum platforms, however, remains an outstanding challenge. Here, we report deterministic generation and site-resolved reconstruction of topological spin textures in a two-dimensional crystal of more than 150 trapped ions. Using globally applied spin-dependent forces, we generate skyrmion configurations and reconstruct the full vector spin field with single-ion resolution, obtaining a winding number of 0.99$\pm0.02andameanlocalfidelityof0.870.02 and a mean local fidelity of 0.870.02andameanlocalfidelityof0.87\pm$0.04. In addition, we implement single-ion-resolved control to deterministically prepare domain-wall states, extending our approach to a broader class of non-uniform spin textures. These results establish trapped-ion crystals as a platform for engineering complex spin textures and open the door to exploring topology-dependent nonequilibrium dynamics in long-range interacting quantum systems.
We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects ("kinks") in purely two-dimensional crystals and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the center of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence saturates at ∼0.5. Simulations reveal a strong anharmonicity of the kink's internal mode of vibration, due to the kink's extension into three dimensions. As a consequence, the periodic Peierls-Nabarro potential experienced by a discrete kink becomes a globally confining potential, capable of trapping one cooled defect at the center of the crystal.