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Physical Review A

Observation of anomalous heat transport in a trapped ion chain

Zhichao Mao, Yong Xu, Q.-X. Mei, W.-D. Zhao, Yue Jiang, Zhenbo Cheng, X.-Y. Chang, Longfei He, Lin Yao, Z.-C. Zhou, Yukai Wu, Luming Duan

Published Mar 15, 2022• 5 citations
Publisher

Abstract

Energy transport in low-dimensional systems or systems with long-range interactions shows unusual properties not observed in conventional three-dimensional materials. Trapped linear ion chains have been proposed as an ideal platform to study such phenomena, but many predicted features have not been demonstrated yet and the existing experiments mainly focus on the weak excitation limit where the dynamics can be described by linearized phonon modes. Here, we study the energy transport in a chain of $^{174}\mathrm{Yb}^{+}$ ions using a focused heating laser beam. Nontrivial effects are observed such as a nonmonotonic energy distribution with reflection symmetry, oscillatory heating dynamics, and a change in the heating pattern due to the competition between the external driving and interion coupling. Our work deepens the understanding about transport in low-dimensional systems and also provides guidelines for the sympathetic cooling of long ion chains, with applications in quantum information processing and precision measurement.

DOI
10.1103/physreva.105.033107

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We analyze the heat transport in an ion chain that is confined in a strongly anisotropic Paul trap. To drive a heat current across the chain different pairs of counterpropagating laser beams are applied to the ions on the edges. The lasers behave as heat reservoirs operating at different temperatures, and a nonequilibrium heat flow can be sustained. The control of the spatial distribution of the ions in the chain by variation of the trapping frequencies makes ion chains an ideal testbed to study heat transport properties in finite open systems of low dimensionality with tunable nonlinearities. We explore heat transport across a structural phase transition between the linear and zigzag configurations, identifying the condition for optimal heat transport.
The solid-liquid phase transition (melting) is a long-standing problem for which a complete understanding is challenging because of the strong many-body interactions. A trapped-ion Wigner crystal is a suitable platform for a controlled study of this phase transition with its unprecedented resolution of individual atomic ions. Here we study the melting dynamics of a linear chain of 174Yb+^{174}\mathrm{Yb}^{+}174Yb+ ions, which is initially cooled to the Doppler temperature and is then periodically heated and detected by a focused laser beam. We achieve controlled melting of the ion chain and observe unusual partial melting of long chains (coexistence of solid and liquid phases). We also observe a counterintuitive nonuniform energy distribution over the chain under localized heating. These results are further confirmed by molecular dynamics simulations to rule out other heating mechanisms.
The interplay of noise and quantum coherence in transport gives rise to rich dynamics relevant for a variety of systems. In this work, we put forward a proposal for an experiment testing noise-induced transport in the vibrational modes of a chain of trapped ions. We focus on the case of transverse modes, considering multiple-isotope chains and an ``angle trap,'' where the transverse trapping varies along the chain. This variation induces localization of the motional modes and therefore suppresses transport. By suitably choosing the action of laser fields that couple to the internal and external degrees of freedom of the ions, we show how to implement effective local dephasing on the modes, broadening the vibrational resonances. This leads to an overlap of the local mode frequencies, giving rise to a pronounced increase in the transport of excitations along the chain. We propose an implementation and measurement scheme which require neither ground-state cooling nor low heating rates, and we illustrate our results with a simulation of the dynamics for a chain of three ions.
In this work, we study quantum heat transport in a single trapped ion, driven by laser excitation and coupled to thermal reservoirs operating at different temperatures. Our focus lies in understanding how different laser coupling scenarios impact the system dynamics. As the laser intensity reaches a regime where the electronic and motional degrees of freedom of the ion couple strongly, traditional approaches using phenomenological models for thermal reservoirs become inadequate. Therefore, the adoption of the dressed master equation formalism becomes crucial, enabling a deeper understanding of how distinct laser intensities influence heat transport. Analyzing the heat current within the parameter space defined by detuning and coupling strength, we observe intriguing circular patterns that are influenced by the vibrational frequency of the ion and laser parameters and reveal nuanced relationships between heat transport and coherence, as well as phenomena such as negative differential heat conductivity and heat rectification, offering insights into the thermal properties of this essential quantum technology setup.
Trapped ions, under electromagnetic confinement and Coulomb repulsion, can behave as non-interacting particles in one-dimensional lattices. Here we explore analytically the possible effects regarding Anderson localization in a chain of trapped ions experiencing laser Bessel beams. Under an experimentally feasible condition, we predict an analytical form of the energy-dependent mobility edges, which is verified to be in good agreement with the exact numerical results except for the top band. Some other important properties regarding the phonon localization in the ion chain are also discussed both analytically and numerically. Our results are relevant to experimental observation of localization–delocalization transition in the ion trap and helpful for deeper understanding of the rich phenomena due to long-range phonon hopping.
Trapped ions are one of the leading platforms in quantum information science. For quantum computing with large circuit depth and quantum simulation with long evolution time, it is of crucial importance to cool large ion crystals at runtime without affecting the internal states of the computational qubits, thus the necessity of sympathetic cooling. Here, we report multi-ion sympathetic cooling on a long ion chain using a narrow cooling beam focused on two adjacent ions, and optimize the choice of the cooling ions according to the collective oscillation modes of the chain. We show that, by cooling a small fraction of ions, cooling effects close to the global Doppler cooling limit can be achieved. This experiment therefore demonstrates an important enabling step for quantum information processing with large ion crystals.