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arXiv:1401.5480 · Physical Review B

Tuning heat transport in trapped-ion chains across a structural phase transition

A. Ruiz, Daniel Alonso, Martin Bodo Plenio, Adolfo del Campo

Published Jun 13, 2014• 33 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.89.214305

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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.
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 174Yb+^{174}\mathrm{Yb}^{+}174Yb+ 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.
The nonequilibrium dynamics of an ion chain in a highly anisotropic trap is studied when the transverse trap frequency is quenched across the value at which the chain undergoes a continuous phase transition from a linear to a zigzag structure. Within Landau theory, an equation for the order parameter, corresponding to the transverse size of the zigzag structure, is determined when the vibrational motion is damped via laser cooling. The number of structural defects produced during a linear quench of the transverse trapping frequency is predicted and verified numerically. It is shown to obey the scaling predicted by the Kibble-Zurek mechanism, when extended to take into account the spatial inhomogeneities of the ion chain in a linear Paul trap.
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.
We study the nonequilibrium dynamics of the linear-to-zigzag structural phase transition exhibited by an ion chain confined in a trap with periodic boundary conditions. The transition is driven by reducing the transverse confinement at a finite quench rate, which can be accurately controlled. This results in the formation of zigzag domains oriented along different transverse planes. The twists between different domains can be stabilized by the topology of the trap, and under laser cooling the system has a chance to relax to a helical chain with nonzero winding number. Molecular dynamics simulations are used to obtain a large sample of possible trajectories for different quench rates. The scaling of the average winding number with different quench rates is compared to the prediction of the Kibble-Zurek theory, and a good quantitative agreement is found.
Laser-cooled ions held in a linear Paul trap with strong transverse confinement organize into a one-dimensional (1-D) linear crystal. If the transverse confinement is relaxed, the linear ion crystal undergoes a continuous, structural phase transition to a 2-D zigzag configuration. We study the dynamics near the critical point of the linear-zigzag transition. In the first part of this thesis, we study the spontaneous nucleation and dynamics of topological kink defects, formed as a result of a rapid quench across the linear-zigzag transition. The experimental results are compared to the Kibble-Zurek mechanism, which provides an intuitive model of defect formation and predicts a power-law scaling for the number of defectsformed as a function of transition quench rate. The second part of this thesis is focused on one of the key requirements for investigations of the near-transition dynamics in the quantum regime. To achieve an efficient ground state cooling of the zigzag vibrational mode, we demonstrate 3-D polarization-gradient cooling of strings of 1-4 trapped ions as an intermediate step between Doppler and sideband cooling, and study the polarization-gradient cooling rate and cooling limit as a function of the cooling beam intensity in and near the Lamb-Dicke regime. The results of this thesis pave the way towards our future experiments aimed at assessing the coherence time of a zigzag superposition state through measurements of tunneling oscillations.
Laser-cooled, trapped ions are a highly controlled experimental system that allows one to engineer novel quantum states of both fundamental and practical interest.For a string of ions in a linear radio frequency (RF) Paul trap, the linear-zigzag structural phase transition is an intriguing system to investigate quantum dynamics near the critical point of a prototype second-order phase transition, including the preparation of superposition states of different structural configurations.This thesis focuses on two technological improvements required for studying the linear-zigzag structural phase transition in the quantum regime.The first is the development of a compact and cost-effective RF synthesizer setup to provide multiple modulation sources for the laser manipulation of ion strings.The functionality and limitations of a prototype design, based on Direct Digital Synthesizer (DDS) development boards with a microcontroller interface, are evaluated and future improvements are identified.The second part of this thesis focuses on the stabilization of the secular trap frequencies in a linear Paul trap, which is necessary to obtain a stable critical point for the studies of the linear-zigzag transition.To this end, this thesis presents the implementation of a Ramsey spectroscopic technique to measure the secular frequencies and presents the preliminary results from the stability tests.