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Register a new userStructure, dynamics and bifurcations of discrete solitons in trapped ion crystals
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We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D configurations, both theoretically and experimentally. We first extend the theoretical understanding of different phenomena predicted and recently experimentally observed in the structure and dynamics of these topological excitations. Employing tools from topological degree theory, we analyze bifurcations of crystal configurations in dependence on the trapping parameters, and investigate the formation of kink configurations and the transformations of kinks between different structures. This allows us to accurately define and calculate the effective potential experienced by solitons within the Wigner crystal, and study how this (so-called Peierls-Nabarro) potential gets modified to a nonperiodic globally trapping potential in certain parameter regimes. The kinks rest mass (energy) and spectrum of modes are computed and the dynamics of linear and nonlinear kink oscillations are analyzed. We also present novel, experimentally observed, configurations of kinks incorporating a large-mass defect realized by an embedded molecular ion, and of pairs of interacting kinks stable for long times, offering the perspective for exploring and exploiting complex collective nonlinear excitations, controllable on the quantum level.
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Laser cooled and trapped ions can crystallize and feature discrete solitons, that are nonlinear, topologically-protected configurations of the Coulomb crystal. Such solitons, as their continuum counterparts, can move within the crystal, while their discreteness leads to the existence of a gap-separated, spatially-localized motional mode of oscillation above the spectrum. Suggesting that these unique properties of discrete solitons can be used for generating entanglement between different sites of the crystal, we study a detailed proposal in the context of state-of-the-art experimental techniques. We analyze the interaction of periodically-driven planar ion crystals with optical forces, revealing the effects of micromotion in radio-frequency traps inherent to such structures, as opposed to linear ion chains. The proposed method requires Doppler cooling of the crystal and sideband cooling of the solitons localized modes alone. Since the gap separation of the latter is nearly independent of the crystal size, this approach could be particularly useful for producing entanglement and studying system-environment interactions in large, two- and possibly three-dimensional systems.
We propose to realize quantized discrete kinks with cold trapped ions. We show that long-lived solitonlike configurations are manifested as deformations of the zigzag structure in the linear Paul trap, and are topologically protected in a circular trap with an odd number of ions. We study the quantum-mechanical time evolution of a high-frequency, gap separated internal mode of a static kink and find long coherence times when the system is cooled to the Doppler limit. The spectral properties of the internal modes make them ideally suited for manipulation using current technology. This suggests that ion traps can be used to test quantum-mechanical effects with solitons and explore ideas for the utilization of the solitonic internal-modes as carriers of quantum information.
Measuring heat flow through nanoscale systems poses formidable practical difficulties as there is no `ampere meter for heat. We propose to overcome this problem by realizing heat transport through a chain of trapped ions. Laser cooling the chain edges to different temperatures induces a current of local vibrations (vibrons). We show how to efficiently control and measure this current, including fluctuations, by coupling vibrons to internal ion states. This demonstrates that ion crystals provide a suitable platform for studying quantum transport, e.g., through thermal analogues of quantum wires and quantum dots. Notably, ion crystals may give access to measurements of the elusive large fluctuations of bosonic currents and the onset of Fouriers law. These results are supported by numerical simulations for a realistic implementation with specific ions and system parameters.
Developing the isolation and control of ultracold atomic systems to the level of single quanta has led to significant advances in quantum sensing, yet demonstrating a quantum advantage in real world applications by harnessing entanglement remains a core task. Here, we realize a many-body quantum-enhanced sensor to detect weak displacements and electric fields using a large crystal of $sim 150$ trapped ions. The center of mass vibrational mode of the crystal serves as high-Q mechanical oscillator and the collective electronic spin as the measurement device. By entangling the oscillator and the collective spin before the displacement is applied and by controlling the coherent dynamics via a many-body echo we are able to utilize the delicate spin-motion entanglement to map the displacement into a spin rotation such that we avoid quantum back-action and cancel detrimental thermal noise. We report quantum enhanced sensitivity to displacements of $8.8 pm 0.4~$dB below the standard quantum limit and a sensitivity for measuring electric fields of $240pm10~mathrm{nV}mathrm{m}^{-1}$ in $1$ second ($240~mathrm{nV}mathrm{m}^{-1}/sqrt{mathrm{Hz}}$).
We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to 10 ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.
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