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arXiv:1812.04347 · Physical Review A

Ion-crystal demonstration of a temperature-driven structural phase transition

Ji Li, L.-L. Yan, Liang Chen, Z. C. Liu, Fei Zhou, Jian‐Qi Zhang, W. L. Yang, Mang Feng

Published Jun 5, 2019• 14 citations
arXivHTMLPDF

Abstract

Thermal fluctuation usually damages observations in physical systems. But here we demonstrate a unique contribution made by thermal fluctuation, that is, our observation of linear-zigzag phase transitions induced solely by temperature of the $^{40}\mathrm{Ca}^{+}$ ion crystals in a surface-electrode trap. In contrast to the previously observed counterparts based on change in the mechanical equilibrium conditions of the ions, our presented structural phase transition occurs due to controllable influence of thermal fluctuation. The ions' temperature is well controlled by tuning the cooling laser and the experimental observation could be fully understood by classical Langevin equation in addition to the effects from thermal fluctuation. Our experimental investigation indicates the possibility of the positive role thermal fluctuation played in the thermodynamic process at the atomic level, which might bridge the thermodynamics from the macroscopic domain to the quantum regime.

DOI
10.1103/physreva.99.063402

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Thermal fluctuation usually damages observations in physical systems. But here we demonstrate a unique contribution made by thermal fluctuation, that is, our observation of linear-zigzag phase transitions induced solely by temperature of the 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion crystals in a surface-electrode trap. In contrast to the previously observed counterparts based on change in the mechanical equilibrium conditions of the ions, our presented structural phase transition occurs due to controllable influence of thermal fluctuation. The ions' temperature is well controlled by tuning the cooling laser and the experimental observation could be fully understood by classical Langevin equation in addition to the effects from thermal fluctuation. Our experimental investigation indicates the possibility of the positive role thermal fluctuation played in the thermodynamic process at the atomic level, which might bridge the thermodynamics from the macroscopic domain to the quantum regime.
The structural phase transition (SPT) occurring in trapped-ion systems is a typical many-body physics, and the SPT induced by the thermal effect represents a special thermodynamic phenomenon between traditional thermodynamics and quantum thermodynamics. We explore this thermal-effect-induced SPT by embedding trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion crystals in an optical lattice, in which the ion crystals are confined by a surface-electrode trap and laser-cooled down to a temperature of several millikelvins. The considered thermal effect, leading to a temperature variation of tens of microkelvins in the SPT, comes completely from the optical lattice, which is independent of the laser irradiation regarding cooling of the ion crystals. In comparison with previous work [J. Li et al., Phys. Rev. A 99, 063402 (2019)], the present investigation helps to further clarify the effect of thermal fluctuation and further explore the positive role of the fluctuation in thermodynamics at the atomic level, even for potentially practical applications.
Phase transitions have been a research focus in many-body physics over past decades. Cold ions, under strong Coulomb repulsion, provide a repealing paradigm of exploring phase transitions in stable confinement by electromagnetic field. We demonstrate various conformations of up to sixteen laser-cooled (40)Ca(+) ion crystals in a home-built surface-electrode trap, where besides the usually mentioned structural phase transition from the linear to the zigzag, two additional phase transitions to more complicated two-dimensional configurations are identified. The experimental observation agrees well with the numerical simulation. Heating due to micromotion of the ions is analysed by comparison of the numerical simulation with the experimental observation. Our investigation implies very rich and complicated many-body behaviour in the trapped-ion systems and provides effective mechanism for further exploring quantum phase transitions and quantum information processing with ultracold trapped ions.
A Wigner crystal formed with trapped ions can undergo a structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be driven solely by a change in the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology.
A quasi-one-dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. Since it is a one-dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In Fishman et al. [Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a ${\ensuremath{\phi}}^{4}$ model. We propose a mapping of the ${\ensuremath{\phi}}^{4}$ field theory to the well-known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures TTT. We focus in particular on a trapped-ion system and estimate the implied limitations on TTT and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is, in principle, accessible.
Abstract Quantum phase transitions (QPTs) are usually associated with many-body systems in the thermodynamic limit when their ground states show abrupt changes at zero temperature with variation of a parameter in the Hamiltonian. Recently it has been realized that a QPT can also occur in a system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report an experimental demonstration of a QPT in the QRM using a 171Yb+ ion in a Paul trap. We measure the spin-up state population and the average phonon number of the ion as two order parameters and observe clear evidence of the phase transition via adiabatic tuning of the coupling between the ion and its spatial motion. An experimental probe of the phase transition in a fundamental quantum optics model without imposing the thermodynamic limit opens up a window for controlled study of QPTs and quantum critical phenomena.
Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of μμμeV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.