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arXiv:1801.03391 · Journal of Physics B Atomic Molecular and Optical Physics

Spin and motion dynamics with zigzag ion crystals in transverse magnetic gradients

Joachim Welzel, Felix Stopp, Ferdinand Schmidt‐Kaler

Published Nov 23, 2018• 16 citations
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Abstract

Abstract We investigate the dynamics of ion crystals in zigzag configuration in transverse magnetic field gradients. A surface-electrode Paul trap is employed to trap 40 Ca + ions and features submerged current wires to generate magnetic field gradients of up to 16.3(9) T m −1 at the ions position. With the gradient aligned in the direction perpendicular to the axis of weakest confinement, along which linear ion crystals are formed, we demonstrate magnetic field gradient induced coupling between the spin and ion motion. We perform sideband spectroscopy upon directly driving the spins with a radiofrequency field for crystals of three ions on their linear-to-zigzag structural transition. Furthermore, we observe the rich excitation spectrum of vibrational modes in a planar crystal comprised of four ions.

DOI
10.1088/1361-6455/aaf347

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Abstract We investigate the dynamics of ion crystals in zigzag configuration in transverse magnetic field gradients. A surface-electrode Paul trap is employed to trap 40 Ca + ions and features submerged current wires to generate magnetic field gradients of up to 16.3(9) T m −1 at the ions position. With the gradient aligned in the direction perpendicular to the axis of weakest confinement, along which linear ion crystals are formed, we demonstrate magnetic field gradient induced coupling between the spin and ion motion. We perform sideband spectroscopy upon directly driving the spins with a radiofrequency field for crystals of three ions on their linear-to-zigzag structural transition. Furthermore, we observe the rich excitation spectrum of vibrational modes in a planar crystal comprised of four ions.
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.
We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 μm above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [J. Phys. B At. Mol. Opt. Phys. 42, 154009 (2009)]. We describe aspects where planar ion traps promise novel physics: spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schrödinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.
In modern ion quantum technology the fields of quantum information and microfabrication are being merged to build devices in which ions are confined near trap electrodes at the micrometer scale -with novel functionality where ion qubits enabling quantum devices. A long term goal in this field is to build a trapped-ion based quantum computer. Today’s quest, however, requires a progressive ion trap development in which materials selection, trap’s design and fabrication methods play a fundamental role. Here, we report on two fabrication methods for planar traps. We present the characterization of a planar trap with integrated electromagnets which is designed to coherently manipulate 40Ca+ ions’ internal states via magnetic field gradients and long-wavelength radiation. By implementing radiofrequency spectroscopy, in the presence of static magnetic fields, and by moving a single 40Ca+ ion about 600 µm along the trap axis we measured the total static magnetic field which yields a gradient of 1.11 +/- 0.18 T/m*A in this direction. We anticipate in this trap magnetic gradients of 10 T/m*A perpendicular to the trap axis. A second generation of this trap, a novel hybrid planar trap, is built by combining the capabilities of thick film technology and laser-induced glass micromachining to structure independent current-carrying wires beneath an ion trap. Into the vacuum chamber, we also incorporate surface cleaning tools such as ion-beam bombardment to diminish possible adsorbed contaminants which may reflect in excessive ion heating rates. Based on numerical simulations, we predict that the wires underneath the ion trap, although far from trap center, will be capable of producing high magnetic field gradients of about 3 T/m*A. Already such robust fields will allow to investigate strong v_ss=30 kHz spin-spin interactions in 40Ca+ ion crystals in planar traps.
We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally using a single ion in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state.
Abstract We present experiments on polarization gradient cooling of Ca + multi-ion Coulomb crystals in a linear Paul trap. Polarization gradient cooling of the collective modes of motion whose eigenvectors have overlap with the symmetry axis of the trap is achieved by two counter-propagating laser beams with mutually orthogonal linear polarizations that are blue-detuned from the S 1/2 ↔ P 1/2 transition. We demonstrate cooling of linear chains of up to 51 ions and 2D-crystals in zig-zag configuration with 22 ions. The cooling results are compared with numerical simulations and the predictions of a simple model of cooling in a moving polarization gradient.
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.