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arXiv:2006.15104 · New Journal of Physics

Polarization-gradient cooling of 1D and 2D ion Coulomb crystals

Manoj K. Joshi, A Fabre, Christine Maier, Tiff Brydges, Dominik Kiesenhofer, Helene Hainzer, R. Blatt, Christian F. Roos

Published Sep 16, 2020• 44 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/abb912

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Chinese Physics Letters•Jul 1, 2019•10 citations
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.
Abstract We implement three-dimensional polarization gradient cooling (PGC) of trapped ions. Counter-propagating laser beams near 393 nm impinge in lin ⊥ lin configuration, at a frequency below the S 1/2 to P 3/2 resonance in 40 Ca + . Our measurements demonstrate that cooling with laser beams detuned to lower frequencies from the resonance is robust against an elevated phonon occupation number and works continuously in the crossover from regular Doppler cooling to detunings of tens of linewidths. It is thus robust against heating events and also works well for an initial ion motion far out of the Lamb–Dicke regime. We show that PGC performance strongly depends on residual micromotion (MM) and find PGC working for a MM modulation index β ⩽ 0.1. Still, we find that the spectral impurity of the laser field affects both, cooling rates and cooling limits. Thus, a Fabry–Pérot cavity filter is employed to efficiently suppress amplified spontaneous emission of the diode laser. We demonstrate mean phonon numbers for a single ion of 5.4(4) at a trap frequency of 2 π × 285 kHz and 3.3(4) at 2 π × 480 kHz, in the axial and radial directions, respectively.
We show that the rotational degree of freedom of a polar heteronuclear molecular ion can be cooled through an optical coupling to the collective motional modes of the molecular ion and a simultaneously trapped and laser cooled atomic ion. Since the dissipative part of the rotational cooling is realized through laser cooling of the two-ion systems motional modes, the scheme should be applicable to a large range of molecules. As a test case for our cooling scheme we consider rotational cooling of a MgH + ion trapped with a laser cooled 40 Ca + ion.
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.
A Coulomb crystal formed in a linear Paul trap by Doppler cooling with a single axial laser often shows undesired oscillatory behavior in the direction perpendicular to the trap axis. This transverse oscillation is found to include two distinct coherent motions; in addition to the well-known micromotion driven by external error fields, there exists another natural oscillatory component. The latter oscillation is a kind of statistical phenomenon that takes place even in the absence of any mechanical errors. A detailed theoretical study is performed to clarify the basic characteristics of these overlapping coherent motions. A simple cooling scheme is proposed to minimize the transverse oscillation amplitude of a Coulomb crystal without use of extra lasers. The validity of theoretical predictions made in the present paper is confirmed through molecular dynamics simulations assuming the three-dimensional electrode geometry of a typical Paul trap.
This paper reports on trapping and laser-cooling of singly-ionized strontium ions in a linear Paul trap. We demonstrate loading of large ion clouds containing as much as 106 ions and laser cooling down to the Coulomb crystal transition. We observe the spatial segregation of the different Sr+ isotopes due to the mass-dependent Paul trap stiffness. Sympathetic cooling of the different isotopes is demonstrated, either by laser-cooling of 88Sr+ (83% abundance) or of 86Sr+ (10% abundance). These demonstrations open the way to the use of a large ion Coulomb crystal for quantum optics and quantum information experiments, where the strong confinement, the long lifetime, and the absence of perturbation by cooling lasers are crucial.
We obtain bi-component Coulomb crystals using laser-cooled 40Ca+ ions to sympathetically cool 9Be+ ions in a linear Paul trap. The shell structures of the bi-component Coulomb crystals are investigated. The secular motion frequencies of the two different ions are determined and compared with those in the single-component Coulomb crystals. In the radial direction, the resonant motion frequencies of the two ionic species shift toward each other due to the strong motion coupling in the ion trap. In the axial direction, the motion frequency of the laser-cooled 40Ca+ is impervious to the sympathetically cooled 9Be+ ions because the spatially separation of the two different ionic species leads to the weak motion coupling in the axial direction.