Two-mode coupling in a single-ion oscillator via parametric resonance

Dylan J Gorman, Philipp Schindler, Sankaranarayanan Selvarajan, Nikos Daniilidis, and Hartmut Häffner

Phys. Rev. A 89, 062332 – Published 27 June 2014

Abstract

Atomic ions, confined in radio-frequency Paul ion traps, are a promising candidate to host a future quantum information processor. In this article, we demonstrate a method to couple two motional modes of a single trapped ion, where the coupling mechanism is based on applying electric fields rather than coupling the ion's motion to a light field. This reduces the design constraints on the experimental apparatus considerably. As an application of this mechanism, we cool a motional mode close to its ground state without accessing it optically. As a next step, we apply this technique to measure the mode's heating rate, a crucial parameter determining the trap quality.

Received 21 May 2014

DOI:https://doi.org/10.1103/PhysRevA.89.062332

Authors & Affiliations

Dylan J Gorman^1,*, Philipp Schindler¹, Sankaranarayanan Selvarajan^1,2, Nikos Daniilidis¹, and Hartmut Häffner¹

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Institut für Experimentalphysik, Universität Innsbruck, A-6020 Innsbruck, Austria

^*[email protected]

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Vol. 89, Iss. 6 — June 2014

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Images

Figure 1
Illustration of the surface trap where the ion's position is represented by the black dot. When the experiment is operated in the $x z$ coupling configuration, the rf parametric drive is applied to the electrodes labeled A and B (blue diagonal shading). When operated in the $x y$ coupling configuration, the drive is applied to the electrode labeled C (red horizontal shading).
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Figure 2
Measured energy spectrum of the $X$ radial sideband illustrating the avoided crossing as a function of the detuning of the parametric drive operated in the $x y$ coupling configuration. The spectrum would look qualitatively identical in the $x z$ configuration. The green squares represent the mean values of Lorentzian fits to determine the frequency splitting.
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Figure 3
Relative Rabi frequency on the carrier (blue squares) and driven motion sideband (red diamonds), compared to the unperturbed Rabi frequency on the unperturbed carrier, as a function of parametric coupling strength in the $x z$ coupling configuration. The solid lines represent fitted Bessel functions of the first kind. The inset illustrates the parametric coupling strength $g_{x z}$ as a function of drive voltage amplitude prior to the in-vacuum low-pass filters.
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Figure 4
(a) Time evolution of the coupling dynamics illustrated by the excitation of the red sideband of the Z (blue squares) and $X$ (red diamonds) mode. Initially, the Z mode is cooled close to its ground state at a mean phonon number of ${\bar{n}}_{z} \approx 0.2$ while the $X$ mode is left at the Doppler temperature of ${\bar{n}}_{x} \approx 6$ quanta. After a coupling time of around 90 $μ$ s, the population of the two modes is swapped and thus the $X$ mode is close to its ground state. Solid lines correspond to a numerical solution of the model with no free parameters. The initial $X$ mode population and coupling frequencies were determined from sideband spectroscopy. Note that the coupling time does not start at zero, because the Blackman-shaped pulse is not adiabatic in this regime. (b) Red sideband excitation of the $X$ (blue squares) and $Y$ (red diamonds) modes. The $X$ mode is initially cooled to a mean phonon number of ${\bar{n}}_{x} \approx 0.3$ . Solid lines indicate a fit to a model where the initial $Y$ mode population and Rabi frequency are adjusted. The out-of-phase oscillations between the $X$ and $Y$ red sideband excitations show the population oscillating between the two modes.
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Figure 5
Mean phonon number as a function of heating time on the $Y$ mode. The $Y$ mode is prepared close to its ground state by cooling the $X$ mode and swapping the motional states. Analysis of the motional state is either performed directly on the $Y$ mode (blue squares) or by a second coupling operation and subsequent analysis on the $X$ mode (red diamonds). The red (bottom) line corresponds to a heating rate of 810(80) quanta/s, while the blue (top) line corresponds to a heating rate of 650(270) quanta/s.
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