arXiv:1905.09011 · New Journal of Physics

Measuring the temperature and heating rate of a single ion by imaging

Bharath Srivathsan, Martin Fischer, Lucas Alber, Markus Weber, Markus Sondermann, Gerd Leuchs

Published Oct 18, 2019• 10 citations

Abstract

Abstract We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the heating rate induced by any kind of effect other than photon scattering. In contrast to other established schemes for measuring the heating rate, the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.

DOI: 10.1088/1367-2630/ab4f43

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arXiv:1905.09011 · New Journal of Physics

Measuring the temperature and heating rate of a single ion by imaging

Bharath Srivathsan, Martin Fischer, Lucas Alber, Markus Weber, Markus Sondermann, Gerd Leuchs

Published Oct 18, 2019• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1367-2630/ab4f43

Related papers

Measuring the temperature and heating rate of a single ion by imaging

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We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the heating rate induced by any kind of effect other than photon scattering. In contrast to other established schemes for measuring the heating rate, the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the heating rate induced by any kind of effect other than photon scattering. In contrast to other established schemes for measuring the heating rate, the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.

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arXiv:1809.10972Physical Review AFeb 11, 201911 citations

\hbarΓ/2 k_\mathrm{B}

. The motion of a single ion is monitored in real-time, allowing for the generation of a feedback signal that is applied to an auxiliary trap electrode. Motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. While the method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence, we expect the method to also be applicable when using lenses with moderate numerical apertures.

We demonstrate the trapping of a single ion in the focus of a deep parabolic mirror that covers 81

%

of the solid angle surrounding the ion. Accounting for the reflectivity of the mirror we infer a photon collection efficiency of 54.8

%

for our setup. The underlying experimentally detected maximum fluorescence rate is $1.91\ifmmode\times\else\texttimes\fi{}{10}^{6}$ s${}^{\ensuremath{-}1}$ from a single

{}^{174}

{}^{+}

ion, mainly limited by the quantum efficiency of our photon detector. Besides the high collection efficiency, the integration of an ion trap into a parabolic mirror is a key ingredient for efficient coupling of light to a single ion in free space.

^{88}\mathrm{Sr}^{+}

ion cooled in a surface radio-frequency trap. We first applied the technique to characterize the heating rate of the surface trap. We then measured the stationary temperature of the ion as a function of cooling laser detuning in the Doppler regime. The results agree with theoretical calculations, with an absolute error smaller than 100 $\ensuremath{\mu}\mathrm{K}$ at 500 $\ensuremath{\mu}\mathrm{K}$, in a temperature range between 0.5 and 3 mK and in the absence of adjustable parameters. This simple-to-implement and reliable method opens the way to fast absolute measurements of single-ion temperatures in future experiments dealing with heat transport in ion chains or thermodynamics at the single-ion level.