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arXiv:1609.06884 · Journal of the European Optical Society Rapid Publications

Focusing characteristics of a 4 πparabolic mirror light-matter interface

Lucas Alber, Martin Fischer, Marianne Bader, Klaus Mantel, Markus Sondermann, Gerd Leuchs

Published May 1, 2017• 21 citations

Abstract

Focusing with a 4 π parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror’s fabrication process and might introduce errors that reduce the focusing quality. To determine these errors, we experimentally examine the focusing properties of a 4 π parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single 174 Yb + ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4 π parabolic mirror.

DOI: 10.1186/s41476-017-0043-y

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Focusing with a 4 π parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror’s fabrication process and might introduce errors that reduce the focusing quality. To determine these errors, we experimentally examine the focusing properties of a 4 π parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single 174 Yb + ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4 π parabolic mirror.

Efficient fluorescence collection is the most challenging part in remote entangled ion qubit state generation. To address this issue, we developed an ion trap consisting of a reflective parabolic surface and a needle electrode. This parabolic trap design covers a solid angle of 2π steradians and allows precise ion placement at the focal point of the parabola. We measured (39 ± 3)% fluorescence collection from a single ion with this trap and analyzed the mirror optical performance. We observed single ion image spot size of 3.4 times diffraction limit, improved to 2.8 times diffraction limit with the help of an external deformable mirror. The micromotion of the ion is determined to be the limiting factor, and the result is consistent with theoretical calculation.

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}

Yb

{}^{+}

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.

Optical dipole-traps are used in various scientific fields, including classical optics, quantum optics and biophysics. Here, we propose and implement a dipole-trap for nanoparticles that is based on focusing from the full solid angle with a deep parabolic mirror. The key aspect is the generation of a linear-dipole mode which is predicted to provide a tight trapping potential. We demonstrate the trapping of rod-shaped nanoparticles and validate the trapping frequencies to be on the order of the expected ones. The described realization of an optical trap is applicable for various other kinds of solid-state targets. The obtained results demonstrate the feasibility of optical dipole-traps which simultaneously provide high trap stiffness and allow for efficient interaction of light and matter in free space.

Our research aims at the free-space interaction of a single ion with a surrounding light field. A particularly important ingredient is the illumination of the ion from almost the full solid angle. Conventional ion traps are not built with wide open optical access as their primary design goal and are thus restricting the solid angle accessible to incoming light. By combining a reflective optical element such as a parabolic mirror with a specially designed wide open ion trap we aim to overcome this limitation.

Abstract. Efficient collection and analysis of trapped ion qubit fluorescence is essential for robust qubit state detection in trapped ion quantum computing schemes. We discuss simple techniques of improving photon collection efficiency using high numerical aperture (N.A.) reflective optics. To test these techniques we placed a spherical mirror with an effective N.A. of about 0.9 inside a vacuum chamber in the vicinity of a linear Paul trap. We demonstrate stable and reliable trapping of single barium ions, in excellent agreement with our simulations of the electric field in this setup. While a large N.A. spherical mirror introduces significant spherical aberration, the ion image quality can be greatly improved by a specially designed aspheric corrector lens located outside the vacuum system. Our simulations show that the spherical mirror/corrector design is an easy and cost-effective way to achieve high photon collection rates when compared to a more sophisticated parabolic mirror setup.

We report on the demonstration of a lightmatter interface coupling light to a single Yb-174(+) ion in free space. The interface is realized through a parabolic mirror partially surrounding the ion. It transforms a La-guerre- Gaussian beam into a linear dipole wave converging at the mirror's focus. By measuring the non-linear response of the atomic transition, we deduce the power required for reaching an upper-level population of 1/4 to be 692 +/- 20pW at half linewidth detuning from the atomic resonance. Performing this measurement while scanning the ion through the focus provides a map of the focal intensity distribution. From the measured power, we infer a coupling efficiency of 7.2 +/- 0.2% on the linear dipole transition when illuminating from half solid angle, being among the best coupling efficiencies reported for a single atom in free space.