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Optimizing free-space light-matter interaction by mode matching

Marianne Bader

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

This thesis describes an experiment to optimize the interaction of light and a single ion in free space. The key to efficient coupling consists in mode-matching the incident electromagnetic field to the radiative properties of the ion. For perfect coupling, the incident mode has to match the emission pattern of the ion. In free space, this requires illumination of the ion with an incoming dipole wave. In the present work, such a situation is realized experimentally. To this end, a radially polarized doughnut mode is focused with a deep parabolic mirror while the ion is localized in the focal point of the parabolic mirror by means of a trap of special geometry. This thesis reports first on the implementation of the two basic components of the experiment: the ion trapping in the focal point of the parabolic mirror and the generation of the required doughnut mode. Then, the coupling efficiency of the combined system is analyzed by means of saturation measurements. Characterization of our setup reveals aberrations of the parabolic mirror which prevent perfect coupling. However, the measured coupling efficiency of (7.2 ± 0.2)% is to date among the highest values reported for coupling experiments with a single atom in free space. A special aim of our group is the full excitation of an ion by a single photon. This requires, in addition to the above mentioned spatial mode matching, temporal shaping of the incident light. Perfect excitation can be achieved if the single-photon wavepacket shows an exponentially rising envelope with a time constant matching the lifetime of the excited state of the ion. The present work demonstrates the power of temporal mode matching using a model system: an empty optical cavity. Both, light inside a cavity and atomic excitation, decay exponentially. Thus, there is an analogy between atomic excitation and field energy inside a cavity. The task of exciting an ion translates to the task of coupling a classical light pulse into a cavity. This thesis confirms experimentally that almost the entire energy of a rising exponential pulse can be coupled into a cavity, provided the pulse time constant matches the cavity lifetime.

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This thesis describes an experiment to optimize the interaction of light and a single ion in free space. The key to efficient coupling consists in mode-matching the incident electromagnetic field to the radiative properties of the ion. For perfect coupling, the incident mode has to match the emission pattern of the ion. In free space, this requires illumination of the ion with an incoming dipole wave. In the present work, such a situation is realized experimentally. To this end, a radially polarized doughnut mode is focused with a deep parabolic mirror while the ion is localized in the focal point of the parabolic mirror by means of a trap of special geometry. This thesis reports first on the implementation of the two basic components of the experiment: the ion trapping in the focal point of the parabolic mirror and the generation of the required doughnut mode. Then, the coupling efficiency of the combined system is analyzed by means of saturation measurements. Characterization of our setup reveals aberrations of the parabolic mirror which prevent perfect coupling. However, the measured coupling efficiency of (7.2 ± 0.2)% is to date among the highest values reported for coupling experiments with a single atom in free space. A special aim of our group is the full excitation of an ion by a single photon. This requires, in addition to the above mentioned spatial mode matching, temporal shaping of the incident light. Perfect excitation can be achieved if the single-photon wavepacket shows an exponentially rising envelope with a time constant matching the lifetime of the excited state of the ion. The present work demonstrates the power of temporal mode matching using a model system: an empty optical cavity. Both, light inside a cavity and atomic excitation, decay exponentially. Thus, there is an analogy between atomic excitation and field energy inside a cavity. The task of exciting an ion translates to the task of coupling a classical light pulse into a cavity. This thesis confirms experimentally that almost the entire energy of a rising exponential pulse can be coupled into a cavity, provided the pulse time constant matches the cavity lifetime.
Today the interaction of light and matter on the single quantum level is a wide research field. Strong coupling between a single photon and a single atom has already been achieved with optical cavities. Here, we treat strong interaction in free space, i.e. strong interaction whilst maintaining the free space density of states of the electromagnetic field. We pursue the coupling of a properly designed single photon wave packet to a single ion aiming at an excitation probability close to unity. For this purpose a linear dipole transition of an ion localized in the focal point of a deep parabolic mirror is addressed by a collimated laser beam focused onto the ion from nearly the full solid angle. In order to reach the highest possible coupling strength, the incident vectorial light field must be matched to the radiation pattern of the corresponding atomic transition both in the spatial and in the temporal domain. Here the generation of such an incident light mode is presented.
We demonstrate the generation of an optical dipole wave suitable for the process of efficiently coupling single quanta of light and matter in free space. We employ a parabolic mirror for the conversion of a transverse beam mode to a focused dipole wave and show the required spatial and temporal shaping of the mode incident onto the mirror. The results include a proof of principle correction of the parabolic mirror's aberrations. For the application of exciting an atom with a single photon pulse, we demonstrate the creation of a suitable temporal pulse envelope. We infer coupling strengths of 89% and success probabilities of up to 87% for the application of exciting a single atom for the current experimental parameters.
The efficient interaction between single photons and single matter objects in free space is of key importance for quantum technologies. An experimental setup for testing this possibility involves single two-level ion trapped at the focus of a parabolic metallic mirror. We study the conditions for the setup, under which the assumption about the free-space mode structure of the radiation field in the vicinity of the atom is justified. In our analysis we apply vectorial properties of light by including the polarization degree of freedom. We look for possible changes in the spontaneous emission rate of the atom resulting from the presence of the parabolic boundary conditions.
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.
The interaction of a cavity with an external field is symmetric under time reversal. Thus, coupling to a resonator is most efficient when the incident light is the time reversed version of a free cavity decay, i.e. when it has a rising exponential shape matching the cavity lifetime. For light entering the cavity from only one side, the maximally achievable coupling efficiency is limited by the choice of the cavity mirrors' reflectivities. Such an empty-cavity experiment serves also as a model system for single-photon single-atom absorption dynamics. We present experiments coupling exponentially rising pulses to a cavity system which allows for high coupling efficiencies. The influence of the time constant of the rising exponential is investigated as well as the effect of a finite pulse duration. We demonstrate coupling 94% of the incident TEM 00 mode into the resonator.
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.