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arXiv:1408.4367 · New Journal of Physics

Frequency splitting of polarization eigenmodes in microscopic Fabry–Perot cavities

Manuel Uphoff, Manuel Brekenfeld, Gerhard Rempe, Stephan Ritter

Published Jan 27, 2015• 86 citations
arXivHTMLPDF

Abstract

We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO 2 laser-machined, high-finesse optical Fabry–Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections to the paraxial resonator theory is in excellent agreement with the measurements, showing that geometric effects are the main source of the frequency splitting of polarization modes for the type of microscopic cavity studied here. By rotating one of the mirrors around the cavity axis, the splitting can be tuned. In the case of an identical differential phase shift per mirror, it can even be eliminated, despite a nonvanishing eccentricity of each mirror. We expect our results to have important implications for many experiments in cavity quantum electrodynamics, where Fabry–Perot cavities with small mode volumes are required.

DOI
10.1088/1367-2630/17/1/013053

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We study the frequency splitting of the polarization eigenmodes of the fundamental transverse mode in CO 2 laser-machined, high-finesse optical Fabry–Perot cavities and investigate the influence of the geometry of the cavity mirrors. Their highly reflective surfaces are typically not rotationally symmetric but have slightly different radii of curvature along two principal axes. We observe that the eccentricity of such elliptical mirrors lifts the degeneracy of the polarization eigenmodes. The impact of the eccentricity increases for smaller radii of curvature. A model derived from corrections to the paraxial resonator theory is in excellent agreement with the measurements, showing that geometric effects are the main source of the frequency splitting of polarization modes for the type of microscopic cavity studied here. By rotating one of the mirrors around the cavity axis, the splitting can be tuned. In the case of an identical differential phase shift per mirror, it can even be eliminated, despite a nonvanishing eccentricity of each mirror. We expect our results to have important implications for many experiments in cavity quantum electrodynamics, where Fabry–Perot cavities with small mode volumes are required.
We demonstrate a type of microcavity with large tunable splitting of polarization modes. This polarization nondegenerate cavity consists of two ellipsoidal concave mirrors with controllable eccentricity by CO2 laser machining on fiber end facets. The experiment shows that the cavities can combine the advantages of high finesse above 104 and large tunable polarization mode splitting to the GHz range. As the splitting of the cavity can be finely controlled to match atom hyperfine levels or optomechanics phonons, it will blaze a way in experiments on cavity quantum electrodynamics and cavity optomechanics.
Fiber Fabry–Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber Fabry–Perot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezo-mechanically actuated cavity with feedback based on the Pound–Drever–Hall locking technique is compared to a novel rigid cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal self-locking and external temperature tuning. Furthermore, we present a general analysis of the mode matching problem in fiber Fabry–Perot cavities, which explains the asymmetry in their reflective line shapes and has important implications for the optimal alignment of the fiber resonators. Finally, we discuss the issue of fiber-generated background photons. We expect that our results contribute toward the integration of high-finesse fiber Fabry–Perot cavities into compact and robust quantum-enabled devices in the future.
Long-distance quantum communication requires a highly efficient interface between light and matter.This thesis describes optical Fabry-Perot microcavities based on CO 2 laser-machined mirror substrates that are ideal to couple single photons and single atoms.The surfaces of the mirrors show ultra-low roughness, which enables cavities with a finesse of up to 1.9 × 10 5 .Because of the small radii of curvature on the order of 100 ➭m achieved with this technique, deviations from the paraxial approximation become relevant, resulting in a frequency splitting of polarization eigenmodes.A theoretical model has been derived and confirmed by measured values and this understanding can be used to tailor this frequency splitting for specific applications.A prime application for these cavities is heralded entanglement generation between single atoms and telecomwavelength photons, which is proposed and analyzed in this thesis.In a theoretical study of a quantum repeater protocol based on this scheme and cavity-assisted quantum gates, remote entanglement is generated faster than without repeater nodes if the distance between the end nodes exceeds 50 km. ZusammenfassungQuantenkommunikation über lange Distanzen erfordert eine hocheffiziente Schnittstelle zwischen Licht und Materie.In der vorliegenden Arbeit werden optische Fabry-Perot-Mikroresonatoren beschrieben, deren Spiegelsubstrate mit einem CO 2 -Laser bearbeitet wurden und die ideal geignet sind, um einzelne Photonen und einzelne Atomen miteinander zu koppeln.Die Spiegeloberflächen zeichnen sich durch extrem niedrige Rauhigkeiten aus, sodass Resonatoren mit einer Finesse von bis zu 1.9 × 10 5 erreicht werden.Aufgrund der kleinen Krümmungsradien in der Größenordnung von 100 ➭m, die mit dieser Methode erreicht wurden, werden Abweichungen von der paraxialen Näherung relevant, die zu einer Frequenzufspaltung der Polarisationseigenmoden führen.Es wurde ein theoretisches Modell erstellt und mit Messungen verifiziert, das benutzt werden kann, um die Frequenzaufspaltung zu kontrollieren.Eine wichtige Anwendung für diese Resonatoren ist die angekündigte Verschränkungserzeugung zwischen Einzelatomen und Photonen bei Telekomwellenlängen, die in dieser Arbeit vorgeschlagen und untersucht wird.In einer theoretischen Analyse eines Quantenrepeaterprotokolls, das auf diesem Schema und resonatorunterstützten Quantengattern basiert, wird Verschränkung zwischen zwei Orten schneller erzeugt als ohne Repeaterstationen, wenn die Entfernung zwischen diesen 50 km übersteigt. CO 2 laser machining of glass
We characterize a high-finesse Fabry-Perot resonator for coupling with single neutral atoms. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitudinal or transverse modes with two lasers simultaneously, and measure those frequencies using a precision wavelength meter (WLM). A major novelty of this method is that the parameters' uncertainty is solely determined by the resolution of the WLM, eliminating all of the temporal environment fluctuations. Moreover, the technique with two lasers consists of a vital approach for determining geometric parameters of a short cavity, with a free spectral range on the order of THz. Our system operates in the strong atom-cavity coupling regime that allows us to explore fundamental quantum optics and implement quantum network protocols.
We have realized a fiber-based Fabry–Perot cavity with CO 2 laser-machined mirrors. It combines very small size, high finesse , small waist and mode volume, and good mode matching between the fiber and cavity modes. This combination of features is a major advance for cavity quantum electrodynamics (CQED), as shown in recent CQED experiments with Bose–Einstein condensates enabled by this cavity (Colombe Y et al 2007 Nature 450 272). It will also be suitable for a wide range of other applications, including coupling to solid-state emitters, gas detection at the single-particle level, fiber-coupled single-photon sources and high-resolution optical filters with large stopband.