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arXiv:1806.03038 · Physical Review A

Operating a near-concentric cavity at the last stable resonance

Chi Huan Nguyen, Adrian Nugraha Utama, Nick Lewty, Christian Kurtsiefer

Published Dec 21, 2018• 20 citations
arXivHTMLPDF

Abstract

Near-concentric optical cavities of spherical mirrors can provide technical advantages over the conventional near-planar cavities in applications requiring strong atom-light interaction, as they concentrate light in a very small region of space. However, such cavities barely support stable optical modes, and thus impose practical challenges. Here, we present an experiment where we maintain a near-concentric cavity at its last resonant length for laser light at 780 nm resonant with an atomic transition. At this point, the spacing of two spherical mirror surfaces is $207(13)\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ shorter than the critical concentric point, corresponding to a stability parameter $g=\ensuremath{-}0.999962(2)$ and a cavity beam waist of $2.4\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$.

DOI
10.1103/physreva.98.063833

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Near-concentric optical cavities of spherical mirrors can provide technical advantages over the conventional near-planar cavities in applications requiring strong atom-light interaction, as they concentrate light in a very small region of space. However, such cavities barely support stable optical modes, and thus impose practical challenges. Here, we present an experiment where we maintain a near-concentric cavity at its last resonant length for laser light at 780 nm resonant with an atomic transition. At this point, the spacing of two spherical mirror surfaces is 207(13)nm207(13)\phantom{\rule{0.16em}{0ex}}\mathrm{nm}207(13)nm shorter than the critical concentric point, corresponding to a stability parameter g=\ensuremath−0.999962(2)g=\ensuremath{-}0.999962(2)g=\ensuremath−0.999962(2) and a cavity beam waist of 2.4\ensuremathμm2.4\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}2.4\ensuremathμm.
Near-concentric cavities are excellent tools for enhancing an atom-light interaction as they combine a small mode volume with a large optical access for atom manipulation. However, they are sensitive to longitudinal and transverse misalignments. To address this sensitivity, we present a compact near-concentric optical cavity system with a residual cavity length variation δLC,rms = 0.36(2) Å. A key part of this system is a cage-like tensegrity mirror support structure that allows us to correct for longitudinal and transverse misalignments. The system is stable enough to allow the use of mirrors with a higher cavity finesse to enhance the atom-light coupling strength in cavity-QED applications.
In the near-concentric regime, the transverse modes of an optical cavity have small mode volumes with a beam waist on the order of the atomic cross section. This shows potential for strong interaction between single atoms and light, which is a key component in distributed quantum computing architectures [1] . Furthermore, with centimetresized near-concentric cavities, the frequency spacing of the transverse modes ranges from tens of MHz to a GHz, matching well with the hyperfine or the Zeeman level splitting of an atom [2] . This near-degeneracy in resonant frequencies close to the critical point allows to explore the physics of atomic nonlinearities with multiple photonic modes strongly coupled to different hyperfine or magnetic energy levels of a quantum emitter.
Abstract Optical cavities are one of the best ways to increase atom-light coupling and will be a key ingredient for future quantum technologies that rely on light–matter interfaces. We demonstrate that traveling-wave ‘ring’ cavities can achieve small mode waists w (i.e. large atom-cavity coupling) while maintaining stability to fluctuations and large mirror separation. Additionally, our ring cavity design can achieve arbitrary transverse-mode spacing simultaneously with the large mode-waist reductions. Following these principles, we build a parabolic atom-ring cavity system that achieves strong collective coupling NC = 15(1) between N = 10 3 Rb atoms and a ring cavity with a single-atom cooperativity C that is significantly larger than what could be achieved with a near-confocal two-mirror cavity with the same mirror separation and finesse. By using parabolic mirrors, we eliminate astigmatism–which can otherwise preclude stable operation–and increase optical access to the atoms. Cavities based on these principles, with enhanced coupling and large mirror separation, will be particularly useful for achieving strong coupling with ions, Rydberg atoms, or other strongly interacting particles, which often have undesirable interactions with nearby surfaces.
Summary form only given. The development of atom interferometry in the last few decades has led to high precision measurements of inertial effects and tests of fundamental physics [1]. New methods for higher sensitivity atom interferometers (AIs) are being explored, in particular the interrogation of atoms with optical cavities. The benefits of optical cavities would be higher optical power allowing large momentum transfer beam splitters, and possibly cleaner and controlled phase profiles [2]. However high sensitivity AIs require long interrogation times, which, combined with cold atom cloud expansion, bring the challenges of large centimetric waists in cavities. We propose an optical resonator composed of a convergent lens with two flat mirrors at its focal planes as shown on figure 1 [3]. When perfectly aligned any input field can be resonating inside. Especially, when a Gaussian beam, with waist w0' on the first mirror, is inputted to the cavity, the lens conjugates it to the second mirror with waist w0= λf/πw0'. This cavity is marginally stable and exhibits a half degenerate behaviour: all modes resonate at the same frequencies, odd and even modes being separated by half a free spectral range. Thus it does not have strong mode cleaning properties but it is able to magnify any input field. When misaligned, this cavity goes out of its degenerate behaviour and the circulating field begins to degrade due to mode filtering. A numerical study of the cavity behaviour, using an ABCD transfer matrix formalism, showed that typical controllable misalignments of a few micrometres would not be critical for atom interrogation. Further degradations due to surface defects and tilts are being investigated.
We propose a procedure for the significant enhancement of the strong coupling rate between photons in an optical cavity and a single quantum emitter, such as an atom, quantum dot or trapped ion. We show that specially designed, non-spherical mirrors can lead to cavity eigenmodes that exhibit a large field enhancement at the center of the cavity while inducing significantly less beam divergence, and therefore smaller round trip losses and higher cooperativity, than can be achieved by operating a spherical-mirror cavity in the near-concentric regime. We verify our designs using mode matching theory and discuss their robustness relative to different kinds of manufacturing deviations.
Concentric cavities can lead to strong photon-atom coupling without a need for high finesse or small physical-cavity volume. In this proof-of-principle experiment we demonstrate coupling of single Rb atoms to an 11-mm-long near-concentric cavity with a finesse F=138(2)F=138(2)F=138(2). Operating the cavity $1.7(1)\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ shorter than the critical length, we observe an atom-cavity coupling constant ${g}_{0}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}5.0(2)$ MHz which exceeds the natural dipole decay rate $\ensuremath{\gamma}$ by a factor of ${g}_{0}/\ensuremath{\gamma}=1.7(1)$.