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Optical fibers play a key role in many different fields of science and technology. In particular, fibers with a diameter of several micrometers are intensively used in photonics. For these applications, it is often important to precisely know and control the fiber radius. Here, we demonstrate a novel technique to determine the local radius variation of a 30-micrometer diameter silica fiber with sub-\AA ngstr\"om precision with axial resolution of several tens of micrometers over a fiber length of more than half a millimeter. Our method relies on taking an image of the fiber's whispering-gallery modes (WGMs). In these WGMs, the speed of light propagating along the fiber axis is strongly reduced. This enables us to determine the fiber radius with a significantly enhanced precision, far beyond the diffraction limit. By exciting different axial modes, we verify the precision and reproducibility of our method and demonstrate that we can achieve a precision better than 0.3 \AA. The method can be generalized to other experimental situations where slow light occurs and, thus, has a large range of potential applications in the realm of precision metrology and optical sensing., Comment: 9 pages, 6 figures

We report on the observation of multimode strong coupling of a small ensemble of atoms interacting with the field of a 30-m long fiber resonator containing a nanofiber section. The collective light--matter coupling strength exceeds the free spectral range and the atoms couple to consecutive longitudinal resonator modes. The measured transmission spectra of the coupled atom-resonator system provide evidence of this regime, realized with a few hundred atoms with an intrinsic single-atom cooperativity of 0.26. These results are the starting point for studies in a new setting of light-matter interaction, with strong quantum non-linearities and a new type of dynamics., Comment: 7 pages including Supplemental Material, 4 figures

Laser-cooled atoms that are trapped and optically interfaced with light in nanophotonic waveguides are a powerful platform for fundamental research in quantum optics as well as for applications in quantum communication and quantum information processing. Ever since the first realization of such a hybrid quantum nanophotonic, heating rates of the atomic motion observed in various experimental settings have typically been exceeding those in comparable free-space optical microtraps by about three orders of magnitude. This excessive heating is a roadblock for the implementation of certain protocols and devices. Its origin has so far remained elusive and, at the typical atom-surface separations of less than an optical wavelength encountered in nanophotonic traps, numerous effects may potentially contribute to atom heating. Here, we theoretically describe the effect of mechanical vibrations of waveguides on guided light fields and provide a general theory of particle-phonon interaction in nanophotonic traps. We test our theory by applying it to the case of laser-cooled cesium atoms in nanofiber-based two-color optical traps. We find excellent quantitative agreement between the predicted heating rates and experimentally measured values. Our theory predicts that, in this setting, the dominant heating process stems from the optomechanical coupling of the optically trapped atoms to the continuum of thermally occupied flexural mechanical modes of the waveguide structure. Beyond unraveling the long-standing riddle of excessive heating in nanofiber-based atom traps, we also study the dependence of the heating rates on the relevant system parameters. Our findings allow us to propose several strategies for minimizing the heating. Finally, our findings are also highly relevant for optomechanics experiments with dielectric nanoparticles that are optically trapped close to nanophotonic waveguides., Comment: Published version. 35 pages (including appendices), 7 figures, 18 tables, and 3 pages of supplemental material

We analyze the coupling of atoms or atom-like emitters to nanophotonic waveguides in the presence of propagating acoustic waves. Specifically, we show that strong index modulations induced by such waves can drastically modify the effective photonic density of states and thereby influence the strength, the directionality, as well as the overall characteristics of photon emission and absorption processes. These effects enable a complete dynamical control of light-matter interactions in waveguide structures, which even in a two dimensional system can be used to efficiently exchange individual photons along selected directions and with a very high fidelity. Such a quantum acousto-optical control provides a versatile tool for various quantum networking applications ranging from the distribution of entanglement via directional emitter-emitter interactions to the routing of individual photonic quantum states via acoustic conveyor belts., Comment: 15 pages, 9 figures

We realize a mechanical analogue of the Dicke model, achieved by coupling the spin of individual neutral atoms to their quantized motion in an optical trapping potential. The atomic spin states play the role of the electronic states of the atomic ensemble considered in the Dicke model, and the in-trap motional states of the atoms correspond to the states of the electromagnetic field mode. The coupling between spin and motion is induced by an inherent polarization gradient of the trapping light fields, which leads to a spatially varying vector light shift. We experimentally show that our system reaches the ultra-strong coupling regime, i.e., we obtain a coupling strength which is a significant fraction of the trap frequency. Moreover, with the help of an additional light field, we demonstrate the in-situ tuning of the coupling strength. Beyond its fundamental interest, the demonstrated one-to-one mapping between the physics of optically trapped cold atoms and the Dicke model paves the way for implementing protocols and applications that exploit extreme coupling strengths.