Direct laser-written optomechanical membranes in fiber Fabry-Perot cavities.

Integrated micro- and nanophotonic optomechanical experiments enable the manipulation of mechanical resonators on the single phonon level. Interfacing these structures requires elaborate techniques limited in tunability, flexibility, and scaling towards multi-mode systems. Here, we demonstrate a cavity optomechanical experiment using 3D-laser-written polymer membranes inside fiber Fabry-Perot cavities. Vacuum coupling rates of g0/2π ≈ 30 kHz to the fundamental megahertz mechanical mode are reached. We observe optomechanical spring tuning of the mechanical resonator frequency by tens of kilohertz exceeding its linewidth at cryogenic temperatures. The direct fiber coupling, its scaling capabilities to coupled resonator systems, and the potential implementation of dissipation dilution structures and integration of electrodes make it a promising platform for fiber-tip integrated accelerometers, optomechanically tunable multi-mode mechanical systems, and directly fiber-coupled systems for microwave to optics conversion.

Controlled multi-photon subtraction with cascaded Rydberg superatoms as single-photon absorbers.

The preparation of light pulses with well-defined quantum properties requires precise control at the individual photon level. Here, we demonstrate exact and controlled multi-photon subtraction from incoming light pulses. We employ a cascaded system of tightly confined cold atom ensembles with strong, collectively enhanced coupling of photons to Rydberg states. The excitation blockade resulting from interactions between Rydberg atoms limits photon absorption to one per ensemble and rapid dephasing of the collective excitation suppresses stimulated re-emission of the photon. We experimentally demonstrate subtraction with up to three absorbers. Furthermore, we present a thorough theoretical analysis of our scheme where we identify weak Raman decay of the long-lived Rydberg state as the main source of infidelity in the subtracted photon number and investigate the performance of the multi-photon subtractor for increasing absorber numbers in the presence of Raman decay.

Photon propagation through dissipative Rydberg media at large input rates.

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency. Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.

Observation of Three-Body Correlations for Photons Coupled to a Rydberg Superatom.

We report on the experimental observation of nontrivial three-photon correlations imprinted onto initially uncorrelated photons through an interaction with a single Rydberg superatom. Exploiting the Rydberg blockade mechanism, we turn a cold atomic cloud into a single effective emitter with collectively enhanced coupling to a focused photonic mode which gives rise to clear signatures in the connected part of the three-body correlation function of the outgoing photons. We show that our results are in good agreement with a quantitative model for a single, strongly coupled Rydberg superatom. Furthermore, we present an idealized but exactly solvable model of a single two-level system coupled to a photonic mode, which allows for an interpretation of our experimental observations in terms of bound states and scattering states.

Emergent Universal Dynamics for an Atomic Cloud Coupled to an Optical Waveguide.

We study the dynamics of a single collective excitation in a cold ensemble of atoms coupled to a one-dimensional waveguide. The coupling between the atoms and the photonic modes provides a coherent and a dissipative dynamics for this collective excitation. While the dissipative part accounts for the collectively enhanced and directed emission of photons, we find a remarkable universal dynamics for increasing atom numbers exhibiting several revivals under the coherent part. While this phenomenon provides a limit on the intrinsic dephasing for such a collective excitation, a setup is presented where the universal dynamics can be explored.

Probing an Electron Scattering Resonance using Rydberg Molecules within a Dense and Ultracold Gas.

We present spectroscopy of a single Rydberg atom excited within a Bose-Einstein condensate. We not only observe the density shift as discovered by Amaldi and Segrè in 1934, but a line shape that changes with the principal quantum number n. The line broadening depends precisely on the interaction potential energy curves of the Rydberg electron with the neutral atom perturbers. In particular, we show the relevance of the triplet p-wave shape resonance in the e^{-}-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10^{14} cm^{-3}, and therefore an interparticle spacing of 1300 a_{0} within a Bose-Einstein condensate, the potential energy curves can be probed at these Rydberg ion-neutral atom separations. We present a simple microscopic model for the spectroscopic line shape by treating the atoms overlapped with the Rydberg orbit as zero-velocity, uncorrelated, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

Electromagnetically induced transparency in an entangled medium.

We theoretically investigate light propagation and electromagnetically induced transparency in a quasi-one-dimensional gas in which atoms interact strongly via exchange interactions. We focus on the case in which the gas is initially prepared in a many-body state that contains a single excitation and conduct a detailed study of the absorptive and dispersive properties of such a medium. This scenario is achieved in interacting gases of Rydberg atoms with two relevant S states that are coupled through exchange. Of particular interest is the case in which the medium is prepared in an entangled spin-wave state. This, in conjunction with the exchange interaction, gives rise to a nonlocal susceptibility that--in comparison to conventional Rydberg electromagnetically induced transparency--qualitatively alters the absorption and propagation of weak probe light, leading to nonlocal propagation and enhanced absorption.

Coupling a single electron to a Bose-Einstein condensate.

The coupling of electrons to matter lies at the heart of our understanding of material properties such as electrical conductivity. Electron-phonon coupling can lead to the formation of a Cooper pair out of two repelling electrons, which forms the basis for Bardeen-Cooper-Schrieffer superconductivity. Here we study the interaction of a single localized electron with a Bose-Einstein condensate and show that the electron can excite phonons and eventually trigger a collective oscillation of the whole condensate. We find that the coupling is surprisingly strong compared to that of ionic impurities, owing to the more favourable mass ratio. The electron is held in place by a single charged ionic core, forming a Rydberg bound state. This Rydberg electron is described by a wavefunction extending to a size of up to eight micrometres, comparable to the dimensions of the condensate. In such a state, corresponding to a principal quantum number of n = 202, the Rydberg electron is interacting with several tens of thousands of condensed atoms contained within its orbit. We observe surprisingly long lifetimes and finite size effects caused by the electron exploring the outer regions of the condensate. We anticipate future experiments on electron orbital imaging, the investigation of phonon-mediated coupling of single electrons, and applications in quantum optics.

Quantum nonlinear optics with single photons enabled by strongly interacting atoms.

The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. In conventional optical materials, the nonlinearity at light powers corresponding to single photons is negligibly weak. Here we demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption of photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Our approach paves the way for quantum-by-quantum control of light fields, including single-photon switching, all-optical deterministic quantum logic and the realization of strongly correlated many-body states of light.

Absorption imaging of ultracold atoms on atom chips.

Imaging ultracold atomic gases close to surfaces is an important tool for the detailed analysis of experiments carried out using atom chips. We describe the critical factors that need be considered, especially when the imaging beam is purposely reflected from the surface. In particular we present methods to measure the atom-surface distance, which is a prerequisite for magnetic field imaging and studies of atom surface-interactions.

Bose-Einstein condensates: microscopic magnetic-field imaging.

Today's magnetic-field sensors are not capable of making measurements with both high spatial resolution and good field sensitivity. For example, magnetic force microscopy allows the investigation of magnetic structures with a spatial resolution in the nanometre range, but with low sensitivity, whereas SQUIDs and atomic magnetometers enable extremely sensitive magnetic-field measurements to be made, but at low resolution. Here we use one-dimensional Bose-Einstein condensates in a microscopic field-imaging technique that combines high spatial resolution (within 3 micrometres) with high field sensitivity (300 picotesla).