Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a first and comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of ^174Yb in 6sns ^1S_0 Rydberg states across nearly two decades in principal quantum number n and three orders of magnitude in molecular binding energy. Using the Coulomb Green's function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy s-wave scattering length and the positions of two spin-orbit split p-wave shape resonances. Our results provide strong evidence that the Yb^- anion exists only as a metastable resonance.

Rydberg atoms provide a powerful platform for exploring strongly interacting quantum systems, both in free space and in structured electromagnetic environments, with growing applications in quantum technology. Accurately modeling their single-atom properties and mutual interactions is essential for interpreting experiments and designing new architectures. We present a unified theoretical framework for Rydberg atoms and their interactions based on multi-channel quantum defect theory (MQDT) and static electromagnetic Green's tensors. MQDT provides a precise description of Rydberg states of divalent atoms such as strontium and ytterbium, while the Green's tensor formalism provides a general and flexible approach for calculating interactions between two Rydberg atoms in arbitrary geometries, including modifications induced by nearby surfaces. We implement this framework in an updated version of the open-source PairInteraction software [Weber et al., J. Phys. B 50 (2017)]. The implementation leverages high-performance libraries and achieves speedups of one order of magnitude for pair-potential calculations compared to prior software. We demonstrate the capabilities of the framework through example applications to divalent atoms and show excellent agreement with experimental data for an exemplary Stark map of ^174Yb. The modular software architecture enables the community to extend it further.

We develop a theory of the transverse spatial dynamics of two interacting photons in a Rydberg nonlinear medium. Extending the well-studied one-dimensional case, we explore both longitudinal and transverse correlations of photons propagating as Rydberg polaritons. We identify distinct behaviors and scaling laws for these correlations, arising from fundamentally different mechanisms in the two directions: diffraction for transverse correlations and diffusion for longitudinal correlations. We develop a model incorporating a Gaussian optical beam and an inhomogeneous atomic density distribution, from which we derive quantitative predictions for correlation functions in both directions. We further show that the propagation equations can be reduced to a single Schrödinger-like equation, allowing approximate solutions that are supported by full numerical results. Our findings indicate that the transverse correlation length is determined primarily by the blockade radius, whereas the longitudinal correlation length is limited by bandwidth. These results establish transverse Rydberg blockade as a distinct and measurable correlation mechanism and show that spatial photon correlations provide a direct means of measuring the blockade radius.

Optomechanical membrane-in-the-middle systems that comprise several coupled compliant membranes offer enhanced optomechanical coupling and collective dynamics. Recent realizations were fundamentally restricted to two membranes and to limited structural optimization of the involved membranes due to their intricate fabrication and experimental integration. Here, we present a fiber-based Fabry-Perot microcavity incorporating monolithically integrated double-membrane resonators fabricated by 3D direct laser writing. We realize controllable mechanical mode hybridization of membranes with coupling rates of up to J_mech/2π= 0.16 MHz, exceeding the mechanical linewidths. We demonstrate enhanced collective optomechanical coupling of the membrane stack's breathing mode, reaching collective coupling strengths of up to g_col^(-)/2π≈ 0.1 MHz. Our transfer-matrix calculations predict further substantial enhancements with realistic reductions of membrane thickness and spacing, and a larger number of membranes. Our results establish direct laser-written membrane arrays as a scalable platform for multimode cavity optomechanics, combining tunable mechanical interactions, enhanced collective optomechanical coupling, and scalability towards larger mechanically coupled resonator systems.

Mechanical systems provide a unique test bed for studying quantum phenomena at macroscopic length scales. However, realizing quantum states that feature quantum correlations among macroscopic mechanical objects remains an experimental challenge. Here, we propose a quantum system in which two micro-electromechanical oscillators interact through a chain of Rydberg atoms confined in optical tweezers. We demonstrate that the coherent dynamics of the system generate entanglement between the oscillators. Furthermore, we utilize the tunability of the radiative decay of the Rydberg atoms for dissipative entanglement generation. Our results highlight the potential to exploit the flexibility and tunability of Rydberg atom chains to generate nonclassical correlations between distant mechanical oscillators.

We present an experimental scheme for producing ultracold ytterbium atoms in a compact dual-chamber setup. A dispenser-loaded two-dimensional magneto-optical trap (MOT) using permanent magnets and operating on the broad 1S0 - 1P1 singlet transition delivers over 107 atoms per second through a differential pumping stage into a three-dimensional MOT. The two-color three-dimensional MOT uses the broad singlet transition to accumulate <^> 2 x 107 atoms of 174Yb within 2.5 s and subsequently the narrow 1S0 - 3P1 intercombination line to cool the atomic cloud to below 10 mu K. We report optimized parameters for each stage of the atom collection sequence, achieving high transfer efficiency. We find that shelving into the triplet state during the broad-transition MOT almost doubles the number of trapped atoms.

We present a photothermal spectroscopy (PTS) sensor utilizing a miniaturized fiber Fabry-Perot cavity (FFPC) for gas detection. This innovative approach lays the groundwork for a new generation of highly selective and sensitive gas sensors with a miniaturized footprint. In conventional laser-based gas sensing, exploiting strong molecular transitions typically requires specialized, now noise detectors. Our system overcomes this limitation through indirect detection, where a pump laser excites gas molecules and the resulting refractive index modulation is probed using a high-finesse FFPC. This configuration leverages the advantages of straightforward gas excitation while using cost-effective near-infrared detection components. The proof-of-concept experiment successfully demonstrated methane detection by exciting molecules directly inside the FFPC. The photothermal-induced refractive index modulation translates into measurable variations in optical power reflected from the cavity. Our experimental results confirmed excellent sensitivity with the capability to detect trace gas concentrations in the parts-perbillion level. A key advantage of our approach is that the wavelength selection for pump lasers is unrestricted, allowing targeting of optimal absorption lines across different spectral regions a significant improvement over hollow-core fiber-based PTS sensors with limited transmission bandwidths. The FFPC design offers inherent stability, miniaturization, and high sensitivity with extremely small interaction volumes. The architecture we developed employs wavelength modulation spectroscopy for enhanced signal processing, resulting in superior noise rejection. This implementation significantly advances the capabilities of photothermal spectroscopy for gas analysis in fields ranging from environmental monitoring to industrial process control and medical diagnostics. While currently demonstrated for methane detection, the platform's versatility makes it readily adaptable for multiple gas species in future implementations.

Despite their application in multiple fields, ranging from quantum sensing to fundamental tests of quantum mechanics, conventional state-of-the-art cavity optomechanical experiments have been limited in their scaling to- wards systems with multiple mechanical resonators. 3D direct laser writing offers a new approach of fabricating multi-membrane structures that can be directly integrated into fiber Fabry-Perot cavities. Here, we experimentally demonstrate direct laser-written stacks of two or more coupled membranes - with normal-mode splittings of up to a MHz - interfaced by fiber cavities. As a first step, we show that simple, uncoupled multi-membrane structures can be properly fabricated with the direct laser writing approach and used for optomechanical experiments, as shown in Fig. 1(a).

Magic trapping of ground and Rydberg states, which equalizes the AC Stark shifts of these two levels, enables increased ground-to-Rydberg state coherence times. We measure via photon storage and retrieval how the ground-to-Rydberg state coherence depends on trap wavelength for two different traps and find different optimal wavelengths for a one-dimensional optical lattice trap and a running wave optical dipole trap. Comparison to theory reveals that this is caused by the Rydberg electron sampling different potential landscapes. The observed difference increases for higher principal quantum numbers, where the extent of the Rydberg electron wave function becomes larger than the optical lattice period. Our analysis shows that optimal magic trapping conditions depend on the trap geometry, in particular for optical lattices and tweezers.

For multi-level systems in hot atomic vapors the interplay between the Doppler shift due to atomic motion and the wavenumber mismatch between driving laser fields strongly influences transmission and absorption properties of the atomic medium. In a three-level atomic ladder-system, Doppler broadening limits the visibility of electromagnetically-induced transparency (EIT) when the probe and control fields are co-propagating, while EIT is recovered under the opposite condition of counter-propagating geometry and kp<kc , with kp and kc being the wavenumbers of the probe and control fields, respectively. This effect has been studied and experimentally demonstrated as an efficient mechanism to realize non-reciprocal probe light transmission, which may enable applications as magnetic-field free optical isolators. Here, we describe the basics of this effect and discuss a simple picture for the underlying mechanism. We illustrate how the non-reciprocity scales with wavelength mismatch and show how to experimentally demonstrate the effect in a simple Rydberg-EIT system using thermal Rubidium atoms.

Quantum information processing with neutral atoms relies on Rydberg excitation for entanglement generation. While the use of heavy divalent or open-shell elements, such as strontium or ytterbium, has benefits due to their optically active core and a variety of possible qubit encodings, their Rydberg structure is generally complex. For some isotopes in particular, hyperfine interactions are relevant even for highly excited electronic states. We employ multichannel quantum defect theory to infer the Rydberg structure of isotopes with nonzero nuclear spin and perform nonperturbative Rydberg-pair interaction calculations. We find that due to the high level density and sensitivities to external fields, experimental parameters must be precisely controlled. Specifically in 87Sr, we study an intrinsic F & ouml;rster resonance, unique to divalent atoms with hyperfine-split thresholds, which simultaneously provides line stability with respect to external field fluctuations and enhanced long-range interactions. Additionally, we provide parameters for pair states that can be effectively described by single-channel Rydberg series. The explored pair states provide exciting opportunities for applications in the blockade regime, as well as for more exotic long-range interactions such as largely flat, distance-independent potentials.

For multi-level systems in hot atomic vapors the interplay between the Doppler shift due to atom velocity and the wavenubmer mismatch between driving laser fields strongly influences transmission and absorption properties of the atomic medium. In a three-level atomic ladder-system, Doppler broadening limits the visibility of electromagnetically-induced transparency (EIT) when the probe and control fields are co-propagating, while EIT is recovered under the opposite condition of counter-propagating geometry and k_p < k_c, with k_p and k_c being the wavenumbers of the probe and control fields, respectively. This effect has been studied and experimentally demonstrated as an efficient mechanism to realize non-reciprocal probe light transmission, opening promising avenues for example for realization of magnetic-field free optical isolators. In this tutorial we discuss the theoretical derivation of this effect and show the underlying mechanism to be an avoided crossing of the states dressed by the coupling laser as a function of atomic velocities when k_p<k_c. We investigate how the non-reciprocity scales with wavelength mismatch and show how to experimentally demonstrate the effect in a simple Rydberg-EIT system using thermal Rubidium atoms.

We demonstrate a robust and miniaturized fiber Fabry-Perot cavity-based sensor for photothermal spectroscopic signal retrieval. The proof-of-concept experiment involved the use of a near-infrared pump laser to detect methane molecules on an isolated overtone 2.3 R(4) transition located at 6057.1 cm-1. The photothermal-related modulation of the gas refractive index was induced at the center of the interferometer, which was filled with the sample. Subsequently, the phase change of the resonating probe beam was measured as a shift in the reflected beam intensity, which was proportional to the methane concentration. A normalized noise equivalent absorption coefficient of 7.06 x 10-8 cm-1 W Hz-1/2 was achieved, suggesting significant potential for the design of small and versatile gas detectors with excellent detectivity. We discuss future improvements of the proposed photothermal gas detection approach.

We present an experimental scheme for producing ultracold Ytterbium atoms in a compact dual-chamber setup. A dispenser-loaded two-dimensional (2D) magneto-optical trap (MOT) using permanent magnets and operating on the broad ^1S_0→^1P_1 singlet transition delivers over 10^7 atoms per second through a differential pumping stage into a three-dimensional (3D) MOT. The two-color 3D MOT uses the broad singlet transition to accumulate ∼2× 10^7 atoms of ^174Yb within 2.5 s and subsequently the narrow ^1S_0→^3P_1 intercombination line to cool the atomic cloud to below 10 μK. We report optimized parameters for each stage of the atom collection sequence, achieving high transfer efficiency. We find that shelving into the triplet state during the broad-transition MOT almost doubles the number of trapped atoms.

Cavity optomechanical experiments in micro- and nanophotonic systems have realized unprecedented optomechanical coupling strengths [1]. However, the process of interfacing these systems can often be challenging and their scaling towards larger systems including many mechanical and optical resonators is limited. Here, we demonstrate a directly fiber-coupled tunable and highly flexible platform for cavity optomechanics based on 3D laser-written polymer membrane structures that are directly integrated into fiber Fabry-Perot cavities [2]. A schematic overview of the experiment is shown in Fig. 1(a).

Creating non-classical states of light from simple quantum systems together with classical resources is a challenging problem. We show how chiral emitters under a coherent drive can generate non-classical photon states. For our analysis, we select a specific temporal mode in the transmitted light field, resulting in a coupled master equation for the relevant mode and the chiral emitters. We characterise the mode's state by its Wigner function and show that the emission from the system predominantly produces mixtures of few-photon-added coherent states. We argue that these non-classical states are experimentally accessible and show their application for quantum metrology.

Quantum optics based on highly excited atoms, also known as Rydberg atoms, has cemented itself as a powerful platform for the manipulation of light at the few-photon level. The Rydberg blockade, resulting from the strong interaction between individual Rydberg atoms, can turn a large ensemble of atoms into a system which collectively resembles a single two-level emitter, a so-called Rydberg superatom. The coupling of this artificial emitter to a driving photonic mode is collectively enhanced by Rydberg interactions, enabling strong coherent coupling at the few-photon level in free-space. The exquisite level of control achievable through this has already demonstrated its utility in applications of quantum computing and information processing. Here, we review the derivation of the collective coupling between a Rydberg superatom and a single light mode and discuss the similarity of this free-space setup to waveguide quantum electrodynamics systems of quantum emitters coupled to photonic waveguides. We also briefly review applications of Rydberg superatoms to quantum optics such as single-photon generation and single-photon subtraction.

Fabry–Perot interferometers have stimulated numerous scientific and technical applications ranging from high-resolution spectroscopy over metrology, optical filters, to interfaces of light and matter at the quantum limit and more. End facet machining of optical fibers has enabled the miniaturization of optical Fabry–Perot cavities. Integration with fiber wave guide technology allows for small yet open devices with favorable scaling properties including mechanical stability and compact mode geometry. These fiber Fabry–Perot cavities (FFPCs) are stimulating extended applications in many fields including cavity quantum electrodynamics, optomechanics, sensing, nonlinear optics and more. Here we summarize the state of the art of devices based on FFPCs, provide an overview of applications and conclude with expected further research activities.

We develop a model of a quantum field confined within a cavity with a movable wall where the position of the wall is quantized. We obtain a full description of the dynamics of both the quantum field and the confining wall depending on the initial state of the whole system. Both the reaction and back-reaction of the field on the wall, and the wall on the field, can be taken into account, as well as external driving forces on both the cavity and the wall. The model exactly reproduces the resonant cavity mode stimulation due to the periodic motion of the mirror (dynamical Casimir effect), as well as the standard radiation pressure effects on the quantized wall(optomechanics). The model also accounts for the interplay of the two scenarios. Finally, the time evolution of the radiation force shows the interplay between the static and dynamical Casimir effect.

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.