We present absolute frequency measurements of $2{\mathrm{S}}_{1/2}\text{−}\mathrm{n}{\mathrm{S}}_{1/2}$ two-photon transitions with $n=8$, 9, and 10 in a cryogenic beam of atomic hydrogen. Each transition has been measured with a fractional uncertainty of $\approx 2.6\times {10}^{-12}$. Combining the results from this Letter and the $1{\mathrm{S}}_{1/2}\text{−}2{\mathrm{S}}_{1/2}$ transition frequency, we extract a root-mean-square proton radius of $r_p=0.8433(31)\mathrm{fm}$ and a Rydberg frequency of $c{R}_{\infty }=3289841960252.9(9.7)\mathrm{kHz}$. These are in good agreement with the CODATA 2022 recommended values.

Squeezed states of light enable quantum-enhanced measurements but are limited by optical loss, particularly at $2\mathrm{\mu }\mathrm{m}$ where photodiode efficiency is low. We report the first loss-tolerant, audio-band squeezed light detection at 1984 nm by using a phase-sensitive amplifier to amplify the squeezed vacuum prior to detection. This technique increases the effective detection efficiency from 74% to 95% and increases the observed squeezing from 4 to 8 dB, the highest level of squeezing observation reported at this wavelength. Additionally, the vacuum to dark-noise clearance increases, extending the effective measurement bandwidth toward lower frequencies. This approach is largely wavelength independent, extending high-fidelity quantum measurements to future gravitational-wave detectors and related quantum technologies.

In 1996, Hatano and Nelson proposed a non-Hermitian lattice model containing an imaginary Peierls phase [Phys. Rev. Lett. 77, 570 (1996)], which subsequent analyses revealed to be an instance of a new class of topological systems. Here, we experimentally realize a continuum analog to this model containing an imaginary gauge potential using a homogeneous spin-orbit coupled Bose-Einstein condensate (BEC). Non-Hermiticity is introduced by adding tunable spin-dependent loss via microwave coupling to a subspace with spontaneous emission. We demonstrate that the resulting Heisenberg equations of motion for position and momentum depend explicitly on the system’s phase-space distribution. First, we observe collective nonreciprocal transport in real space, with a “self-acceleration” that decreases with the BEC’s spatial extent, consistent with non-Hermitian Gross-Pitaevskii simulations. We then examine localized edge states: the relatively strong interactions in our BEC suppress the formation of topological edge states, yielding instead highly excited states localized by an interplay between self-acceleration and wave function spreading. Finally, we confirm that our non-Hermitian description remains valid at all times by comparing it to a multilevel master equation treatment.

Photonic molecules can mimic interactions of atomic energy levels, offering new ways to manipulate cavity eigenstates. Current methods using evanescent coupling of multiple cavities face challenges in scalability, flexibility, and coupling control, especially for complex systems. Here we introduce a new method that uses a single multimode optical ring resonator to create photonic molecules. Our design uses multiple waveguide transverse modes in one resonator, providing flexibility to engineer complex interactions without typical coupling constraints. We demonstrate arbitrary intermode coupling through transmissive mode converters, allowing precise tuning of resonance splitting and intrinsic losses. This approach enables selective bright-dark mode pair generation and the exploration of novel photonic phenomena such as exceptional points. This multimode photonic molecule overcomes traditional limitations and offers new possibilities for integrated photonic circuits, optical processing, and studies in non-Hermitian and nonlinear photonics.

Polarized single-photon sources (SPSs) are valuable for quantum information applications and can be implemented by exploiting an elliptical or birefringent cavity that provide polarization-selective Purcell enhancement. However, current designs suffer from similar quality ($Q$) factors of split cavity modes, requiring both high Purcell factor and substantial mode splitting for ideal polarization performance. Here, we report a low-Purcell anisotropic Dirac cavity that supports orthogonally polarized modes with significantly distinct $Q$ factors (1032 vs 98). When coupled to a single quantum dot, this cavity enables single-photon emission [$g^{(2)}(0)=0.028$] with $>99\%$ degree of linear polarization (DoLP). The high DoLP is tolerant to emission wavelength, originating from suppression of competing radiative channels. Lifetime measurements demonstrate a 1.72-fold enhancement at cavity resonance and a 3.47-fold inhibition in a photonic band gap. Additionally, the anisotropic Dirac cavity exhibits vertical directionality with simulated collection efficiency up to 92.7%. Our results offer a novel strategy toward ideal solid-state polarized SPSs.

Entangled states hold the promise of improving the precision and accuracy of quantum sensors. We experimentally demonstrate that spectroscopy of an optical clock transition using entangled states can outperform its classical counterpart. Two ${{}^{40}\mathrm{Ca}}^{+}$ ions are entangled in a quantum state with vanishing first-order magnetic field sensitivity, extending the coherence time of the atoms and enabling near-lifetime-limited probe times of up to 550 ms. In our protocol, entangled ions reach the same instability as uncorrelated ions, but at half the probe time, enabling faster cycle times of the clock. We run two entangled ${{}^{40}\mathrm{Ca}}^{+}$ ions as an optical clock and compare its frequency instability with a ${}^{87}\mathrm{Sr}$ lattice clock. The instability of the entangled ion clock is below a clock operated with classically correlated states for all probe times. We observe instabilities below the theoretically expected quantum projection noise limit of two uncorrelated ions for interrogation times below 100 ms. The lowest fractional frequency instability of $7\times {10}^{-16}/\sqrt{\tau /1\mathrm{s}}$ is reached for 250 ms probe time, limited by residual phase noise of the probe laser. This represents the lowest instability reported to date for a ${{}^{40}\mathrm{Ca}}^{+}$ ion clock.

Solitons are the cornerstone of nonlinear physics. The integrability of nonlinear equations is the basis of this universal concept. However, most multidimensional systems lack integrability, a fundamental limitation that challenges the existence of solitons in high dimensions. A remarkable exception would be the lump soliton, a two-dimensional solution of the Kadomtsev-Petviashvili (KP) equation with the unique property of propagating unperturbed in three-dimensional space. Due to the difficulty of implementing the KP dynamics in any physical system, lump solitons have never been observed. Here, we report the first experimental observation of the lump soliton. The lump is realized in nonlinear optics, in a photorefractive crystal under the action of paraxial diffraction and defocusing nonlinearity, ruled by the $(2+1)\mathrm{D}$ nonlinear Schrödinger (NLS) equation. We tailor the input field shape and the nonlinearity to realize the hydrodynamic KP integrable regime of the NLS equation. The lump emerges as a self-localized wave that propagates unaltered with a transverse velocity. We confirm its integrable nature by reporting, for the first time, the elastic collision of lumps in two dimensions. As the first experimental evidence of integrable solitons in high dimensions, our observation paves the way for a new era in the study of nonlinear systems.

Dissipative Kerr solitons in optical microresonators offer unparalleled platforms for ultralow-noise, high-repetition rate frequency comb generation with a compact form and driven by a continuous-wave laser. However, despite their attractive properties suited for practical applications, fundamental limitations regarding their output power and conversion efficiency still remain crucial problems that must be overcome. Here we discover unexplored operation regimes of Kerr soliton microcombs yielding high power and a picosecond pulse width by exploiting the strong mode interaction in birefringent crystalline microresonators. We demonstrate experimentally single-soliton microcombs with average powers of up to 24 and 38 mW as well as an improved conversion efficiency with a double-digit percentage and a microwave soliton repetition rate as low as 15.5 GHz. The observations are in agreement with numerical analyses based on the Lugiato-Lefever equation. The presented results not only facilitate novel applications and an architecture based on microresonator frequency combs, but also contribute to a further understanding of soliton physics.

The $2{{}^3\mathrm{S}}_1\to 2{}^3{\mathrm{P}}_2$ interval (${\nu }_2$) in positronium has been measured using a phase-variation separated oscillatory fields technique. A beam of positronium atoms in the $2{}^3{\mathrm{S}}_1$ state was passed through two spatially separated coherent microwave fields tuned close to the ${\nu }_2$ resonance frequency ($8626.71\pm 0.08\mathrm{MHz}$), and the surviving beam fraction was recorded as a function of the relative phase between the fields. The resonance frequency was obtained from the frequency dependence of the phase of the interference signal without scanning over the full spectral line shape of the transition. We obtain ${\nu }_2=8626.39\pm 1.17_{\mathrm{stat}}\pm 0.80_{\mathrm{sys}}\mathrm{MHz}$, which is in agreement with QED theory.

We experimentally demonstrate that the rotation of molecules embedded in helium nanodroplets can be controlled with an optical centrifuge, allowing for the study of molecular dynamics inside the strongly interacting many-body environment of superfluid helium at variable levels of rotational excitation. By doping the droplets with dimers of nitric oxide, $(\mathrm{NO}{)}_2$, and measuring the degree of their centrifuge-induced alignment as a function of time, we show both the forced in-field rotation of molecules in a continuous range of frequencies, as well as the field-free resonant rotation with a long nanosecond-scale decay. The ability to control and monitor the rotational dynamics of molecular rotors inside the superfluid medium may shed new light on superfluidity and the interaction of superfluids with defects at the atomic level.

Developments in ultrastable lasers have fueled remarkable advances in optical frequency metrology and quantum science. A key ingredient in further improving laser frequency stability is the use of low-noise mirror materials such as AlGaAs crystalline coatings. However, excess noise observed with these coatings limits the performance of cryogenic silicon cavities with AlGaAs mirrors to similar levels achieved with conventional dielectric coatings. With a new pair of crystalline coated mirrors in a 6-cm-long cryogenic silicon cavity operated at 17 K, we demonstrate a clear advantage of crystalline coatings over dielectric coatings. The achieved fractional frequency stability of $2.5\times {10}^{-17}$ at 10 s is four times better than expected for dielectric mirrors and corresponds to more than a tenfold reduction in the coating mechanical loss factor. We also combine two silicon cavities to demonstrate optical frequency averaging for enhanced stability. In addition, we present a long-term frequency drift record of four cryogenic silicon cavities measured over several years. These results open up realistic prospects for cavity-stabilized lasers with ${10}^{-18}$ fractional stability, as well as an all-optical timescale with continuously operating optical local oscillators.

We present an experimental study of molecular alignment echoes driven by ultrashort structured light fields carrying orbital angular momentum (OAM). By combining two time-delayed pump pulses with spatially varying polarization, we produce a molecular “$q$ plate” in a gaseous ${\mathrm{CO}}_2$ sample that can be rephased in a controllable manner. This approach enables the storage of OAM information within the rotational coherences of molecules and its retrieval at adjustable times. The concept is validated using vortex beams of various topological charges $\ell =\pm 1$, 2. These results extend the mechanism of molecular alignment echoes to vector light fields and establish a new route for optical processing of ultrashort OAM pulses, advancing molecular-based quantum interfaces for structured light.

We demonstrate the general failure of the famous concept of tight binding and mode hybridization underlying modern theories of coupled open resonators. Despite sophisticated examples in the literature illustrating these theories, they fail to describe planar systems. This includes even the simplest case of two dielectric slabs placed next to each other or separated by a distance, which is straightforward to verify analytically. We present a rigorous theory capable of calculating correctly the eigenmodes of arbitrary three-dimensional dispersive coupled resonators in terms of their individual modes, revealing proper mode hybridization and formation of bonding and antibonding supermodes. Planar optical resonators, such as coupled slabs and Bragg-mirror microcavities, are used for illustration since they allow reliable verification of the theory.

Conventional approaches to generating and distributing entangled quantum states usually rely on bulky traditional optical devices, posing significant challenges to system miniaturization and integration. Here we report an entanglement engineering scheme that utilizes quantum interference on a metasurface, combined with postselection, to generate and distribute multiple polarization-entangled photon pairs. Two unentangled identical photons, differing only in polarization, are incident on a multichannel metasurface where each channel supports a specific polarization transformation. The metasurface facilitates two-photon interference, generating postselected polarization-entangled states and forming a fully connected entanglement distribution among every two output channels. Experiments demonstrate the generation and distribution of four Bell states across 21 channel pairs, underscoring the potential of metasurfaces as compact, scalable entanglement sources for quantum networking.

We study the dependence of the $p$-wave contact on the Fermi temperature $T_F$ and reduced temperature $T/T_F$ based on the number of closed-channel molecules. From the anisotropic pattern of dissociated molecules, we resolve the narrow $m=0$ and $m=\pm 1$ dipolar splitting of the $p$-wave Feshbach resonance in ${}^6\mathrm{Li}$, enabling the independent determination of the contact for all three $m$ components. For each component, we identify a near-resonant scaling with $\sqrt{T_F}$, indicating the contribution of the normalized effective range $k_F{R}_{\mathrm{e}}$. In addition, we show that the peak contacts observed near resonance increase as $T/T_F$ is lowered, a trend that is accurately captured by estimates based on the second-order virial expansion. Our results, together with estimates from the $p$-wave virial expansion, provide a route toward a complete understanding of the thermodynamics of resonantly enhanced $p$-wave Fermi gases.

We report on the successful trapping of micrometer-sized, multiply-charged helium droplets over periods of several seconds up to a minute—the first observation of trapped charged helium droplets. Within a meter-long multireflection mass spectrometer, the droplets complete thousands of revolutions, opening up new possibilities for precision measurements of these unique systems. Their confinement is limited by collisions with residual gas, which gradually reduce their kinetic energy through evaporation of helium atoms from the droplet and prevent extraction from the trap below a critical value. The rate of energy loss is strongly influenced not only by the residual gas density, but also by the type of species picked up by the droplets. In particular, infrared absorption by water cluster ions inside the droplets enhances energy transfer to the helium matrix, leading to accelerated evaporation of helium atoms.

Optical atomic clocks play a crucial role in fundamental physics, relativistic geodesy, and the future redefinition of the Systeme International second. Standard operation relies on cyclic interrogation sequences, which alternate between atomic interrogation and dead time used for state preparation and readout. This approach introduces the Dick effect, where laser frequency noise aliases onto the atomic transition frequency. Although reducing laser noise improves clock stability, the Dick effect remains a key limitation. In this Letter, we demonstrate a zero-dead-time optical clock based on two interleaved ensembles of cold ${}^{87}\mathrm{Sr}$ atoms. Our system significantly suppresses this noise and achieves a fractional frequency instability at the ${10}^{-19}$ level between 10 000 and 20 000 s over repeated measurements, with a best value of $2.9\times {10}^{-19}$ at $\tau =20000\mathrm{s}$. The estimated long-term stability based on the combined data of these measurements reaches $2.5\times {10}^{-19}$ at 1 day. These results represent a more than ninefold improvement over a conventional single-ensemble clock, highlighting its potential for next-generation timekeeping applications.

We report fast atom diffraction through single-layer graphene using hydrogen atoms at kinetic energies from 150 to 1200 eV. High-resolution images reveal overlapping hexagonal patterns from coexisting monocrystalline domains. Time-of-flight tagging confirms negligible energy loss, making the method suitable for matter-wave interferometry. The diffraction is well described by the eikonal approximation, with accurate modeling requiring the full 3D interaction potential from density functional theory. Simpler models fail to reproduce the data, highlighting the exceptional sensitivity of diffraction patterns to atom-surface interactions and their potential for spectroscopic applications.

We report the experimental observation of discrete bright matter-wave solitons with attractive interaction in an optical lattice. Using an accordion lattice with adjustable spacing, we prepare a Bose-Einstein condensate of cesium atoms across a defined number of lattice sites. By quenching the interaction strength and the trapping potential, we generate both single-site and multisite solitons. Our results reveal the existence and characteristics of these solitons across a range of lattice depths and spacings. We identify stable regions of the solitons based on interaction strength and lattice properties, and compare these findings with theoretical predictions. The experimental results qualitatively agree with a Gaussian variational model and match quantitatively with numerical simulations of the three-dimensional Gross-Pitaevskii equation extended with a quintic term to account for the loss of atoms. Our results provide insights into the quench dynamics and collapse mechanisms, paving the way for further studies of transport and dynamical properties of matter-wave solitons in lattices.

Interferometers are known for precise measurements of the effects inside of them. Here we show that placing a Dove prism in one of the interferometer arms allows for also detecting minute effects happening outside the device. We derive how the additional reflection in one arm can amplify small tilts or displacements of the input beam in the dark output port of the interferometer, in analogy to weak value amplification. The experiment demonstrates a clear improvement of the measurement signal. Moreover, in the bright output port, small disturbances in the input beam get largely filtered, thereby enabling beam stabilization with a fully passive device.