We analyze the ground-state entanglement entropy of the extended Bose-Hubbard model with infinite-range interactions. This model describes the low-energy dynamics of ultracold bosons tightly bound to an optical lattice and dispersively coupled to a cavity mode. The competition between on-site repulsion and global cavity-induced interactions leads to a rich phase diagram, which exhibits superfluid, supersolid, and insulating (Mott and checkerboard) phases. We use a slave-boson treatment of harmonic quantum fluctuations around the mean-field solution and calculate the entanglement entropy across the phase transitions. At commensurate filling, the insulator-superfluid transition is signaled by a singularity in the area-law scaling coefficient of the entanglement entropy, which is similar to the one reported for the standard Bose-Hubbard model. Remarkably, at the continuous ${\mathbb{Z}}_2$ superfluid-to-supersolid transition we find a critical logarithmic term, regardless of the filling. This behavior originates from the appearance of a roton mode in the excitation and entanglement spectrum, becoming gapless at the critical point, and it is characteristic of collective models.

Tailoring the decay rate of structured quantum emitters into their environment opens new avenues for nonlinear quantum optics, collective phenomena, and quantum communications. Here, we demonstrate a novel coupling scheme between an artificial molecule comprising two identical, strongly coupled transmon qubits and two microwave waveguides. In our scheme, the coupling is engineered so that transitions between states of the same (opposite) symmetry, with respect to the permutation operator, are predominantly coupled to one (the other) waveguide. The symmetry-based coupling selectivity, as quantified by the ratio of the coupling strengths, exceeds a factor of 30 for both waveguides in our device. In addition, we implement a Raman process activated by simultaneously driving both waveguides, and show that it can be used to coherently couple states of different symmetry in the single-excitation manifold of the molecule. Using that process, we implement frequency conversion across the waveguides, mediated by the molecule, with efficiency of about 95%. Finally, we show that this coupling arrangement makes it possible to straightforwardly generate spatially separated Bell states propagating across the waveguides. We envisage further applications to quantum thermodynamics, microwave photodetection, and photon-photon gates.

We prepare high-filling two-component arrays of tens of fermionic ${}^6\mathrm{Li}$ atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.

We explore a wide range of fundamental magnetic phenomena by measuring the dephasing of matter-wave interference fringes upon application of a variable magnetic gradient. The versatility of our interferometric Stern-Gerlach technique enables us to study the magnetic properties of alkali atoms, organic radicals, and fullerenes in the same device, with magnetic moments ranging from a Bohr magneton to less than a nuclear magneton. We find evidence for magnetization of a supersonic beam of organic radicals and, most notably, observe a strong magnetic response of a thermal ${\mathrm{C}}_{60}$ beam consistent with high-temperature atomlike deflection of rotational magnetic moments.

Laser cooling is a key ingredient for quantum control of atomic systems in a variety of settings. In divalent atoms, two-stage Doppler cooling is typically used to bring atoms to the $\mu \mathrm{K}$ regime. Here, we implement a pulsed radial cooling scheme using the ultranarrow ${{}^1\mathrm{S}}_0\text{−}{{}^3\mathrm{P}}_0$ clock transition in ytterbium to realize subrecoil temperatures, down to tens of nK. Together with sideband cooling along the one-dimensional lattice axis, we efficiently prepare atoms in shallow lattices at an energy of 6 lattice recoils. Under these conditions key limits on lattice clock accuracy and instability are reduced, opening the door to dramatic improvements. Furthermore, tunneling shifts in the shallow lattice do not compromise clock accuracy at the ${10}^{-19}$ level.

A mobility edge, a critical energy separating localized and extended excitations, is a key concept for understanding quantum localization. The Aubry-André (AA) model, a paradigm for exploring quantum localization, does not naturally allow mobility edges due to self-duality. Using the momentum-state lattice of quantum gas of Cs atoms to synthesize a nonlinear AA model, we provide experimental evidence for a mobility edge induced by interactions. By identifying the extended-to-localized transition of different energy eigenstates, we construct a mobility-edge phase diagram. The location of a mobility edge in the low- or high-energy region is tunable via repulsive or attractive interactions. Our observation is in good agreement with the theory and supports an interpretation of such interaction-induced mobility edge via a generalized AA model. Our Letter also offers new possibilities to engineer quantum transport and phase transitions in disordered systems.

Understanding the origins of unconventional superconductivity has been a major focus of condensed matter physics for many decades. While many questions remain unanswered, experiments have found the highest critical temperatures in layered two-dimensional materials. However, to what extent the remarkable stability of these strongly correlated 2D superfluids is affected by their reduced dimensionality is still an open question. Here, we use dilute gases of ultracold fermionic atoms as a model system to directly observe the influence of dimensionality on the stability of strongly interacting fermionic superfluids. We find that the superfluid gap follows the same universal function of the interaction strength regardless of dimensionality, which suggests that there is no inherent difference in the stability of two- and three-dimensional fermionic superfluids. Finally, we compare our data to results from solid state systems and find a similar relation between the interaction strength and the gap for a wide range of two- and three-dimensional superconductors.

Synchronization and frequency locking between remote mechanical oscillators are of scientific and technological importance. The key challenges are to align the oscillation frequencies and realize strong nonlinear interaction of both oscillators to a common carrier capable of long-distance transmission. Here, we experimentally realize the all-optical synchronization between two different optomechanical systems, a microsphere and a microdisk. The mechanical oscillation of the microsphere induced by the radiation pressure is loaded onto the pump laser via the optomechanical interaction, which is directly transmitted through a 5-km-long single-mode fiber to excite the mechanical oscillation of the microdisk. By finely tuning both the optical and mechanical frequencies of the two microresonators, the oscillation of the microdisk is injection locked to the microsphere, resulting in a synchronized phase relation of the two systems. Our results push a step forward the long-distance synchronization network using optomechanical microresonators.

Quantum measurements of mechanical systems can generate optical squeezing via ponderomotive forces. Its observation requires high environmental isolation and efficient detection, typically achieved by using cryogenic cooling and optical cavities. Here, we realize these conditions by measuring the position of an optically levitated nanoparticle at room temperature and without the overhead of an optical cavity. We use a fast heterodyne detection to reconstruct simultaneously orthogonal optical quadratures, and observe a noise reduction of $9\%\pm 0.5\%$ below shot noise. Our experiment offers a novel, cavityless platform for squeezed-light enhanced sensing. At the same time it delineates a clear and simple strategy toward observation of stationary optomechanical entanglement.

A mechanically compliant element can be set into motion by the interaction with light. In turn, this light-driven motion can give rise to ponderomotive correlations in the electromagnetic field. In optomechanical systems, cavities are often employed to enhance these correlations up to the point where they generate quantum squeezing of light. In free-space scenarios, where no cavity is used, observation of squeezing remains possible but challenging due to the weakness of the interaction, and has not been reported so far. Here, we measure the ponderomotively squeezed state of light scattered by a nanoparticle levitated in a free-space optical tweezer. We observe a reduction of the optical fluctuations by up to 25% below the vacuum level, in a bandwidth of about 15 kHz. Our results are explained well by a linearized dipole interaction between the nanoparticle and the electromagnetic continuum. These ponderomotive correlations open the door to quantum-enhanced sensing and metrology with levitated systems, such as force measurements below the standard quantum limit.

Intensities of lines in the near-infrared second overtone band (3–0) of ${}^{12}\mathrm{C}{}^{16}\mathrm{O}$ are measured and calculated to an unprecedented degree of precision and accuracy. Agreement between theory and experiment to better than 1‰ is demonstrated by results from two laboratories involving two independent absorption- and dispersion-based cavity-enhanced techniques. Similarly, independent Fourier transform spectroscopy measurements of stronger lines in this band yield mutual agreement and consistency with theory at the 1‰ level. This set of highly accurate intensities can provide an intrinsic reference for reducing biases in future measurements of spectroscopic peak areas.

Interferometric methods for detecting the motion of a levitated nanoparticle provide a route to the quantum ground state, but such methods are currently limited by mode mismatch between the reference beam and the dipolar field scattered by the particle. Here we demonstrate a self-interference method to detect the particle’s motion that solves this problem. A Paul trap confines a charged dielectric nanoparticle in high vacuum, and a mirror retro-reflects the scattered light. We measure the particle’s motion with a sensitivity of $1.7\times {10}^{-12}\mathrm{m}/\sqrt{\mathrm{Hz}}$, corresponding to a detection efficiency of 2.1%, with a numerical aperture of 0.18. As an application of this method, we cool the particle, via feedback, to temperatures below those achieved in the same setup using a standard position measurement.

We report two-dimensional electron energy-loss spectra of ${\mathrm{CO}}_2$. The high-resolution experiment reveals a counterintuitive fine structure at energy losses where ${\mathrm{CO}}_2$ states form a vibrational pseudocontinuum. Guided by the symmetry of the system, we constructed a four-dimensional nonlocal model for the vibronic dynamics involving two shape resonances (forming a Renner-Teller ${\mathrm{\Pi }}_u$ doublet at the equilibrium geometry) coupled to a virtual ${\mathrm{\Sigma }}_g^{+}$ state. The model elucidates the extremely non-Born-Oppenheimer dynamics of the coupled nuclear motion and explains the origin of the observed structures. It is a prototype of the vibronic coupling of metastable states in continuum.

Rotational dynamics of ${\mathrm{D}}_2$ molecules inside helium nanodroplets is induced by a moderately intense femtosecond pump pulse and measured as a function of time by recording the yield of ${\mathrm{HeD}}^{+}$ ions, created through strong-field dissociative ionization with a delayed femtosecond probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant $B_{\mathrm{He}}$ of the in-droplet ${\mathrm{D}}_2$ molecule, determined by Fourier analysis, is the same as $B_{\mathrm{gas}}$ for an isolated ${\mathrm{D}}_2$ molecule. Our observations show that the ${\mathrm{D}}_2$ molecules inside helium nanodroplets essentially rotate as free ${\mathrm{D}}_2$ molecules.

Detection of weak electromagnetic waves and hypothetical particles aided by quantum amplification is important for fundamental physics and applications. However, demonstrations of quantum amplification are still limited; in particular, the physics of quantum amplification is not fully explored in periodically driven (Floquet) systems, which are generally defined by time-periodic Hamiltonians and enable observation of many exotic quantum phenomena such as time crystals. Here we investigate the magnetic-field signal amplification by periodically driven ${}^{129}\mathrm{Xe}$ spins and observe signal amplification at frequencies of transitions between Floquet spin states. This “Floquet amplification” allows us to simultaneously enhance and measure multiple magnetic fields with at least one order of magnitude improvement, offering the capability of femtotesla-level measurements. Our findings extend the physics of quantum amplification to Floquet spin systems and can be generalized to a wide variety of existing amplifiers, enabling a previously unexplored class of “Floquet spin amplifiers”.

We use lithium-6 atoms in an optical tweezer array to realize an eight-site Fermi-Hubbard chain near half filling. We achieve single site detection by combining the tweezer array with a quantum gas microscope. By reducing disorder in the energy offsets to less than the tunneling energy, we observe Mott insulators with strong antiferromagnetic correlations. The measured spin correlations allow us to put an upper bound on the entropy of $0.26(4)k_B$ per atom, comparable to the lowest entropies achieved with optical lattices. Additionally, we establish the flexibility of the tweezer platform by initializing atoms on one tweezer and observing tunneling dynamics across the array for uniform and staggered 1D geometries.

We present state-selected measurements of rotational cooling and excitation rates of ${\mathrm{CH}}^{+}$ molecular ions by inelastic electron collisions. The experiments are carried out at a cryogenic storage ring, making use of a monoenergetic electron beam at matched velocity in combination with state-sensitive laser dissociation of the ${\mathrm{CH}}^{+}$ ions for simultaneous monitoring of the rotational level populations. Employing storage times of up to 600 s, we create conditions where electron-induced cooling to the $J=0$ ground state dominates over radiative relaxation, allowing for the experimental determination of inelastic electron collision rates to benchmark state-of-the-art theoretical calculations. On a broader scale, our experiments pave the way to probe inelastic electron collisions for a variety of molecular ions relevant in various plasma environments.

The quantum Hall effect occurring in two-dimensional electron gases was first explained by Laughlin, who developed a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a quantum Hall cylinder periodically driven by an axial magnetic field, resulting in the quantized motion of electrons. We realize this milestone experiment with an ultracold gas of dysprosium atoms, the cyclic dimension being encoded in the electronic spin and the axial field controlled by the phases of laser-induced spin-orbit couplings. Our experiment provides a straightforward manifestation of the nontrivial topology of quantum Hall insulators, and could be generalized to strongly correlated topological systems.

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the standard model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ${{}^{2}S}_{1/2}\to {{}^{2}F}_{7/2}$ octupole transition of trapped ${}^{168,170,172,174,176}\mathrm{Yb}$ ions. When combined with previous measurements in ${\mathrm{Yb}}^{+}$ and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to $240\sigma$. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with $4.3\sigma$ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.

We report the first observation of intermolecular Coulombic decay (ICD) in liquid water following inner-valence ionization. By combining a monochromatized tabletop high-harmonic source with a liquid microjet, we record electron-electron coincidence spectra at two photon energies that identify the ICD electrons, together with the photoelectrons originating from the $2a_1$ inner-valence band of liquid water. Our results confirm the importance of ICD as a source of low-energy electrons in bulk liquid water and provide quantitative results for modeling the velocity distribution of the slow electrons that are thought to dominate radiation damage in aqueous environments.