We study the collapse of an attractive atomic Bose-Einstein condensate prepared in the uniform potential of an optical-box trap. We characterize the critical point for collapse and the collapse dynamics, observing universal behavior in agreement with theoretical expectations. Most importantly, we observe a clear experimental signature of the counterintuitive weak collapse, namely, that making the system more unstable can result in a smaller particle loss. We experimentally determine the scaling laws that govern the weak-collapse atom loss, providing a benchmark for the general theories of nonlinear wave phenomena.

Echo in mountains is a well-known phenomenon, where an acoustic pulse is mirrored by the rocks, often with reverberating recurrences. For spin echoes in magnetic resonance and photon echoes in atomic and molecular systems, the role of the mirror is played by a second, time-delayed pulse that is able to reverse the flow of time and recreate the original impulsive event. Recently, alignment and orientation echoes were discussed in terms of rotational-phase-space filamentation, and they were optically observed in laser-excited molecular gases. Here, we observe hitherto unreported fractional echoes of high order, spatially rotated echoes, and the counterintuitive imaginary echoes at negative times. Coincidence Coulomb explosion imaging is used for a direct spatiotemporal analysis of various molecular alignment echoes, and the implications to echo phenomena in other fields of physics are discussed.

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work, we study the effect of a space-dependent Weyl node separation, which we interpret as an emergent background axial-vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or nonuniform magnetization and can also be engineered in cold atomic systems. Using a semiclassical approach, we show that the resulting axial magnetic field ${\mathbf{B}}_5$ is observable through an enhancement of the conductivity as $\sigma \sim {\mathbf{B}}_5^2$ due to an underlying chiral pseudomagnetic effect. We then use two lattice models to analyze the effect of ${\mathbf{B}}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau-level structure for different spatial profiles of ${\mathbf{B}}_5$, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as $n=0$ pseudo-Landau levels resulting from a ${\mathbf{B}}_5$ confined to the surface, (ii) as a consequence of position-momentum locking, a bulk ${\mathbf{B}}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces, and (iii) there are equilibrium bound currents proportional to ${\mathbf{B}}_5$ that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

In contrast to classical empty space, the quantum vacuum fundamentally alters the properties of embedded particles. This paradigm shift allows one to explain the discovery of the celebrated Lamb shift in the spectrum of the hydrogen atom. Here, we engineer a synthetic vacuum, building on the unique properties of ultracold atomic gas mixtures, offering the ability to switch between empty space and quantum vacuum. Using high-precision spectroscopy, we observe the phononic Lamb shift, an intriguing many-body effect originally conjectured in the context of solid-state physics. We find good agreement with theoretical predictions based on the Fröhlich model. Our observations establish this experimental platform as a new tool for precision benchmarking of open theoretical challenges, especially in the regime of strong coupling between the particles and the quantum vacuum.

In a joint experimental and theoretical effort, we report on the formation of a macrodroplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the $s$-wave scattering length below the so-called dipolar length, we observe a smooth crossover of the ground state from a dilute Bose-Einstein condensate to a dense macrodroplet state of more than $2\times {10}^4\mathrm{atoms}$. Based on the study of collective excitations and loss features, we prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by mean-field interactions. Finally, we perform expansion measurements, showing that although self-bound solutions are prevented by losses, the interplay between quantum stabilization and losses results in a minimal time-of-flight expansion velocity at a finite scattering length.

Entanglement, and, in particular, the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation, together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.

A “best-of-both-worlds” van der Waals (vdW) density functional is constructed, seamlessly supplementing the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation for short- and intermediate-range interactions with the long-range vdW interaction from $r\mathrm{VV}10$, the revised Vydrov–van Voorhis nonlocal correlation functional. The resultant $\mathrm{SCAN}+r\mathrm{VV}10$ is the only vdW density functional to date that yields excellent interlayer binding energies and spacings, as well as intralayer lattice constants in 28 layered materials. Its versatility for various kinds of bonding is further demonstrated by its good performance for 22 interactions between molecules; the cohesive energies and lattice constants of 50 solids; the adsorption energy and distance of a benzene molecule on coinage-metal surfaces; the binding energy curves for graphene on Cu(111), Ni(111), and Co(0001) surfaces; and the rare-gas solids. We argue that a good semilocal approximation should (as SCAN does) capture the intermediate-range vdW through its exchange term. We have found an effective range of the vdW interaction between 8 and 16 Å for systems considered here, suggesting that this interaction is negligibly small at the larger distances where it reaches its asymptotic power-law decay.

Ultracold atoms, produced by laser cooling and trapping, have led to recent advances in quantum information, quantum chemistry, and quantum sensors. A lack of ultraviolet narrow-band lasers precludes laser cooling of prevalent atoms such as hydrogen, carbon, oxygen, and nitrogen. Broadband pulsed lasers can produce high power in the ultraviolet, and we demonstrate that the entire spectrum of an optical frequency comb can cool atoms when used to drive a narrow two-photon transition. This multiphoton optical force is also used to make a magneto-optical trap. These techniques may provide a route to ultracold samples of nature’s most abundant building blocks for studies of pure-state chemistry and precision measurement.

The accurate prediction of electronic and optical properties of molecules and solids is a persistent challenge for methods based on density functional theory. We propose a generalization of dielectric-dependent hybrid functionals to finite systems where the definition of the mixing fraction of exact and semilocal exchange is physically motivated, nonempirical, and system dependent. The proposed functional yields ionization potentials, and fundamental and optical gaps of many, diverse molecular systems in excellent agreement with experiments, including organic and inorganic molecules and semiconducting nanocrystals. We further demonstrate that this hybrid functional gives the correct alignment between energy levels of the exemplary TTF-TCNQ donor-acceptor system.

Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper, we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting fermionic and bosonic quantum systems subject to periodic driving, which we dub Floquet SPTs (FSPTs). For physical realizations of interacting FSPTs, many-body localization by disorder is a crucial ingredient, required to obtain a stable phase that does not catastrophically heat to infinite temperature. We demonstrate that 1D bosonic and fermionic FSPT phases are classified by the same criteria as equilibrium phases but with an enlarged symmetry group $\tilde{G}$, which now includes discrete time translation symmetry associated with the Floquet evolution. In particular, 1D bosonic FSPTs are classified by projective representations of the enlarged symmetry group $H^2\mathbf{(}\tilde{G},U(1)\mathbf{)}$. We construct explicit lattice models for a variety of systems and then formalize the classification to demonstrate the completeness of this construction. We advocate that a prototypical ${\mathbb{Z}}_2$ bosonic FSPT may be realized by very simple Hamiltonians of the type currently available in existing cold atoms and trapped ion experiments.

High-order harmonic spectroscopy allows one to extract information on fundamental quantum processes, such as the exit time in the tunneling of an electron through a barrier with attosecond time resolution and molecular structure with angstrom spatial resolution. Here, we study the spatial motion of the electron during high-order harmonic generation in an in situ pump-probe measurement using high-density liquid water droplets as a target. We show that molecules adjacent to the emitting electron-ion pair can disrupt the electron’s trajectory when positioned within the range of the maximum electronic excursion distance. This allows us to use the parent ion and the neighboring molecules as boundaries for the electronic motion to measure the maximum electronic excursion distance during the high-order harmonic generation process. Our analysis of the process is relevant for optimizing high-harmonic yields in dense media.

We describe the creation of a long-lived spin-orbit-coupled gas of quantum degenerate atoms using the most magnetic fermionic element, dysprosium. Spin-orbit coupling arises from a synthetic gauge field created by the adiabatic following of degenerate dressed states composed of optically coupled components of an atomic spin. Because of dysprosium’s large electronic orbital angular momentum and large magnetic moment, the lifetime of the gas is limited not by spontaneous emission from the light-matter coupling, as for gases of alkali-metal atoms, but by dipolar relaxation of the spin. This relaxation is suppressed at large magnetic fields due to Fermi statistics. We observe lifetimes up to 400 ms, which exceeds that of spin-orbit-coupled fermionic alkali atoms by a factor of 10–100 and is close to the value obtained from a theoretical model. Elastic dipolar interactions are also observed to influence the Rabi evolution of the spin, revealing an interacting fermionic system. The long lifetime of this weakly interacting spin-orbit-coupled degenerate Fermi gas will facilitate the study of quantum many-body phenomena manifest at longer time scales, with exciting implications for the exploration of exotic topological quantum liquids.

Within a dense environment ($\rho \approx {10}^{14}\mathrm{atoms}/{\mathrm{cm}}^3$) at ultracold temperatures ($T<1\mu \mathrm{K}$), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures, almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for $nS$ ${}^{87}\mathrm{Rb}$ Rydberg states, and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum $l$, with the released energy being converted into kinetic energy of the Rydberg atom. Unexpectedly, the measurements show a threshold behavior at $n\approx 100$ for the inelastic collision time leading to increased lifetimes of the Rydberg state independent of the densities investigated. Even at very high densities ($\rho \approx 4.8\times {10}^{14}{\mathrm{cm}}^{-3}$), the lifetime of a Rydberg atom exceeds $10\mu \mathrm{s}$ at $n>140$ compared to $1\mu \mathrm{s}$ at $n=90$. In addition, a second observed reaction mechanism, namely, ${\mathrm{Rb}}_2^{+}$ molecule formation, was studied. Both reaction products are equally probable for $n=40$, but the fraction of ${\mathrm{Rb}}_2^{+}$ created drops to below 10% for $n\ge 90$.

Understanding x-ray radiation damage is a crucial issue for both medical applications of x rays and x-ray free-electron-laser (XFEL) science aimed at molecular imaging. Decrypting the charge and fragmentation dynamics of nucleobases, the smallest units of a macro-biomolecule, contributes to a bottom-up understanding of the damage via cascades of phenomena following x-ray exposure. We investigate experimentally and by numerical simulations the ultrafast radiation damage induced on a nucleobase analogue (5-iodouracil) by an ultrashort (10 fs) high-intensity radiation pulse generated by XFEL at SPring-8 Angstrom Compact free electron Laser (SACLA). The present study elucidates a plausible underlying radiosensitizing mechanism of 5-iodouracil. This mechanism is independent of the exact composition of 5-iodouracil and thus relevant to other such radiosensitizers. Furthermore, we found that despite a rapid increase of the net molecular charge in the presence of iodine, and of the ultrafast release of hydrogen, the other atoms are almost frozen within the 10-fs duration of the exposure. This validates single-shot molecular imaging as a consistent approach, provided the radiation pulse used is brief enough.

We report on a detailed experimental investigation of the equation of state (EoS) of the three-dimensional Fermi-Hubbard model (FHM) in its generalized $\mathrm{SU}(N)$-symmetric form, using a degenerate ytterbium gas in an optical lattice. In its more common spin-$1/2$ form, the FHM is a central model of condensed-matter physics. The generalization to $N>2$ was first used to describe multi-orbital materials and is expected to exhibit novel many-body phases in a complex phase diagram. By realizing and locally probing the $\mathrm{SU}(N)$ FHM with ultracold atoms, we obtain model-free access to thermodynamic quantities. The measurement of the EoS and the local compressibility allows us to characterize the crossover from a compressible metal to an incompressible Mott insulator. We reach specific entropies above Néel order but below that of uncorrelated spins. Having access to the EoS of such a system represents an important step towards probing predicted novel $\mathrm{SU}(N)$ phases.

The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work, we show the existence of an infinite number of such states for some boson impurity models. They describe free bosons coupled to an impurity and include some of the most representative models in quantum optics. We also propose a family of wave functions to describe the bound states and verify that it accurately characterizes all parameter regimes by comparing its predictions with exact numerical calculations for a one-dimensional tight-binding Hamiltonian. For that model, we also analyze the nature of the bound states by studying the scaling relations of physical quantities, such as the ground-state energy and localization length, and find a nonanalytical behavior as a function of the coupling strength. Finally, we discuss how to test our theoretical predictions in experimental platforms, such as photonic crystal structures and cold atoms in optical lattices.

Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena. As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice. Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator. Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization. In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry. In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions. The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.

The low-temperature unitary Bose gas is a fundamental paradigm in few-body and many-body physics, attracting wide theoretical and experimental interest. Here, we present experiments performed with unitary ${}^{133}\mathrm{Cs}$ and ${}^7\mathrm{Li}$ atoms in two different setups, which enable quantitative comparison of the three-body recombination rate in the low-temperature domain. We develop a theoretical model that describes the dynamic competition between two-body evaporation and three-body recombination in a harmonically trapped unitary atomic gas above the condensation temperature. We identify a universal “magic” trap depth where, within some parameter range, evaporative cooling is balanced by recombination heating and the gas temperature stays constant. Our model is developed for the usual three-dimensional evaporation regime as well as the two-dimensional evaporation case, and it fully supports our experimental findings. Combined ${}^{133}\mathrm{Cs}$ and ${}^7\mathrm{Li}$ experimental data allow investigations of loss dynamics over 2 orders of magnitude in temperature and 4 orders of magnitude in three-body loss rate. We confirm the $1/T^2$ temperature universality law. In particular, we measure, for the first time, the Efimov inelasticity parameter ${\eta }_{*}=0.098(7)$ for the 47.8-G $d$-wave Feshbach resonance in ${}^{133}\mathrm{Cs}$. Our result supports the universal loss dynamics of trapped unitary Bose gases up to a single parameter ${\eta }_{*}$.

We present a study of the collisional relaxation of ion velocities in a strongly coupled, ultracold neutral plasma on short time scales compared to the inverse collision rate. The measured average velocity of a tagged population of ions is shown to be equivalent to the ion-velocity autocorrelation function. We thus gain access to fundamental aspects of the single-particle dynamics in strongly coupled plasmas and to the ion self-diffusion constant under conditions where experimental measurements have been lacking. Nonexponential decay towards equilibrium of the average velocity heralds non-Markovian dynamics that are not predicted by traditional descriptions of weakly coupled plasmas. This demonstrates the utility of ultracold neutral plasmas for studying the effects of strong coupling on collisional processes, which is of interest for dense laboratory and astrophysical plasmas.

The use of optical clocks or oscillators in future ultraprecise navigation, gravitational sensing, coherent arrays, and relativity experiments will require time comparison and synchronization over terrestrial or satellite free-space links. Here, we demonstrate full unambiguous synchronization of two optical time scales across a free-space link. The time deviation between synchronized time scales is below 1 fs over durations from 0.1 to 6500 s, despite atmospheric turbulence and kilometer-scale path length variations. Over 2 days, the time wander is 40 fs peak to peak. Our approach relies on the two-way reciprocity of a single-spatial-mode optical link, valid to below 225 attoseconds across a turbulent 4-km path. This femtosecond level of time-frequency transfer should enable optical networks using state-of-the-art optical clocks or oscillators.