Self-bound many-body systems are formed through a balance of attractive and repulsive forces and occur in many physical scenarios. Liquid droplets are an example of a self-bound system, formed by a balance of the mutual attractive and repulsive forces that derive from different components of the inter-particle potential. It has been suggested(1,2) that self-bound ensembles of ultracold atoms should exist for atom number densities that are 10(8) times lower than in a helium droplet, which is formed from a dense quantum liquid. However, such ensembles have been elusive up to now because they require forces other than the usual zero-range contact interaction, which is either attractive or repulsive but never both. On the basis of the recent finding that an unstable bosonic dipolar gas can be stabilized by a repulsive many-body term(3), it was predicted that three-dimensional self-bound quantum droplets of magnetic atoms should exist(4,5). Here we report the observation of such droplets in a trap-free levitation field. We find that this dilute magnetic quantum liquid requires a minimum, critical number of atoms, below which the liquid evaporates into an expanding gas as a result of the quantum pressure of the individual constituents. Consequently, around this critical atom number we observe an interaction-driven phase transition between a gas and a self-bound liquid in the quantum degenerate regime with ultracold atoms. These droplets are the dilute counterpart of strongly correlated self-bound systems such as atomic nuclei(6) and helium droplets(7).

The variation in molar tooth size in humans and our closest relatives (hominins) has strongly influenced our view of human evolution. The reduction in overall size and disproportionate decrease in third molar size have been noted for over a century, and have been attributed to reduced selection for large dentitions owing to changes in diet or the acquisition of cooking(1,2). The systematic pattern of size variation along the tooth row has been described as a 'morphogenetic gradient' in mammal, and more specifically hominin, teeth since Butler(3) and Dahlberg(4). However, the underlying controls of tooth size have not been well understood, with hypotheses ranging from morphogenetic fields(3) to the clone theory(5). In this study we address the following question: are there rules that govern how hominin tooth size evolves? Here we propose that the inhibitory cascade, an activator-inhibitor mechanism that affects relative tooth size in mammals(6), produces the default pattern of tooth sizes for all lower primary postcanine teeth (deciduous premolars and permanent molars) in hominins. This configuration is also equivalent to a morphogenetic gradient, finally pointing to a mechanism that can generate this gradient. The pattern of tooth size remains constant with absolute size in australopiths (including Ardipithecus, Australopithecus and Paranthropus). However, in species of Homo, including modern humans, there is a tight link between tooth proportions and absolute size such that a single developmental parameter can explain both the relative and absolute sizes of primary postcanine teeth. On the basis of the relationship of inhibitory cascade patterning with size, we can use the size at one tooth position to predict the sizes of the remaining four primary postcanine teeth in the row for hominins. Our study provides a development-based expectation to examine the evolution of the unique proportions of human teeth.

That two photons pass each other undisturbed in free space is ideal for the faithful transmission of information, but prohibits an interaction between the photons. Such an interaction is, however, required for a plethora of applications in optical quantum information processing(1). The long-standing challenge here is to realize a deterministic photon-photon gate, that is, a mutually controlled logic operation on the quantum states of the photons. This requires an interaction so strong that each of the two photons can shift the other's phase by pi radians. For polarization qubits, this amounts to the conditional flipping of one photon's polarization to an orthogonal state. So far, only probabilistic gates(2) based on linear optics and photon detectors have been realized(3), because no known or foreseen material has an optical nonlinearity strong enough to implement this conditional phase shift(4). Meanwhile, tremendous progress in the development of quantum-nonlinear systems has opened up new possibilities for single-photon experiments(5). Platforms range from Rydberg blockade in atomic ensembles(6) to single-atom cavity quantum electrodynamics(7). Applications such as single-photon switches(8) and transistors(9,10), two-photon gateways(11), nondestructive photon detectors(12), photon routers(13) and nonlinear phase shifters(14-18) have been demonstrated, but none of them with the ideal information carriers: optical qubits in discriminable modes. Here we use the strong light-matter coupling provided by a single atom in a high-finesse optical resonator to realize the Duan-Kimble protocol(19) of a universal controlled phase flip (p phase shift) photon-photon quantum gate. We achieve an average gate fidelity of (76.2 +/- 3.6) per cent and specifically demonstrate the capability of conditional polarization flipping as well as entanglement generation between independent input photons. This photon-photon quantum gate is a universal quantum logic element, and therefore could perform most existing two-photon operations. The demonstrated feasibility of deterministic protocols for the optical processing of quantum information could lead to new applications in which photons are essential, especially long-distance quantum communication and scalable quantum computing.

Many important natural products are produced by multidomain non-ribosomal peptide synthetases (NRPSs)(1-4). During synthesis, intermediates are covalently bound to integrated carrier domains and transported to neighbouring catalytic domains in an assembly line fashion(5). Understanding the structural basis for catalysis with non-ribosomal peptide synthetases will facilitate bioengineering to create novel products. Here we describe the structures of two different holo-non-ribosomal peptide synthetase modules, each revealing a distinct step in the catalytic cycle. One structure depicts the carrier domain cofactor bound to the peptide bond-forming condensation domain, whereas a second structure captures the installation of the amino acid onto the cofactor within the adenylation domain. These structures demonstrate that a conformational change within the adenylation domain guides transfer of intermediates between domains. Furthermore, one structure shows that the condensation and adenylation domains simultaneously adopt their catalytic conformations, increasing the overall efficiency in a revised structural cycle. These structures and the single-particle electron microscopy analysis demonstrate a highly dynamic domain architecture and provide the foundation for understanding the structural mechanisms that could enable engineering of novel non-ribosomal peptide synthetases.

Photon emitters placed in an optical cavity experience an environment that changes how they are coupled to the surrounding light field. In the weak-coupling regime, the extraction of light from the emitter is enhanced. But more profound effects emerge when single-emitter strong coupling occurs: mixed states are produced that are part light, part matter(1,2), forming building blocks for quantum information systems and for ultralow-power switches and lasers(3-6). Such cavity quantum electrodynamics has until now been the preserve of low temperatures and complicated fabrication methods, compromising its use(5,7,8). Here, by scaling the cavity volume to less than 40 cubic nanometres and using host-guest chemistry to align one to ten protectively isolated methylene-blue molecules, we reach the strong-coupling regime at room temperature and in ambient conditions. Dispersion curves from more than 50 such plasmonic nanocavities display characteristic light-matter mixing, with Rabi frequencies of 300 millielectronvolts for ten methylene-blue molecules, decreasing to 90 millielectronvolts for single molecules-matching quantitative models. Statistical analysis of vibrational spectroscopy time series and dark-field scattering spectra provides evidence of single-molecule strong coupling. This dressing of molecules with light can modify photochemistry, opening up the exploration of complex natural processes such as photosynthesis(9) and the possibility of manipulating chemical bonds(10).

Ghost imaging is a counter-intuitive phenomenon-first realized in quantum optics(1,2)-that enables the image of a two-dimensional object (mask) to be reconstructed using the spatio-temporal properties of a beam of particles with which it never interacts. Typically, two beams of correlated photons are used: one passes through the mask to a single-pixel (bucket) detector while the spatial profile of the other is measured by a high-resolution (multi-pixel) detector. The second beam never interacts with the mask. Neither detector can reconstruct the mask independently, but temporal cross-correlation between the two beams can be used to recover a 'ghost' image. Here we report the realization of ghost imaging using massive particles instead of photons. In our experiment, the two beams are formed by correlated pairs of ultracold, metastable helium atoms(3), which originate from s-wave scattering of two colliding Bose-Einstein condensates(4,5). We use higher-order Kapitza-Dirac scattering(6-8) to generate a large number of correlated atom pairs, enabling the creation of a clear ghost image with submillimetre resolution. Future extensions of our technique could lead to the realization of ghost interference(9), and enable tests of Einstein-Podolsky-Rosen entanglement(9) and Bell's inequalities(10) with atoms.