We investigate the minimal Hilbert-space dimension for a system to be synchronized. We first show that qubits cannot be synchronized due to the lack of a limit cycle. Moving to larger spin values, we demonstrate that a single spin 1 can be phase locked to a weak external signal of similar frequency and exhibits all the standard features of the theory of synchronization. Our findings rely on the Husimi $Q$ representation based on spin coherent states which we propose as a tool to obtain a phase portrait.

Conventional solids deform elastically for small stresses—reversibly with a linear, rate-independent relationship between stress and strain. Beyond the yield point, plastic deformation begins—irreversible, nonlinear, and time dependent. Plasticity involves the motion and multiplication of dislocations, and here we report observations of such “metallurgical” phenomena in hcp ${}^4\mathrm{He}$, a solid whose defect behavior is dominated by quantum effects. Below 0.4 K, there is a strain threshold for elastic deformation above which sudden stress drops and acoustic emissions appear, the signatures of dislocation avalanches. The dimensions of these slip events range from millimeters to microns. At higher temperatures, the avalanches are replaced by continuous creep involving dislocations, and we observe steady flow at stresses as low as 400 Pa.

The work required to detach microparticles from fluid interfaces depends on the shape of the liquid meniscus. However, measuring the capillary force on a single microparticle and simultaneously imaging the shape of the liquid meniscus has not yet been accomplished. To correlate force and shape, we combined a laser scanning confocal microscope with a colloidal probe setup. While moving a hydrophobic microsphere (radius $5–10\mu \mathrm{m}$) in and out of a $2–5\mu \mathrm{m}$ thick glycerol film, we simultaneously measured the force and imaged the shape of the liquid meniscus. In this way we verified the fundamental equations [D. F. James, J. Fluid Mech. 63, 657 (1974); A. D. Scheludko, A. D. Nikolov, Colloid Polymer Sci. 253, 396 (1975)] that describe the adhesion of particles in flotation, deinking of paper, the stability of Pickering emulsions and particle-stabilized foams. Comparing experimental results with theory showed, however, that the receding contact angle has to be applied, which can be much lower than the static contact angle obtained right after jump in of the particle.

We introduce a generalized form of gelation theory that incorporates individual heterogeneity and show that it can explain the asynchronous, sudden appearance and growth of online extremist groups supporting ISIS (so-called Islamic State) that emerged globally post-2014. The theory predicts how heterogeneity impacts their onset times and growth profiles and suggests that online extremist groups present a broad distribution of heterogeneity-dependent aggregation mechanisms centered around homophily. The good agreement between the theory and empirical data suggests that existing strategies aiming to defeat online extremism under the assumption that it is driven by a few “bad apples” are misguided. More generally, this generalized theory should apply to a range of real-world systems featuring aggregation among heterogeneous objects.

Generative adversarial networks represent a powerful tool for classical machine learning: a generator tries to create statistics for data that mimics those of a true data set, while a discriminator tries to discriminate between the true and fake data. The learning process for generator and discriminator can be thought of as an adversarial game, and under reasonable assumptions, the game converges to the point where the generator generates the same statistics as the true data and the discriminator is unable to discriminate between the true and the generated data. This Letter introduces the notion of quantum generative adversarial networks, where the data consist either of quantum states or of classical data, and the generator and discriminator are equipped with quantum information processors. We show that the unique fixed point of the quantum adversarial game also occurs when the generator produces the same statistics as the data. Neither the generator nor the discriminator perform quantum tomography; linear programing drives them to the optimal. Since quantum systems are intrinsically probabilistic, the proof of the quantum case is different from—and simpler than—the classical case. We show that, when the data consist of samples of measurements made on high-dimensional spaces, quantum adversarial networks may exhibit an exponential advantage over classical adversarial networks.

We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.

Several dynamical properties of electromagnetic waves such as energy, momentum, angular momentum, and optical helicity have been recently reexamined in dispersive and lossless media. Here, we address an alternative derivation for the optical chirality, extending it so as to include dissipative effects as well. To this end, we first elaborate on the most complete form of the conservation law for the optical chirality, without any restrictions on the nature of the medium. As a result we find a general expression for the optical chirality density both in lossless and lossy dispersive media. Our definition is perfectly consistent with that originally introduced for electromagnetic fields in free space, and is applicable to any material system, including dielectrics, plasmonic nanostructures, and left-handed metamaterials.

We report how individual defects affect single graphene nanoribbons by scanning tunneling and atomic force microscopy pulling experiments simultaneously accessing their electrical and mechanical properties. The on-surface polymerization of the graphene nanoribbons is controlled by cooperative effects as theoretically suggested. Further, we find, with the help of atomistic simulations, that defects substantially vary the molecule-substrate coupling and drastically increase the flexibility of the graphene nanoribbons while keeping their desirable electronic properties intact.

We observe the unconventional photon blockade effect in quantum dot cavity QED, which, in contrast to the conventional photon blockade, operates in the weak coupling regime. A single quantum dot transition is simultaneously coupled to two orthogonally polarized optical cavity modes, and by careful tuning of the input and output state of polarization, the unconventional photon blockade effect is observed. We find a minimum second-order correlation $g^{(2)}(0)\approx 0.37$, which corresponds to $g^{(2)}(0)\approx 0.005$ when corrected for detector jitter, and observe the expected polarization dependency and photon bunching and antibunching; close by in parameter space, which indicates the abrupt change from phase to amplitude squeezing.

We have observed the unconventional photon blockade effect for microwave photons using two coupled superconducting resonators. As opposed to the conventional blockade, only weakly nonlinear resonators are required. The blockade is revealed through measurements of the second order correlation function $g^{(2)}(t)$ of the microwave field inside one of the two resonators. The lowest measured value of $g^{(2)}(0)$ is 0.4 for a resonator population of approximately ${10}^{-2}$ photons. The time evolution of $g^{(2)}(t)$ exhibits an oscillatory behavior, which is characteristic of the unconventional photon blockade.

We show that, despite stringent constraints on the shape of the main part of the cosmic microwave background (CMB) spectrum, there is considerable room for its modification within its Rayleigh-Jeans (RJ) end, $\omega \ll T_{\mathrm{CMB}}$. We construct explicit new physics models that give an order one (or larger) increase of photon count in the RJ tail, which can be tested by existing and upcoming experiments aiming to detect the cosmological 21 cm emission or absorption signal. This class of models stipulates the decay of unstable particles to dark photons $A^{\prime }$ that have a small mass, $m_{A^{\prime }}\sim {10}^{-14}–{10}^{-9}\mathrm{eV}$, nonvanishing mixing angle $\epsilon$ with electromagnetism, and energies much smaller than $T_{\mathrm{CMB}}$. The nonthermal number density of dark photons can be many orders of magnitude above the number density of CMB photons, and even a small probability of $A^{\prime }\to A$ oscillations, for values as small as $\epsilon \sim {10}^{-9}$, can significantly increase the number of RJ photons. In particular, we show that resonant oscillations of dark photons into regular photons in the interval of redshifts $20<z<1700$ can be invoked as an explanation of the recent tentative observation of a stronger-than-expected absorption signal of 21 cm photons. We present a model that realizes this possibility, where meV mass dark matter decays to dark photons, with a lifetime longer than the age of the Universe.

We report on rotating an optically trapped silica nanoparticle in vacuum by transferring spin angular momentum of light to the particle’s mechanical angular momentum. At sufficiently low damping, realized at pressures below ${10}^{-5}\mathrm{mbar}$, we observe rotation frequencies of single 100 nm particles exceeding 1 GHz. We find that the steady-state rotation frequency scales linearly with the optical trapping power and inversely with pressure, consistent with theoretical considerations based on conservation of angular momentum. Rapidly changing the polarization of the trapping light allows us to extract the pressure-dependent response time of the particle’s rotational degree of freedom.

Levitated optomechanics has great potential in precision measurements, thermodynamics, macroscopic quantum mechanics, and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell. This levitated nanodumbbell torsion balance is a novel analog of the Cavendish torsion balance, and provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1 GHz, which is the fastest nanomechanical rotor realized to date. Smaller silica nanodumbbells can sustain higher rotation frequencies. Such ultrafast rotation may be used to study material properties and probe vacuum friction.

We report on the observation of nearly maximally entangled photon pairs from semiconductor quantum dots, without resorting to postselection techniques. We use GaAs quantum dots integrated on a patterned piezoelectric actuator capable of suppressing the exciton fine structure splitting. By using a resonant two-photon excitation, we coherently drive the biexciton state and demonstrate experimentally that our device generates polarization-entangled photons with a fidelity of 0.978(5) and a concurrence of 0.97(1) taking into account the nonidealities stemming from the experimental setup. By combining fine-structure-dependent fidelity measurements and a theoretical model, we identify an exciton spin-scattering process as a possible residual decoherence mechanism. We suggest that this imperfection may be overcome using a modest Purcell enhancement so as to achieve fidelities $>0.99$, thus making quantum dots evenly matched with the best probabilistic entangled photon sources.

Electrons in clean macroscopic samples of graphene exhibit an astonishing variety of quantum phases when strong perpendicular magnetic field is applied. These include integer and fractional quantum Hall states as well as symmetry broken phases and quantum Hall ferromagnetism. Here we show that mesoscopic graphene flakes in the regime of strong disorder and magnetic field can exhibit another remarkable quantum phase described by holographic duality to an extremal black hole in two-dimensional anti–de Sitter space. This phase of matter can be characterized as a maximally chaotic non-Fermi liquid since it is described by a complex fermion version of the Sachdev-Ye-Kitaev model known to possess these remarkable properties.

A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this Letter we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.

Artificially engineered geometric phase optical elements may have tunable photonic functionalities owing to their sensitivity to external fields, as is the case for liquid crystal based devices. However, liquid crystal technology combining high-resolution topological ordering with tunable spectral behavior remains elusive. Here, by using a magnetoelectric external stimulus, we create robust and efficient self-engineered liquid crystal geometric phase vortex masks with a broadly tunable operating wavelength, centimeter-size clear aperture, and high-quality topological ordering.

In a number of widely studied materials, such as Si, AlAs, Bi, graphene, ${\mathrm{MoS}}_2$, and many transition metal dichalcogenide monolayers, electrons acquire an additional, spinlike degree of freedom at the degenerate conduction band minima, also known as “valleys.” External symmetry-breaking fields such as mechanical strain, or electric or magnetic fields, can tune the valley polarization of these materials, making them suitable candidates for “valleytronics.” Here we study a quantum well of AlAs, where the two-dimensional electrons reside in two energetically degenerate valleys. By fabricating a strain-inducing grating on the sample surface, we engineer a spatial modulation of the electron population in different valleys, i.e., a “valley superlattice” in the quantum well plane. Our results establish a novel manipulation technique of the valley degree of freedom, paving the way to realizing a valley-selective layered structure in multivalley materials, with potential application in valleytronics.

The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of $d$-wave superconductivity, with a negative answer: the scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: the chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal value $G=\frac{1}{2}{g}_0\mathrm{\Phi }/{\mathrm{\Phi }}_0$, with $\mathrm{\Phi }$ as the magnetic flux through the system, ${\mathrm{\Phi }}_0$ as the superconducting flux quantum, and $g_0$ as the thermal conductance quantum.

The influence of natural cosolvent mixtures on the pressure-dependent structure and protein-protein interaction potential of dense protein solutions is studied and analyzed using small-angle X-ray scattering in combination with a liquid-state theoretical approach. The deep-sea osmolyte trimethylamine-$N$-oxide is shown to play a crucial and singular role in its ability to not only guarantee sustainability of the native protein’s folded state under harsh environmental conditions, but it also controls water-mediated intermolecular interactions at high pressure, thereby preventing contact formation and hence aggregation of proteins.