Decomposing unitaries into a sequence of elementary operations is at the core of quantum computing. Information theoretic arguments show that approximating a random unitary with precision $\epsilon$ requires $\Omega \mathbf{(}\log (1/\epsilon )\mathbf{)}$ gates. Prior to our work, the state of the art in approximating a single qubit unitary included the Solovay-Kitaev algorithm that requires $O\mathbf{(}{log}^{3+\delta }(1/\epsilon )\mathbf{)}$ gates and does not use ancillae and the phase kickback approach that requires $O\mathbf{(}{log}^2(1/\epsilon )\log \log (1/\epsilon )\mathbf{)}$ gates but uses $O\mathbf{(}{log}^2(1/\epsilon )\mathbf{)}$ ancillae. Both algorithms feature upper bounds that are far from the information theoretic lower bound. In this Letter, we report an algorithm that saturates the lower bound, and as such it guarantees asymptotic optimality. In particular, we present an algorithm for building a circuit that approximates single qubit unitaries with precision $\epsilon$ using $O\mathbf{(}\log (1/\epsilon )\mathbf{)}$ Clifford and $T$ gates and employing up to two ancillary qubits. We connect the unitary approximation problem to the problem of constructing solutions corresponding to Lagrange’s four-square theorem, and thereby develop an algorithm for computing an approximating circuit using an average of $O\mathbf{(}{log}^2(1/\epsilon )\log \log (1/\epsilon )\mathbf{)}$ operations with integers.

Recent measurements of the azimuthal anisotropy of direct photons in heavy-ion collisions at the energies of Relativistic Heavy Ion Collider show that it is of the same order as the hadronic one. This finding appears to contradict the expected dominance of photon production from a quark-gluon plasma at an early stage of a heavy-ion collision. A possible explanation of the strong azimuthal anisotropy of the photons, given recently, is based on the presence of a large magnetic field in the early phase of a collision. In this Letter, we propose a method to experimentally measure the degree to which a magnetic field in heavy-ion collisions is responsible for the observed anisotropy of photon production. The experimental test proposed in this Letter may potentially change our understanding of the nonequilibrium stage and possible thermalization in heavy-ion collisions.

The fundamental ground tone vibration of ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ is determined to an accuracy of $2\times {10}^{-4}{\mathrm{cm}}^{-1}$ from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the $X^1{\Sigma }_g^{+}$, $v=0$, and $v=1$ levels to a common $E{F}^1{\Sigma }_g^{+}$, $v=0$ level. Agreement within $1\sigma$ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically bound system.

We predict the existence of a new class of self-accelerating, exponentially localized pulses consisting of two interacting frequency components propagating at opposite group velocity dispersion. Compared to previous approaches no external force is required and accelerations of both signs can be realized. This seemingly paradoxical behavior resembles an all optical wave realization of a classical diametric drive, where a continuously propulsive effect is achieved by a combination of two fields having effective masses of opposite sign.

We explain the rotating polygon instability on a swirling fluid surface [G. H. Vatistas, J. Fluid Mech. 217, 241 (1990) and Jansson et al., Phys. Rev. Lett. 96, 174502 (2006)] in terms of resonant interactions between gravity waves on the outer part of the surface and centrifugal waves on the inner part. Our model is based on potential flow theory, linearized around a potential vortex flow with a free surface for which we show that unstable resonant states appear. Limiting our attention to the lowest order mode of each type of wave and their interaction, we obtain an analytically soluble model, which, together with estimates of the circulation based on angular momentum balance, reproduces the main features of the experimental phase diagram. The generality of our arguments implies that the instability should not be limited to flows with a rotating bottom (implying singular behavior near the corners), and indeed we show that we can obtain the polygons transiently by violently stirring liquid nitrogen in a hot container.

We report on model studies of stimulated $L\to H$ transitions. These studies use a novel reduced mesoscale model. Studies reveal that $L\to H$ transitions can be triggered by particle injection into a subcritical state (i.e., $P<P_{\mathrm{Thresh}}$). Particle injection alters the edge mean flow shear via changes of density and temperature gradients. The change of edge mean flow shear is critical to turbulence collapse and the subsequent stimulated transition. For low ambient heating, strong injection is predicted to trigger a transient turbulence collapse. We predict that repetitive injection can maintain the turbulence collapse and so sustain a driven $H$-mode-like state. The total number of particles required to induce a transition by either injection or gas puffing is estimated. Results indicate that the total number of injected particles required is much smaller than that required for inducing a transition by gas puffing. Thus, we show that internal injection is more efficient than gas puffing of comparable strength. We also observe that zonal flows do not play a critical role in stimulated transitions.

Cross-field diffusion and plasma expansion in a rapidly diverging magnetic nozzle are controlled while maintaining constant plasma production in a contiguously attached radio frequency plasma source. It is demonstrated that the measured electron-diamagnetic-induced axial momentum increases with increasing magnetic field strength to approach the theoretical limit derived using an ideal nozzle approximation. The measured axial momentum exerted onto the axial and radial plasma source boundaries validate the prediction from a maximum electron pressure model on the back wall and from a zero net axial momentum model on the radial wall.

The current-voltage characteristics in the charge order state of the two-dimensional organic conductor $\alpha \mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2{\mathrm{I}}_3$ exhibit power law behavior at low temperatures. The power law is understood in terms of the electric-field-dependent potential between electrons and holes, which are thermally excited from the charge order state. The power law exponent steeply changes from 1 to 3 in the range from 30 to 45 K with decreasing temperature, thereby suggesting the occurrence of a Kosterlitz-Thouless-type transition; many (few) unbound electron-hole pairs are thermally excited above (below) the transition. The effects of the finite size and interlayer coupling on the power law behavior are discussed.

We investigate phonon-induced spin and charge relaxation mediated by spin-orbit and hyperfine interactions for a single electron confined within a double quantum dot. A simple toy model incorporating both direct decay to the ground state of the double dot and indirect decay via an intermediate excited state yields an electron spin relaxation rate that varies nonmonotonically with the detuning between the dots. We confirm this model with experiments performed on a GaAs double dot, demonstrating that the relaxation rate exhibits the expected detuning dependence and can be electrically tuned over several orders of magnitude. Our analysis suggests that spin-orbit mediated relaxation via phonons serves as the dominant mechanism through which the double-dot electron spin-flip rate varies with detuning.

Colloidal gel networks are disordered elastic solids that can form even in extremely dilute particle suspensions. With interaction strengths comparable to the thermal energy, their stress-bearing network can locally restructure via breaking and reforming interparticle bonds. This allows for yielding, self-healing, and adaptive mechanics under deformation. Designing such features requires controlling stress transmission through the complex structure of the gel and this is challenging because the link between local restructuring and overall response of the network is still missing. Here, we use a space resolved analysis of dynamical processes and numerical simulations of a model gel to gain insight into this link. We show that consequences of local bond breaking propagate along the gel network over distances larger than the average mesh size. This provides the missing microscopic explanation for why nonlocal constitutive relations are necessary to rationalize the nontrivial mechanical response of colloidal gels.

The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it may also be an innate property of certain isolated, periodically driven quantum systems. Here, we experimentally realize the simplest such system, consisting of two coupled, kicked quantum rotors, by subjecting a coherent atomic matter wave to two periodically pulsed, incommensurate optical lattices. Momentum transport in this system is found to be radically different from that in a single kicked rotor, with a breakdown of dynamical localization and the emergence of classical diffusion. Our observation, which confirms a long-standing prediction for many-dimensional quantum-chaotic systems, sheds new light on the quantum-classical correspondence.

We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling. In particular, we explore the regime of strong fields, demonstrating contrasting quantum behaviors: quantum resonances versus dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of $2\pi$.

We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next-to-leading order (NNLO). The resulting new chiral force ${\mathrm{NNLO}}_{\mathrm{opt}}$ yields ${\chi }^2\approx 1$ per degree of freedom for laboratory energies below approximately 125 MeV. In the $A=3$, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use ${\mathrm{NNLO}}_{\mathrm{opt}}$ to study properties of key nuclei and neutron matter, and we demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitly invoking three-nucleon forces.

We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.

The adsorption of CO on Ag(110) was recently explained using substrate mediated intermolecular interactions, but the underlying mechanism remains unclear. This study investigates both short- and long-range relaxation patterns for CO adsorption on Ag(110) surfaces and suggests that the relaxation mode can be explained by the interaction of heavy electrons on metal substrates in electron momentum space. The long-range relaxation mode for CO on Ag(110) involved a ($6\times 6$) commensurate phase, whereas the short-range relaxation involved an alleviation of Fermi surface nesting along the $⟨1\overline{1}0⟩$ direction of the Ag(110) substrate. The symmetry broken ground state structure at high CO coverage from this work is consistent with the interpretation of available experimental data at low temperature.

Oxygen vacancies created in anatase ${\mathrm{TiO}}_2$ by UV photons (80–130 eV) provide an effective electron-doping mechanism and induce a hitherto unobserved dispersive metallic state. Angle resolved photoemission reveals that the quasiparticles are large polarons. These results indicate that anatase can be tuned from an insulator to a polaron gas to a weakly correlated metal as a function of doping and clarify the nature of conductivity in this material.

It was recently discovered that the low-temperature, charge-ordered phase of $1T\mathrm{\text{−}}{\mathrm{TiSe}}_2$ has a chiral character. This unexpected chirality in a system described by a scalar order parameter could be explained in a model where the emergence of relative phase shifts between three charge density wave components breaks the inversion symmetry of the lattice. Here, we present experimental evidence for the sequence of phase transitions predicted by that theory, going from disorder to nonchiral and finally to chiral charge order. Employing x-ray diffraction, specific heat, and electrical transport measurements, we find that a novel phase transition occurs $\sim 7\mathrm{K}$ below the main charge ordering transition in ${\mathrm{TiSe}}_2$, in agreement with the predicted hierarchy of charge-ordered phases.

We found that ${\mathrm{Ba}}_2{\mathrm{Ti}}_{13}{\mathrm{O}}_{22}$ with ${\mathrm{Ti}}^{3+}$ ($3d^1$) ions on a triangle-based lattice exhibits a phase transition at $T_c\sim 200\mathrm{K}$, below which the increase of electrical resistivity and decrease of magnetic susceptibility were observed. Transmission electron microscopy and optical reflectivity measurements indicate that the low-temperature phase of the present compound shares characteristics in common with a charge-density-wave state with remnant carriers, although a commensurate wave vector of the modulation and a linear temperature dependence of the magnetic susceptibility below $T_c$ suggest an exotic ordered state.

The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice symmetry, the Dirac-point conductivity is either exceptionally robust against disorder (supermetallic state) or suppressed through a gap opening or by algebraic localization of zero-energy modes, whereas weak localization and the Anderson insulating regime are obtained for higher energies. These findings clarify the contribution of zero-energy modes to transport at the Dirac point, hitherto controversial.

Although the stoichiometry of bulk lead sulfide (PbS) is exactly $1:1$, that of quantum dots (QDs) can be considerably different from this crystalline limit. Employing first-principles calculations, we show that the impact of PbS QD stoichiometry on the electronic structure can be enormous, suggesting that control over the overall stoichiometry in the QD will play a critical role for improving the efficiency of optoelectronic devices made with PbS QDs. In particular, for bare PbS QDs, we find that: (i) stoichiometric PbS QDs are free from midgap states even without ligand passivation and independent of shape, (ii) off stoichiometry in PbS QDs introduces new states in the gap that are highly localized on certain surface atoms, and (iii) further deviations in stoichiometry lead to QDs with “metallic” behavior, with a dense number of energy states near the Fermi level. We further demonstrate that this framework holds for the case of passivated QDs by considering the attachment of ligand molecules as stoichiometry variations. Our calculations show that an optimal number of ligands makes the QD stoichiometric and heals unfavorable electronic structure, whereas too few or too many ligands cause effective off stoichiometry, resulting in QDs with defect states in the gap.