We define the anisotropic Rabi model as the generalization of the spin-boson Rabi model: The Hamiltonian system breaks the parity symmetry; the rotating and counterrotating interactions are governed by two different coupling constants; a further parameter introduces a phase factor in the counterrotating terms. The exact energy spectrum and eigenstates of the generalized model are worked out. The solution is obtained as an elaboration of a recently proposed method for the isotropic limit of the model. In this way, we provide a long-sought solution of a cascade of models with immediate relevance in different physical fields, including (i) quantum optics, a two-level atom in single-mode cross-electric and magnetic fields; (ii) solid-state physics, electrons in semiconductors with Rashba and Dresselhaus spin-orbit coupling; and (iii) mesoscopic physics, Josephson-junction flux-qubit quantum circuits.

We study nonlinear interferometry applied to a measurement of atomic spin and demonstrate a sensitivity that cannot be achieved by any linear-optical measurement with the same experimental resources. We use alignment-to-orientation conversion, a nonlinear-optical technique from optical magnetometry, to perform a nondestructive measurement of the spin alignment of a cold ${}^{87}\mathrm{Rb}$ atomic ensemble. We observe state-of-the-art spin sensitivity in a single-pass measurement, in good agreement with covariance-matrix theory. Taking the degree of measurement-induced spin squeezing as a figure of merit, we find that the nonlinear technique’s experimental performance surpasses the theoretical performance of any linear-optical measurement on the same system, including optimization of probe strength and tuning. The results confirm the central prediction of nonlinear metrology, that superior scaling can lead to superior absolute sensitivity.

We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the two nuclei are prepared in opposite spin states. This can be exploited to switch SWAP operations on and off with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective resonant excitation. The latter requires no dynamic tuning of the exchange interaction at all and offers a very attractive scheme to implement two-qubit logic gates under realistic experimental conditions.

When a measurement has limited strength, only partial information, regarding the initial state, is extracted, and, correspondingly, there is a probability to reverse its effect on the system and retrieve the original state. Recently, a clear and direct quantitative description of this complementary relationship, in terms of a tradeoff relation, was developed by Y. K. Cheong and S. W. Lee. [Phys. Rev. Lett. 109, 150402 (2012)]. Here, this tradeoff relation is experimentally verified using polarization-encoded single photons from a quantum dot. Measurement operators representing a complete range, from not affecting the system to a projection to a single polarization state, are realized. In addition, for each measurement operator, an optimal reversal operator is also implemented. The upper bound of the tradeoff relation is mapped to experimental parameters representing the measurement strength. Our results complement the theoretical work and provide a hands-on characterization of general quantum measurements.

A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits locally both the Néel and ferromagnetic orders, even for weak Hubbard interaction. Whereas the Néel order parameter remains of the same sign in the entire system, the magnetization at the boundary takes the opposite sign from the bulk. The total magnetization vanishes this way, and the magnetic ground state is globally only an antiferromagnet. This peculiar ordering stems from the nature of the strain-induced single-particle zero-energy states, which have support on one sublattice of the honeycomb lattice in the bulk, and on the other sublattice near the boundary of a finite system. We support our claim with the self-consistent numerical calculation of the order parameters, as well as by the Monte Carlo simulations of the Hubbard model in both uniformly and nonuniformly strained honeycomb lattice. The present result is contrasted with the magnetic ground state of the same Hubbard model in the presence of a true magnetic field (and for vanishing Zeeman coupling), which is exclusively Néel ordered, with zero local magnetization everywhere in the system.

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a series of architecturally scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigenspectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large-scale quantum computing.

Undoped-graphene (Gr) sheets at low temperatures are known, via random-phase-approximation (RPA) calculations, to exhibit unusual van der Waals (vdW) forces. Here, we show that graphene is the first known system where effects beyond the RPA within each interacting subsystem make qualitative changes to the vdW force, observable via its local exponent $d\log (F)/d\log (D)$. For large separations $D\gtrsim 10\mathrm{nm}$, where only the ${\pi }_z$ vdW forces remain, we find that the Gr-Gr vdW interaction is substantially reduced from the RPA prediction. Its $D$ dependence is very sensitive to the form of the long-wavelength, in-plane many-body enhancement of the velocity of the massless Dirac fermions and may provide independent confirmation of the latter via direct force measurements. The simple connection that we expose is a strong motivation for further refinement of recent successful direct vdW force measurements.

Networks of model neurons with balanced recurrent excitation and inhibition capture the irregular and asynchronous spiking activity reported in cortex. While mean-field theories of spatially homogeneous balanced networks are well understood, a mean-field analysis of spatially heterogeneous balanced networks has not been fully developed. We extend the analysis of balanced networks to include a connection probability that depends on the spatial separation between neurons. In the continuum limit, we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. Notably, this implies that network models with broad recurrent inhibition are inconsistent with the balanced state. For finite size networks, we investigate the pattern-forming dynamics arising when balanced conditions are not satisfied. Our study highlights the new challenges that balanced networks pose for the spatiotemporal dynamics of complex systems.

Leukemia epitomizes the class of highly complex diseases that new technologies aim to tackle by using large sets of single-cell-level information. Achieving such a goal depends critically not only on experimental techniques but also on approaches to interpret the data. A most pressing issue is to identify the salient quantitative features of the disease from the resulting massive amounts of information. Here, I show that the entropies of cell-population distributions on specific multidimensional molecular and morphological landscapes provide a set of measures for the precise characterization of normal and pathological states, such as those corresponding to healthy individuals and acute myeloid leukemia (AML) patients. I provide a systematic procedure to identify the specific landscapes and illustrate how, applied to cell samples from peripheral blood and bone marrow aspirates, this characterization accurately diagnoses AML from just flow cytometry data. The methodology can generally be applied to other types of cell populations and establishes a straightforward link between the traditional statistical thermodynamics methodology and biomedical applications.

We demonstrate theoretically and experimentally that the three-dimensional orientation of a single fluorescent nanoemitter can be determined by polarization analysis of the emitted light (while excitation polarization analysis provides only the in-plane orientation). The determination of the emitter orientation by polarimetry requires a theoretical description, including the objective numerical aperture, the 1D or 2D nature of the emitting dipole, and the environment close to the dipole. We develop a model covering most experimentally relevant microscopy configurations and provide analytical relations that are useful for orientation measurements. We perform polarimetric measurements on high-quality core-shell CdSe/CdS nanocrystals and demonstrate that they can be approximated by two orthogonal degenerated dipoles. Finally, we show that the orientation of a dipole can be inferred by polarimetric measurement, even for a dipole in the vicinity of a gold film, while in this case, the well-established defocused microscopy is not appropriate.

Lévy flights are random walks in which the probability distribution of the step sizes is fat-tailed. Lévy spatial diffusion has been observed for a collection of ultracold ${}^{87}\mathrm{Rb}$ atoms and single ${{}^{24}\mathrm{Mg}}^{+}$ ions in an optical lattice, a system which allows for a unique degree of control of the dynamics. Using the semiclassical theory of Sisyphus cooling, we formulate the problem as a coupled Lévy walk, with strong correlations between the length $\chi$ and duration $\tau$ of the excursions. Interestingly, the problem is related to the area under the Bessel and Brownian excursions. These are overdamped Langevin motions that start and end at the origin, constrained to remain positive, in the presence or absence of an external logarithmic potential, respectively. In the limit of a weak potential, i.e., shallow optical lattices, the celebrated Airy distribution describing the areal distribution of the Brownian excursion is found as a limiting case. Three distinct phases of the dynamics are investigated: normal diffusion, Lévy diffusion and, below a certain critical depth of the optical potential, $x\sim t^{3/2}$ scaling, which is related to Richardson’s diffusion from the field of turbulence. The main focus of the paper is the analytical calculation of the joint probability density function $\psi (\chi ,\tau )$ from a newly developed theory of the area under the Bessel excursion. The latter describes the spatiotemporal correlations in the problem and is the microscopic input needed to characterize the spatial diffusion of the atomic cloud. A modified Montroll-Weiss equation for the Fourier-Laplace transform of the density $P(x,t)$ is obtained, which depends on the statistics of velocity excursions and meanders. The meander, a random walk in velocity space, which starts at the origin and does not cross it, describes the last jump event $\chi$ in the sequence. In the anomalous phases, the statistics of meanders and excursions are essential for the calculation of the mean-square displacement, indicating that our correction to the Montroll-Weiss equation is crucial and pointing to the sensitivity of the transport on a single jump event. Our work provides general relations between the statistics of velocity excursions and meanders on the one hand and the diffusivity on the other, both for normal and anomalous processes.

Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show that another emergent two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall. The domain wall has long been studied as an ingredient of both old-fashioned and leading-edge spintronics. The domain wall here, as an interface of seemingly trivial antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes with robust two-dimensional Fermi surfaces, where pyrochlore iridium oxides proposed to host the condensed-matter realization of Weyl fermions offer such examples at low temperatures. The existence of in-gap states that are pinned at domain walls, theoretically resembling spin or charge solitons in polyacetylene, and protected as the edges of hidden one-dimensional weak Chern insulators characterized by a zero-dimensional class-A topological invariant, solves experimental puzzles observed in $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ with rare-earth elements $R$. The domain wall realizes a novel quantum confinement of electrons and embosses a net uniform magnetization that enables magnetic control of electronic interface transports beyond the semiconductor paradigm.

We demonstrate single-atom trapping in two-dimensional arrays of microtraps with arbitrary geometries. We generate the arrays using a spatial light modulator, with which we imprint an appropriate phase pattern on an optical dipole-trap beam prior to focusing. We trap single ${}^{87}\mathrm{Rb}$ atoms in the sites of arrays containing up to approximately 100 microtraps separated by distances as small as $3\mu \mathrm{m}$, with complex structures such as triangular, honeycomb, or kagome lattices. Using a closed-loop optimization of the uniformity of the trap depths ensures that all trapping sites are equivalent. This versatile system opens appealing applications in quantum-information processing and quantum simulation, e.g., for simulating frustrated quantum magnetism using Rydberg atoms.

Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These rhythmic dynamics can be considered limit cycles of reaction-diffusion systems. However, the conventional phase-reduction theory, which provides a simple unified framework for analyzing synchronization properties of limit-cycle oscillators subjected to weak forcing, has mostly been restricted to low-dimensional dynamical systems. Here, we develop a phase-reduction theory for stable limit-cycle solutions of reaction-diffusion systems with infinite-dimensional state space. By generalizing the notion of isochrons to functional space, the phase-sensitivity function—a fundamental quantity for phase reduction—is derived. For illustration, several rhythmic dynamics of the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase-response properties and synchronization dynamics are revealed, reflecting their complex spatiotemporal organization. Our theory will provide a general basis for the analysis and control of spatiotemporal rhythms in various reaction-diffusion systems.

A fundamental problem in network science is to predict how certain individuals are able to initiate new networks to spring up “new ideas.” Frequently, these changes in trends are triggered by a few innovators who rapidly impose their ideas through “viral” influence spreading, producing cascades of followers and fragmenting an old network to create a new one. Typical examples include the rise of scientific ideas or abrupt changes in social media, like the rise of Facebook to the detriment of Myspace. How this process arises in practice has not been conclusively demonstrated. Here, we show that a condition for sustaining a viral spreading process is the existence of a multiplex-correlated graph with hidden “influence links.” Analytical solutions predict percolation-phase transitions, either abrupt or continuous, where networks are disintegrated through viral cascades of followers, as in empirical data. Our modeling predicts the strict conditions to sustain a large viral spreading via a scaling form of the local correlation function between multilayers, which we also confirm empirically. Ultimately, the theory predicts the conditions for viral cascading in a large class of multiplex networks ranging from social to financial systems and markets.

We propose an experiment to search for QCD axion and axionlike-particle dark matter. Nuclei that are interacting with the background axion dark matter acquire time-varying $CP$-odd nuclear moments such as an electric dipole moment. In analogy with nuclear magnetic resonance, these moments cause precession of nuclear spins in a material sample in the presence of an electric field. Precision magnetometry can be used to search for such precession. An initial phase of this experiment could cover many orders of magnitude in axionlike-particle parameter space beyond the current astrophysical and laboratory limits. And with established techniques, the proposed experimental scheme has sensitivity to QCD axion masses $m_a\lesssim 10^{-9}\mathrm{eV}$, corresponding to theoretically well-motivated axion decay constants $f_a\gtrsim 10^{16}\mathrm{GeV}$. With further improvements, this experiment could ultimately cover the entire range of masses $m_a\lesssim \mu \mathrm{eV}$, complementary to cavity searches.

Silicon is arguably the best electronic material, but it is not a good optoelectronic material. By employing first-principles calculations and the cluster-expansion approach, we discover that hydrogenated bilayer silicene (BS) shows promising potential as a new kind of optoelectronic material. Most significantly, hydrogenation converts the intrinsic BS, a strongly indirect semiconductor, into a direct-gap semiconductor with a widely tunable band gap. At low hydrogen concentrations, four ground states of single- and double-sided hydrogenated BS are characterized by dipole-allowed direct (or quasidirect) band gaps in the desirable range from 1 to 1.5 eV, suitable for solar applications. At high hydrogen concentrations, three well-ordered double-sided hydrogenated BS structures exhibit direct (or quasidirect) band gaps in the color range of red, green, and blue, affording white light-emitting diodes. Our findings open opportunities to search for new silicon-based light-absorption and light-emitting materials for earth-abundant, high-efficiency, optoelectronic applications.

Quasifree field-driven electron trajectories are a key element of strong-field dynamics. Upon recollision with the parent ion, the energy transferred from the field to the electron may be released as attosecond-duration extreme ultaviolet emission in the process of high-harmonic generation. The conventional sinusoidal driver fields set limitations on the maximum value of this energy transfer and the efficient return of the launched electron trajectories. It has been predicted that these limits can be significantly exceeded by an appropriately ramped-up cycle shape [L. E. Chipperfield et al., Phys. Rev. Lett. 102, 063003 (2009)]. Here, we present an experimental realization of similar cycle-shaped waveforms and demonstrate control of the high-harmonic generation process on the single-atom quantum level via attosecond steering of the electron trajectories. With our improved optical cycles, we boost the field ionization launching the electron trajectories, increase the subsequent field-to-electron energy transfer, and reduce the trajectory duration. We demonstrate, in realistic experimental conditions, 2 orders of magnitude enhancement of the generated extreme ultraviolet flux together with an increased spectral extension. This application, which is only one example of what can be achieved with cycle-shaped high-field light waves, has significant implications for attosecond spectroscopy and molecular self-probing.

The new challenges posed by the need of finding strong rare-earth-free magnets demand methods that can predict magnetization and magnetocrystalline anisotropy energy (MAE). We argue that correlated electron effects, which are normally underestimated in band-structure calculations, play a crucial role in the development of the orbital component of the magnetic moments. Because magnetic anisotropy arises from this orbital component, the ability to include correlation effects has profound consequences on our predictive power of the MAE of strong magnets. Here, we show that incorporating the local effects of electronic correlations with dynamical mean-field theory provides reliable estimates of the orbital moment, the mass enhancement, and the MAE of ${\mathrm{YCo}}_5$.

By combining the advantages of both a metallic metamaterial and a dielectric interlayer, we demonstrate the general mechanism to construct the dispersion-free metastructure, in which the intrinsic dispersion of the metallic structures is perfectly cancelled out by the thickness-dependent dispersion of the dielectric spacing layer. As examples to apply this concept, a broadband quarter-wave plate and a half-wave plate are demonstrated. By selecting the structural parameters, the polarization state of light can be freely tuned across a broad frequency range, and all of the polarization states on the Poincaré sphere can be realized dispersion free.