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We show how to apply a generalization of local control design to the problem of the saturation of a spin-1/2 particle by magnetic fields in nuclear magnetic resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with that of the time-optimal solution that has recently been derived using geometric methods.

We investigate the spontaneous emission (SE) spectrum of a qubit in a lossy resonant cavity. We use neither the rotating-wave approximation nor the Markov approximation. For the weak-coupling case, the SE spectrum of the qubit is a single peak, with its location depending on the spectral density of the qubit environment. Then, the asymmetry (of the location and heights of the two peaks) of the two SE peaks (which are related to the vacuum Rabi splitting) changes as the qubit–cavity coupling increases. Explicitly, for a qubit in a low-frequency intrinsic bath, the height asymmetry of the splitting peaks is enhanced as the qubit–cavity coupling strength increases. However, for a qubit in an Ohmic bath, the height asymmetry of the spectral peaks is inverted compared to the low-frequency bath case. With further increasing the qubit–cavity coupling to the ultra-strong regime, the height asymmetry of the left and right peaks is slightly inverted, which is consistent with the corresponding case of a low-frequency bath. This inversion of the asymmetry arises from the competition between the Ohmic bath and the cavity bath. Therefore, after considering the anti-rotating terms, our results explicitly show how the height asymmetry in the SE spectrum peaks depends on the qubit–cavity coupling and the type of intrinsic noise experienced by the qubit.

We report on our experimental and theoretical investigations on the generation of high-order harmonics driven by 1500 nm few-cycle laser pulses in xenon. In contrast to the common belief, we found experimental evidence suggesting that harmonic generation driven by mid-infrared laser pulses can be realized with high efficiency; in particular, an enhancement of very high harmonic orders can be achieved under suitable conditions of the laser–medium interaction. The experimental results were simulated by a 3D non-adiabatic model. The theoretical outcomes confirm the experimental findings and provide a physical explanation for the counter-intuitive results. In particular, a time-dependent phase-matching analysis threw light on the generation mechanisms at a timescale of half optical cycle of the fundamental pulse.

We study the effects of Ar⁺, He⁺ and C⁺ ion irradiation on multi-walled carbon nanotubes at room and elevated temperatures with transmission electron microscopy (TEM) and Raman spectroscopy. Based on the TEM data, we introduce a universal damage scale for the visual analysis and characterization of irradiated nanotubes. We show for the first time that the amount of irradiation-induced damage in nanotubes is larger than the value predicted for bulk materials using the simple binary collision approximation, which may be associated with higher defect production due to electronic stopping in these nanoscale systems. The Raman spectra of the irradiated samples are in qualitative agreement with the TEM data and indicate the presence of irradiation-induced defects. However, it is difficult to obtain quantitative information on defect concentration due to non-uniform distribution of defects in the nanotube films and in part due to the presence of other carbon nanosystems in the samples, such as graphitic crystallites and carbon onions.

The influence of a uniform magnetic field on the density of states (DoS) for carriers confined in a cylindrical semiconductor quantum wire irradiated by a monochromatic, linearly polarized, intense laser field is computed here non-perturbatively, following the Green's function scheme introduced by some of the authors in a recent work (Lima et al 2009 Solid State Commun.149 678). Besides the known changes in the DoS provoked by an intense terahertz laser field—namely, a significant reduction and the appearance of Franz–Keldysh-like oscillations—our model reveals that the inclusion of a longitudinal magnetic field induces additional blueshifts on the energy levels of the allowed states. Our results show that the increase of the blueshifts with the magnitude of the magnetic field depends only on the azimuthal quantum number m (m=0, 1, 2, ...), being more pronounced for states with higher values of m, which leads to some energy crossovers. For all states, we have obtained, even in the absence of a magnetic field, a localization effect that leads to a transition in the DoS from the usual profile of quasi-1D systems to a peaked profile typical of quasi-0D systems, as e.g. those found for electrons confined in a quantum dot.

The third phase of the Sudbury Neutrino Observatory (SNO) experiment added an array of ³He proportional counters to the detector. The purpose of this neutral-current detection (NCD) array was to observe neutrons resulting from neutral-current solar-neutrino–deuteron interactions. We have developed a detailed simulation of current pulses from NCD array proportional counters, from the primary neutron capture on ³He through NCD array signal-processing electronics. This NCD array MC simulation was used to model the alpha-decay background in SNO's third-phase ⁸B solar-neutrino measurement.

In a semiconductor superlattice (SL), phonon-assisted electron transitions can occur under a quasi-population inversion, brought about by electrical biasing. This paper demonstrates the amplification of an optically excited quasi-monochromatic phonon beam by stimulated emission of phonons. Coherent phonons are generated by ultrafast optical excitation of a generator SL and passed once through a dc biased, GaAs/AlAs gain SL. A 20% increase in the phonon flux is detected when pumping is applied to the gain superlattice, which corresponds to an acoustic gain coefficient of 3600 cm⁻¹. A theoretical model of the phonon amplification is presented that also includes the effects of disorder in the SL. It is found that the amplification process is robust in the presence of disorder and good agreement is obtained with the main features of the experimental observations.

We show how a quantum mechanical vortex state of a two-mode system can be generated from a squeezed vacuum by subtracting a photon. The vortex state has nonclassical properties; for example, its Wigner function can be negative, in contrast to the Wigner function of the two-mode squeezed vacuum. We show, by calculating the logarithmic negativity parameter, that the vortex state has stronger entanglement than the two-mode squeezed vacuum.

The mechanisms by which cytoskeletal flows and cell–substrate interactions interact to generate cell motion are explored by using a simplified model of the cytoskeleton as a viscous gel containing active stresses. This model yields explicit general results relating cell speed and traction forces to the distributions of active stress and cell–substrate friction. It is found that (i) the cell velocity is given by a function that quantifies the asymmetry of the active-stress distribution, (ii) gradients in cell–substrate friction can induce motion even when the active stresses are symmetrically distributed, (iii) the traction-force dipole is enhanced by protrusive stresses near the cell edges or contractile stresses near the center of the cell and (iv) the cell velocity depends biphasically on the cell–substrate adhesion strength if active stress is enhanced by adhesion. Specific experimental tests of the calculated dependences are proposed.

The production of extreme ultraviolet (XUV) radiation via nanoplasmonic field-enhanced high-harmonic generation (HHG) in gold nanostructures at MHz repetition rates is investigated theoretically in this paper. Analytical and numerical calculations are employed and compared in order to determine the plasmonic fields in gold ellipsoidal nanoparticles. The comparison indicates that numerical calculations can accurately predict the field enhancement and plasmonic decay, but may encounter difficulties when attempting to predict the oscillatory behavior of the plasmonic field. Numerical calculations for coupled symmetric and asymmetric ellipsoids for different carrier-envelope phases (CEPs) of the driving laser field are combined with time-dependent Schrödinger equation simulations to predict the resulting HHG spectra. The studies reveal that the plasmonic field oscillations, which are controlled by the CEP of the driving laser field, play a more important role than the nanostructure configuration in finding the optimal conditions for the generation of isolated attosecond XUV pulses via nanoplasmonic field enhancement.

It was recently shown that, for solving NP-complete problems, adiabatic paths always exist without finite-order perturbative crossings between local and global minima, which could lead to anticrossings with exponentially small energy gaps if present. However, it was not shown whether such a path could be found easily. Here, we give a simple construction that deterministically eliminates all such anticrossings in polynomial time, space and energy, for any Ising models with polynomial final gap. Thus, in order for adiabatic quantum optimization to require exponential time to solve any NP-complete problem, some quality other than this type of anticrossing must be unavoidable and necessitate exponentially long runtimes.

Colour centres in diamond are promising candidates as a platform for quantum technologies and biomedical imaging based on spins and/or photons. Controlling the emission properties of colour centres in diamond is a key requirement for the development of efficient single-photon sources having high collection efficiency. A number of groups have achieved an enhancement in the emission rate over narrow wavelength ranges by coupling single emitters in nanodiamond crystals to resonant electromagnetic structures. In this paper, we characterize in detail the spontaneous emission rates of nitrogen-vacancy centres at various locations on a structured substrate. We found a factor of 1.5 average enhancement of the total emission rate when nanodiamonds are on an opal photonic crystal surface, and observed changes in the lifetime distribution. We present a model for explaining these observations and associate the lifetime properties with dipole orientation and polarization effects.

Suppose that several parties jointly possess a pure multipartite state, |ψ⟩. Using local operations on their respective systems and classical communication (i.e. LOCC), it may be possible for the parties to transform deterministically |ψ⟩ into another joint state |ϕ⟩. In the bipartite case, the Nielsen majorization theorem gives the necessary and sufficient conditions for this process of entanglement transformation to be possible. In the multipartite case, such a deterministic local transformation is possible only if both the states are in the same stochastic LOCC (SLOCC) class. Here, we generalize the Nielsen majorization theorem to the multipartite case, and find necessary and sufficient conditions for the existence of a local separable transformation between two multipartite states in the same SLOCC class. When such a deterministic conversion is not possible, we find an expression for the maximum probability to convert one state to another by local separable operations. In addition, we find necessary and sufficient conditions for the existence of a separable transformation that converts a multipartite pure state into one of a set of possible final states all in the same SLOCC class. Our results are expressed in terms of (i) the stabilizer group of the state representing the SLOCC orbit and (ii) the associate density matrices (ADMs) of the two multipartite states. The ADMs play a similar role to that of the reduced density matrices when considering local transformations that involve pure bipartite states. We show, in particular, that the requirement that one ADM majorizes another is a necessary condition but is, in general, far from also being sufficient as it happens in the bipartite case. In most of the results the twirling operation with respect to the stabilizer group (of the representative state in the SLOCC orbit) plays an important role that provides a deep link between entanglement theory and the resource theory of reference frames.

The angle-resolved resonant Auger spectrum of Xe is investigated with a record high meV energy resolution in the kinetic energy region of 34.45–39.20 eV at hν=65.110 eV, corresponding to the resonant excitation of the Auger Xe^* 4d_5/2⁻¹6p state. New lines have been observed and assigned in the spectra. The results of previous measurements concerning energies, intensities and angular distribution asymmetry parameters have been refined, complemented and, for some of the lines, corrected.

The Bialynicki-Birula–Sipe photon wave function formalism is extended to include the interaction between photons and continuous non-absorptive media. When the second quantization of this formalism is introduced, a new method for describing the quantum interactions between light and matter emerges. As an example of the application of the method, an expression for the quantum state of the twin photons generated by parametric downconversion is derived in agreement with previous treatments, but with a more intuitive interpretation.

Among various definitions of quantum correlations, quantum discord has attracted considerable attention. To find an analytical expression for quantum discord is an intractable task. Exact results are known only for very special states, namely two-qubit X-shaped states. We present in this paper a geometric viewpoint, from which two-qubit quantum discord can be described clearly. The known results on X state discord are restated in the directly perceivable geometric language. As a consequence, the dynamics of classical correlations and quantum discord for an X state in the presence of decoherence is endowed with geometric interpretation. More importantly, we extend the geometric method to the case of more general states, for which numerical as well as analytical results on quantum discord have not yet been obtained. Based on the support of numerical computations, some conjectures are proposed to help us establish the geometric picture. We find that the geometric picture for these states has an intimate relationship with that for X states. Thereby, in some cases, analytical expressions for classical correlations and quantum discord can be obtained.

Pattern formation on Si(001) through 2 keV Kr⁺ ion beam erosion of Si(001) at an incident angle of ϑ=30° and in the presence of sputter co-deposition or co-evaporation of Fe is investigated by using in situ scanning tunneling microscopy, ex situ atomic force microscopy and electron microscopy. The phenomenology of pattern formation is presented, and experiments are conducted to rule out or determine the processes of relevance in ion beam pattern formation on Si(001) with impurities. Special attention is given to the determination of morphological phase boundaries and their origin. Height fluctuations, local flux variations, induced chemical inhomogeneities, silicide formation and ensuing composition-dependent sputtering are found to be of relevance for pattern formation.

Quantum noise correlations have been employed in several areas of physics, including condensed matter, quantum optics and ultracold atoms, to reveal the non-classical states of the systems. To date, such analyses have mostly focused on systems in equilibrium. In this paper, we show that quantum noise is also a useful tool for characterizing and studying the non-equilibrium dynamics of a one-dimensional (1D) system. We consider the Ramsey sequence of 1D, two-component bosons, and obtain simple, analytical expressions for time evolutions of the full distribution functions for this strongly correlated, many-body system. The analysis can also be directly applied to the evolution of interference patterns between two 1D quasi-coindensates created from a single condensate through splitting. Using the tools developed in this paper, we demonstrate that 1D dynamics in these systems exhibits the phenomenon known as 'prethermalization', where the observables of non-equilibrium, long-time transient states become indistinguishable from those of thermal equilibrium states.

Turbulent magnetohydrodynamic (MHD) dynamo action in a spherically bounded electrically conducting flow is investigated numerically. A large-scale two-vortex flow driven by a constant body force is simulated. The numerical setup models the spherical Madison Dynamo Experiment, which uses an impeller-driven flow of liquid sodium. The study focuses on small magnetic Prandtl numbers (Pm), the regime relevant to liquid sodium experimental flows. The critical magnetic Reynolds number (Rm_c) of the dynamo model is determined. It initially rises steeply quasi-linearly as a function of the Reynolds number (Re) by about a factor of 10. Finally, it starts to flatten for Pm ≲ 0.1. Further investigations yield that the initial rise of the stability curve is caused in concert with large- and small-scale fluctuations of the velocity field. As an inertial range of turbulence develops with increasing Re, small-scale dynamo modes become unstable, indicating a transition from large-scale (dipolar) to small-scale dynamo action. It is argued that the flattening of the stability curve is related to a saturation of detrimental large-scale velocity fluctuations, the activation of small-scale dynamo action, and the separation of resistive and viscous cutoff scales for Pm < 1. Moreover, it is shown that only the turbulent fluctuations obtained by subtracting the precomputed mean flow from the dynamically evolving flow can act as a small-scale dynamo.

One of the most fundamental concepts of evolutionary dynamics is the 'fixation' probability, i.e. the probability that a gene spreads through the whole population. Most natural communities are geographically structured into habitats exchanging individuals among themselves. The topology of the migration patterns is believed to influence the spread of a new mutant, but no general analytical results were known for its fixation probability. We show that, for large populations, the fixation probability of a beneficial mutation can be evaluated for any migration pattern between local communities. Specifically, we demonstrate that for large populations, in the framework of the Voter model of the Moran model, the fixation probability is always smaller than or, at best, equal to the fixation probability of a non-structured population. In the 'invasion processes' version of the Moran model, the fixation probability can exceed that of a non-structured population; our method allows migration patterns to be classified according to their amplification effect. The theoretical tool we have developed in order to perform these computations uses the fixed points of the probability-generating function which are obtained by a system of second-order algebraic equations.

We have studied experimentally the collective behavior of self-propelling liquid droplets, which closely mimic the locomotion of some protozoal organisms, the so-called squirmers. For the sake of simplicity, we concentrate on quasi-two-dimensional (2D) settings, although our swimmers provide a fully 3D propulsion scheme. At an areal density of 0.46, we find strong polar correlation of the locomotion velocities of neighboring droplets, which decays over less than one droplet diameter. When the areal density is increased to 0.78, distinct peaks show up in the angular correlation function, which point to the formation of ordered rafts. This shows that pronounced textures, beyond what has been seen in simulations so far, may show up in crowds of simple model squirmers, despite the simplicity of their (purely physical) mutual interaction.

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model using a low-dimensional system of equations permitting analytical investigation. We find that the model reproduces several characteristic features of swarms, including spontaneous symmetry breaking, noise- and density-driven order–disorder transitions that can be of first or second order, and intermittency. Reproducing these experimental observations using a non-spatial model suggests that spatial geometry may have less of an impact on collective motion than previously thought.

The expansion of a dense plasma through a more rarefied ionized medium has been studied by means of two-dimensional particle-in-cell simulations. The initial conditions involve a density jump by a factor of 100, located in the middle of an otherwise equally dense electron–proton plasma with uniform proton and electron temperatures of 10 eV and 1 keV, respectively. Simulations show the creation of a purely electrostatic collisionless shock together with an ion-acoustic soliton tied to its downstream region. The shock front is seen to evolve in filamentary structures consistently with the onset of the ion–ion instability. Meanwhile, an un-magnetized drift instability is triggered in the core part of the dense plasma. Such results explain recent experimental laser–plasma experiments, carried out in similar conditions, and are of intrinsic relevance to non-relativistic shock scenarios in the solar and astrophysical systems.

The security of quantum key distribution (QKD) can easily be obscured if the eavesdropper can utilize technical imperfections in the actual implementation. Here, we describe and experimentally demonstrate a very simple but highly effective attack that does not need to intercept the quantum channel at all. Only by exploiting the dead time effect of single-photon detectors is the eavesdropper able to gain (asymptotically) full information about the generated keys without being detected by state-of-the-art QKD protocols. In our experiment, the eavesdropper inferred up to 98.8% of the key correctly, without increasing the bit error rate between Alice and Bob significantly. However, we find an even simpler and more effective countermeasure to inhibit this and similar attacks.

It is known that an inductively coupled plasma (ICP) sustained by a radiofrequency current coil has a mode transition and hysteresis characteristics of the internal plasma parameter as a function of the external plasma parameter. We focus on the contributions of low- and high-energy electrons to the phase transition between the capacitive E-mode and the inductive H-mode in an ICP. Our analysis is based on the diagnostics for a time-resolved two-dimensional net excitation rate of short-lived excited atoms, mainly produced collisionally by low- and high-energy electrons by using an intensified charge coupled device optical image. Short-lived excited atoms Ar(2p₁) and Ar(2p₉) with different excitation processes have been employed as optical probes in an axisymmetric configuration of the ICP chamber, driven at 13.56 MHz by an external single-turn current coil at 300 mTorr in pure Ar. The E-to-H transition is characterized by two time constants of electrons: establishment of an axisymmetric distribution by electron diffusion and the accumulation of symmetric high-density electrons in order to sustain the inductive discharge under a weak electromagnetic field. On the other hand, the H-to-E transition is strongly influenced by the presence of a long-lived excited atom (i.e. metastables).

We theoretically and experimentally examine the effects of anharmonic terms in the trapping potential for linear chains of trapped ions. We concentrate on two different effects that become significant at different levels of anharmonicity. The first is a modification of the oscillation frequencies and amplitudes of the ions' normal modes of vibration for multi-ion crystals, resulting from each ion experiencing a different curvature in the potential. In the second effect, which occurs with increased anharmonicity or higher excitation amplitude, amplitude-dependent shifts of the normal-mode frequencies become important. We evaluate normal-mode frequency and amplitude shifts, and comment on the implications for quantum information processing and quantum state engineering. Since the ratio of the anharmonic to harmonic terms typically increases as the ion–electrode distance decreases, anharmonic effects will become more significant as ion trap sizes are reduced. To avoid unwanted problems, anharmonicities should therefore be taken into account at the design stage of trap development.

We demonstrate high-fidelity Zeeman qubit state detection in a single trapped ⁸⁸Sr⁺ ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm, followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent estimates of the detection error threshold required for fault-tolerant computation, whereas high-fidelity state tomography opens the way for high-precision quantum process tomography.

In this paper, we present the significant progress made by an experiment dedicated to the determination of the Boltzmann constant, k_B, by accurately measuring the Doppler absorption profile of a line in ammonia gas at thermal equilibrium. This optical method based on the first principles of statistical mechanics is an alternative to the acoustical method, which has led to the unique determination of k_B published by the Committee on Data for Science and Technology with a relative accuracy of 1.7×10⁻⁶. We report on the first measurement of the Boltzmann constant carried out by using laser spectroscopy with a statistical uncertainty below 10 p.p.m., more specifically 6.4 p.p.m. This progress results from the improvement in the detection method and in the statistical treatment of the data. In addition, we have recorded the hyperfine structure of the probed ν₂ saQ(6,3) rovibrational line of ammonia by saturation spectroscopy and thus determine very precisely the induced 4.36 (2) p.p.m. broadening of the absorption linewidth. We also show that in our well-chosen experimental conditions, saturation effects have negligible impact on the linewidth. Finally, we suggest directions for future work to achieve an absolute determination of k_B with an accuracy of a few p.p.m.

Efficient algorithms are of fundamental importance for the discovery of optimal control designs for coherent control of quantum processes. One important class of algorithms is sequential update algorithms, generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad hoc penalty terms. The latter, despite being necessary for regularizing the problem in the limit of infinite time resolution, i.e. the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.

By using two generic polymer models, namely self-consistent field theory and bond-fluctuation Monte-Carlo simulations, we investigate numerically the properties of a polymer melt in a hexagonal array of nanotubes as a function of the polymer length, the interaction with the nanotubes and the compressibility or average density. The combined effect of the attractive interaction with the nanotube walls, the entropy decrease due to the impenetrability of the walls and the hexagonal arrangement of the nanotubes with varying gap size in between them leads to a wide array of possible density profiles and polymer configurations as a function of the model parameters. Even in the case of the Monte-Carlo simulations, where the contact interaction affects only the first layer of monomers, the effect of the wall can nevertheless be felt throughout the entire melt at intermediate temperatures.

Neural network devices that inherently possess parallel computing capabilities are generally difficult to construct because of the large number of neuron–neuron connections. However, there exists a theoretical approach (Hoppensteadt and Izhikevich 1999 Phys. Rev. Lett.82 2983) that forgoes the individual connections and uses only a global coupling: systems of weakly coupled oscillators with a time-dependent global coupling are capable of performing pattern recognition in an associative manner similar to Hopfield networks. The information is stored in the phase shifts of the individual oscillators. However, to date, even the feasibility of controlling phase shifts with this kind of coupling has not yet been established experimentally. We present an experimental realization of this neural network device. It consists of eight sinusoidal electrical van der Pol oscillators that are globally coupled through a variable resistor with the electric potential as the coupling variable. We estimate an effective value of the phase coupling strength in our experiment. For that, we derive a general approach that allows one to compare different experimental realizations with each other as well as with phase equation models. We demonstrate that individual phase shifts of oscillators can be experimentally controlled by a weak global coupling. Furthermore, supplied with a distorted input image, the oscillating network can indeed recognize the correct image out of a set of predefined patterns. It can therefore be used as the processing unit of an associative memory device.

Quantum detectors provide information about the microscopic properties of quantum systems by establishing correlations between those properties and a set of macroscopically distinct events that we observe. The question of how much information a quantum detector can extract from a system is therefore of fundamental significance. In this paper, we address this question within a precise framework: given a measurement apparatus implementing a specific POVM measurement, what is the optimal performance achievable with it for a specific information readout task and what is the optimal way to encode information in the quantum system in order to achieve this performance? We consider some of the most common information transmission tasks—the Bayes cost problem, unambiguous message discrimination and the maximal mutual information. We provide general solutions to the Bayesian and unambiguous discrimination problems. We also show that the maximal mutual information is equal to the classical capacity of the quantum-to-classical channel describing the measurement, and study its properties in certain special cases. For a group covariant measurement, we show that the problem is equivalent to the problem of accessible information of a group covariant ensemble of states. We give analytical proofs of optimality in some relevant cases. The framework presented here provides a natural way to characterize generalized quantum measurements in terms of their information readout capabilities.

We consider the problem of distinguishing between a set of arbitrary quantum states in a setting in which the time available to perform the measurement is limited. We provide simple upper bounds on how well we can perform state discrimination in a given time as a function of either the average energy or the range of energies available during the measurement. We exhibit a specific strategy that nearly attains this bound. Finally, we consider several applications of our result. Firstly, we obtain a time-dependent Tsirelson's bound that limits the extent of the Bell inequality violation that can be in principle be demonstrated in a given time t. Secondly, we obtain a Margolus–Levitin type bound when considering the special case of distinguishing orthogonal pure states.

Employing the microscopic superexchange model incorporating the effect of spin–orbit interaction, we have investigated the Dzyaloshinsky–Moriya (DM) interaction in perovskite transition-metal (TM) oxides and explored the interplay between the DM interaction and the TM-3d orbital symmetry. For d³ and d⁵ systems with isotropic orbital symmetry, the DM vectors are well described by a simple symmetry analysis considering only the bond geometry. In contrast, the DM interaction for d⁴ systems with anisotropic orbital symmetry shows slightly different behavior, which does not obey simple symmetry analysis. The direction as well as the strength of the DM vector varies depending on the occupied orbital shape. We have understood this behavior based on the orbital symmetry induced by local crystal field variation.

We examine the characteristics of high-order harmonics generated with 800 nm, 25 mJ, 160 fs laser pulses in an Ar gas cell with the objective of seeding a free electron laser. We measure the energy per pulse and per harmonic, the energy jitter, the divergence and the position stability of the harmonic beam. We perform ab initio numerical simulations based on integration of the time-dependent Schrödinger equation and of the wave equation within the slowly varying envelope approximation. The results reproduce the experimental measurements to better than a factor of two. The interaction of a frequency comb of harmonic fields with an electron bunch in an undulator is examined with a simple model consisting of calculating the energy modulation owing to the seed–electron interaction. The model indicates that the undulator acts as a spectral filter selecting a given harmonic.

In Korean culture, the names of family members are recorded in special family books. This makes it possible to follow the distribution of Korean family names far back in history. It is shown here that these name distributions are well described by a simple null model, the random group formation (RGF) model. This model makes it possible to predict how the name distributions change and these predictions are shown to be borne out. In particular, the RGF model predicts that for married women entering a collection of family books in a certain year, the occurrence of the most common family name 'Kim' should be directly proportional to the total number of married women with the same proportionality constant for all the years. This prediction is also borne out to a high degree. We speculate that it reflects some inherent social stability in the Korean culture. In addition, we obtain an estimate of the total population of the Korean culture down to the year 500 AD, based on the RGF model, and find about ten thousand Kims.

We explore the electrical transport and magneto-conductance (MC) in quasi-two-dimensional strongly correlated ultra-thin films of LaNiO₃ (LNO) to investigate the effect of hetero-epitaxial strain on electron–electron and electron–lattice interactions from the low to intermediate temperature range (2–170 K). The fully epitaxial 10 unit cell thick films spanning tensile strain up to ∼4% are used to investigate the effects of enhanced carrier localization driven by a combination of weak localization (WL) and electron–electron interactions at low temperatures. The MC data show the importance of the increased contribution of WL to low-temperature quantum corrections. The obtained results demonstrate that with increasing tensile strain and reduced temperature, the quantum-confined LNO system gradually evolves from the Mott into the Mott–Anderson regime.

We study quantum Darwinism, the redundant recording of information about the preferred states of a decohering system by its environment, for an object illuminated by a blackbody. We calculate the quantum mutual information between the object and its photon environment for blackbodies that cover an arbitrary section of the sky. In particular, we demonstrate that more extended sources have a reduced ability to create redundant information about the system, in agreement with previous evidence that initial mixedness of an environment slows—but does not stop—the production of records. We also show that the qualitative results are robust for more general initial states of the system.

We have studied the dynamics of electron transfer between the molecules of an organic donor–acceptor pair upon absorption of light. Specifically, we considered the tetrathiafulvalene (TTF)–7,7,8,8-tetracyanoquinodimethane (TCNQ) donor–acceptor pair using time-dependent density functional theory with local-density approximation. The molecular planes of the two components are parallel to each other, and the optical transition probability is found to be highest when the optical electric field is parallel to these planes. Under these conditions, absorption induces additional electron transfer from TTF to TCNQ in the π-orbitals perpendicular to the molecular plane and, consequently, we found that the dimer's dipole moment perpendicular to the molecular axes is enhanced with the increase rate of 1% in 15 fs. This enhancement reflects the fact that photo-excited electron–hole pairs tend to dissociate, i.e. electrons and holes move away from each other. We thus suggest potential photovoltaic devices employing these molecules as building blocks.

In this paper, the plasmon coupling effect between two gold nanospheres on a gold slab is investigated. At plasmon resonance frequencies, electrons on the surface of the slab are absorbed into spheres and contribute to plasmon oscillation. This effect can enhance the local electric field and optical coupling force between the two spheres.

Metamaterials are, in general, characterized by the bianisotropic response that relates the displacement vector D and the magnetic induction B to the electric and magnetic fields E and H via the permittivity, permeability and magnetoelectric dyadics, respectively, , and . For the first time, we derived these dyadics with great generality with the photonic crystal (PC) description as the starting point. The PC can have one- (1D), two- (2D) or three-dimensional (3D) periodicity with an arbitrary Bravais lattice and arbitrary shape of the inclusions in the unit cell, and these inclusions can be dielectric or metallic. Moreover, unlike most theories of homogenization, our theory is, in principle, applicable to band-pass or optical bands, as well as to low-pass or acoustic bands. The generalized conductivity is assumed to be given at every point in the unit cell, and we relate , and analytically to . The long-wavelength limit having been taken, these dyadics depend only on the direction of the Bloch wave vector k and not on its magnitude. In the case of inversion symmetry, the bianisotropic response simplifies to and . Applying our theory to a 2D array of metallic wires, we find that the response is paramagnetic or diamagnetic, depending on whether it is the electric or the magnetic field that is parallel to the wires. For a 3D array of mutually perpendicular wires (3D crosses), the behavior is found to change from plasma-like to free-photon-like when the wires are severed, leading to a spectral region where ε and μ are both negative. Finally, our theory confirms several well-known results for particular PCs and inclusions.

The vibrational properties of out-of-plane elastic waves in hexagonal monolayer granular membranes were studied theoretically. The predicted propagation modes involve an out-of-plane displacement and two rotations with axes in the membrane plane. Shear and bending rigidities at the contact between beads were considered. Both the cases of freely suspended membranes and membranes coupled to a rigid substrate were analyzed. Dispersion relations and the existence of band gaps are presented and discussed for various contact properties. For freely suspended membranes with sufficient contact bending rigidity, it is shown that complete band gaps exist. The results obtained may be of interest for testing with acoustic waves the elasticity of recently developed granular membranes composed of nanoparticles (of interest because of their phoxonic properties) and more generally for the control of designing devices for membrane wave propagation.

We describe the advantages of two-dimensional (2D), addressable arrays of spherical Paul traps. They would provide the ability to address and tailor the interaction strengths of trapped objects in 2D and could be a valuable new tool for quantum information processing. Simulations of trapping ions are compared to first tests utilizing printed circuit board trap arrays loaded with dust particles. Pair-wise interactions in the array are addressed by means of an adjustable radio-frequency (RF) electrode shared between trapping sites. By attenuating this RF electrode potential, neighboring pairs of trapped objects have their interaction strength increased and are moved closer to one another. In the limit of the adjustable electrode being held at RF ground, the two formerly spherical traps are merged into one linear Paul trap.

We show how to create long-range interactions between alkali atoms in different hyperfine ground states, with the goal of coherent quantum transport. The scheme uses off-resonant dressing with atomic Rydberg states. We demonstrate coherent migration of electronic excitation through dressed dipole–dipole interaction by full solutions of models with four essential states per atom and give the structure of the spectrum of dressed states for a dimer. In addition, we present an effective (perturbative) Hamiltonian for the ground-state manifold and show that it correctly describes the full multi-state dynamics. We discuss excitation transport in detail for a chain of five atoms. In the presented scheme, the actual population in the Rydberg state is kept small. Dressing offers many advantages over the direct use of Rydberg levels: it reduces ionization probabilities and provides an additional tuning parameter for lifetimes and interaction strengths.

A theoretical model is presented for the scattering of light and surface plasmon polaritons (SPPs) by finite-size subwavelength metallic defects. Based on the decomposition of the scattered fields into SPPs and quasi-cylindrical waves (CWs), an SPP–CW model is developed to depict the multiple scattering of SPPs and CWs in finite-size defects using the elementary scattering processes in a single one. The involved elementary scattering of the CW, as well as the CW-related coefficients, which are difficult or even impossible to define and calculate according to classical scattering theory, is clarified. A close relationship between the scattering coefficients of the SPP and those of the CW has been pointed out and used to simplify the developed model. Compared to the corresponding pure SPP model and the fully vectorial computational data, the SPP–CW model is shown to be versatile and quantitatively accurate for finite-size defects such as grooves, ridges, slits or even hybrid systems of various geometrical parameters, over a broad spectral range from the visible to the thermal infrared regime.

We demonstrate electrical control of the single-photon emission spectrum from chromium-based colour centres implanted in monolithic diamond. Under an external electric field, the tunability range is typically three orders of magnitude larger than the radiative linewidth and at least one order of magnitude larger than the observed linewidth. The electric and magnetic field dependence of luminescence gives indications of the inherent symmetry, and we propose Cr–X or X–Cr–Y-type non-centrosymmetric atomic configurations as the most probable candidates for these centres.

We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single-photon absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle–light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot–Lau-like interference effect with a characteristic dependence on the pulse delay time.

Integrated optics provides an ideal testbed for the emulation of quantum systems via continuous-time quantum walks. Here, we study the evolution of two-photon states in an elliptic array of waveguides. We characterize the photonic chip via coherent light tomography and use the results to predict distinct differences between temporally indistinguishable and distinguishable two-photon inputs, which we then compare with experimental observations. This work highlights the feasibility of emulation of coherent quantum phenomena in three-dimensional waveguide structures.

Relativistic heavy-ion collisions have reached energies that enable the creation of a novel state of matter termed the quark–gluon plasma. Many observables point to a picture of the medium as rapidly equilibrating and expanding as a nearly inviscid fluid. In this paper, we explore the evolution of experimental flow observables as a function of collision energy and attempt to reconcile the observed similarities across a broad energy regime in terms of the initial conditions and viscous hydrodynamics. If the initial spatial anisotropies for all collision energies from 39 GeV to 2.76 TeV are very similar, we find that viscous hydrodynamics might be consistent with the level of agreement for v₂ of unidentified hadrons as a function of p_T. However, we predict a strong collision energy dependence for the proton v₂(p_T). The results presented in this paper highlight the need for more systematic studies and for a re-evaluation of previously reported sensitivities to the early time dynamics and properties of the medium.

We address the issue of segregation in bidisperse suspensions of glass beads, by using a liquid fluidized bed in the inertialess regime and an acoustic technique for acquiring the axial composition along the column. Fluidization balances the buoyancy of the particles by a constant uniform upward flow, and therefore enables long-time experiments. From the analysis of the transient segregation fronts, we have collected precise measurements on the sedimentation velocities of small and large beads, U_s and U_l, in homogeneous suspensions at the same volume fraction, , for both the bead species, and for different size ratios, 1.13⩽λ⩽1.64, and solid concentrations, . Our measurements provide evidence for a difference in the sedimentation velocities, U_s and U_l, over all the ranges of λ and covered. These results make one expect that a long-term fluidization should then result in a stationary segregated state, which was indeed always obtained for large enough particle size ratios, λ⩾1.43. However, at high concentration and for particles of close sizes, λ⩽1.41, we observed a surprising pseudo-periodic intermittency of slow segregation and quick mixing phases. The intermittency time is much longer than the batch sedimentation time and becomes noisy at very high concentration, for which metastable states have been observed. The origin of the mixing destabilization remains an open issue, but we note however that the domain of occurrence, λ⩽1.41, also corresponds, in our experiments, to a continuous size distribution of the particles.

The Abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-Abelian states emanating from the ν=5/2 Moore–Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the Abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions, which allows us to formulate an extension of the bulk–edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results.

We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.

We present a detailed analysis of a gigahertz clock rate environmentally robust phase-encoded quantum key distribution (QKD) system utilizing several different single-photon detectors, including the first implementation of an experimental resonant cavity thin-junction silicon single-photon avalanche diode. The system operates at a wavelength of 850 nm using standard telecommunications optical fibre. A general-purpose theoretical model for the performance of QKD systems is presented with reference to these experimental results before predictions are made about realistic detector developments in this system. We discuss, with reference to the theoretical model, how detector operating parameters can be further optimized to maximize key exchange rates.

We study the collective states of interacting non-Abelian anyons that emerge in Kitaev's honeycomb lattice model. Vortex–vortex interactions are shown to lead to the lifting of topological degeneracy and the energy is found to exhibit oscillations that are consistent with Majorana fermions being localized at vortex cores. We show how to construct states corresponding to the fusion channel degrees of freedom and obtain the energy gaps characterizing the stability of the topological low-energy spectrum. To study the collective behavior of many vortices, we introduce an effective lattice model of Majorana fermions. We find the necessary conditions for the model to approximate the spectrum of the honeycomb lattice model, and show that bi-partite interactions are responsible for the lifting of degeneracy also in many-vortex systems.

We argue that there exist simple effective field theories describing the long-distance dynamics of holographic liquids. The degrees of freedom responsible for the transport of charge and energy–momentum are Goldstone modes. These modes are coupled to a strongly coupled infrared (IR) sector through emergent gauge and gravitational fields. The IR degrees of freedom are described holographically by the near-horizon part of the metric, whereas the Goldstone bosons are described by a field-theoretical Lagrangian. In the cases where the holographic dual involves a black hole, this picture allows for a direct connection between the holographic prescription where currents live on the boundary and the membrane paradigm where currents live on the horizon. The zero-temperature sound mode in the D3–D7 system is also re-analyzed and re-interpreted within this formalism.

In this paper, we examine in a unified-fashion dissipative transport in strongly correlated systems. We thereby demonstrate the connection between 'bad metals' (such as high-temperature superconductors) and 'perfect fluids' (such as ultracold Fermi gases, near unitarity). One aim of this paper is to communicate to the high-energy physics community some of the central unsolved problems in high-T_c superconductors. Because of the interest in the nearly perfect fluidity of cold gases and because of new tools such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, the communication may lead to significant progress in a variety of different fields. A second aim is to draw attention to the great power of transport measurements, which reflect the excitation spectrum more directly than, say, thermodynamics, and therefore strongly constrain microscopic theories of correlated fermionic superfluids. Our calculations show that bad metal and perfect fluid behavior is associated with the presence of a normal state excitation gap that suppresses the effective number of carriers leading to anomalously low conductivity and viscosity above the transition temperature T_c. Below T_c, we demonstrate that the condensate collective modes ('phonons') do not couple to transverse probes, such as shear viscosity or conductivity. As a result, our calculated shear viscosity at low T becomes arbitrarily small, as observed in experiments. In both homogeneous and trap calculations, we do not find the upturn in η or η/s (where s is the entropy density) that is found in most theories. In the process of these studies, we demonstrate compatibility with the transverse sum rule and find reasonable agreement with viscosity experiments.

We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.

We discuss the recently developed bosonic dynamical mean-field theory (B-DMFT) framework, which maps a bosonic lattice model onto the self-consistent solution of a bosonic impurity model with coupling to a reservoir of normal and condensed bosons. The effective impurity action is derived in several ways: (i) as an approximation to the kinetic energy functional of the lattice problem, (ii) using a cavity approach and (iii) using an effective medium approach based on adding a one-loop correction to the self-consistently defined condensate. To solve the impurity problem, we use a continuous-time Monte Carlo algorithm based on the sampling of a perturbation expansion in the hybridization functions and the condensate wave function. As applications of the formalism, we present finite-temperature B-DMFT phase diagrams for the bosonic Hubbard model on a three-dimensional (3D) cubic and a 2D square lattice, the condensate order parameter as a function of chemical potential, critical exponents for the condensate, the approach to the weakly interacting Bose gas regime for weak repulsions and the kinetic energy as a function of temperature.

We present a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state-dependent interactions between Rydberg ions to implement quantum information processing protocols and simulate the dynamics of strongly interacting spin systems. We highlight the promise of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss anticipated theoretical and experimental challenges on the way to its realization.

We study the non-equilibrium dynamics and equilibration in a dissipative quantum many-body system—a chain of ions with two points of the chain driven by a thermal bath under different temperatures. Instead of a simple linear temperature gradient (characterized by the local motional excitation) as one expects from a typical classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the rate of ion coupling to the bath, the location of driven ions and the dissipation rates of the other ions in the chain. By simulating the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale.

The Fermi two-atom problem illustrates an apparent causality violation in quantum field theory that has to do with the nature of the built-in correlations in the vacuum. It has been a constant subject of theoretical debate and discussion in the last few decades. Nevertheless, although the issues at hand could in principle be tested experimentally, the smallness of such apparent violations of causality in quantum electrodynamics have prevented the observation of the predicted effect. In this paper, we show that the problem can be simulated within the framework of discrete systems that can be manifested, for instance, by trapped atoms in optical lattices or trapped ions. Unlike the original continuum case, the causal structure is no longer sharp. Nevertheless, as we show, it is possible to distinguish between 'trivial' effects due to 'direct' causality violations and the effects associated with Fermi's problem, even in such discrete settings. The ability to control externally the strength of the atom–field interactions enables us also to study both the original Fermi problem with 'bare atoms' and correction in the scenario that involves 'dressed' atoms. Finally, we show that, in principle, the Fermi effect can be detected using trapped ions.

We study the ground-state phases of the S=1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice (SATL) and on the square lattice with up to next-next-nearest-neighbor coupling (the J₁J₂J₃ model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that the MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular, collinear magnetic order is promoted at the expense of non-collinear (spiral) order, and several spiral states that are stable at the classical level disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which the MSW theory breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the SATL, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains. This shows that the MSW theory is—despite its apparent simplicity—a versatile tool for finding candidate regions in the case of spin-liquid phases, which are among prime targets for relevant quantum simulations.

We present the design, fabrication and experimental implementation of surface ion traps with Y-shaped junctions. The traps are designed to minimize the pseudopotential variations in the junction region at the symmetric intersection of three linear segments. We experimentally demonstrate robust linear and junction shuttling with greater than 10⁶ round-trip shuttles without ion loss. By minimizing the direct line of sight between trapped ions and dielectric surfaces, negligible day-to-day and trap-to-trap variations are observed. In addition to high-fidelity single-ion shuttling, multiple-ion chains survive splitting, ion-position swapping and recombining routines. The development of two-dimensional trapping structures is an important milestone for ion-trap quantum computing and quantum simulations.

We present a complete recipe to extract the density–density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density–density correlations of atomic samples. We determine the static structure factor and report the results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.

The proposal by Jerkins et al (2010 New J. Phys.12 043022) to determine the neutrino mass from a complete kinematic reconstruction of the β-decay of trapped, cold tritium atoms is reanalyzed here. It is found that this innovative concept will hardly lead to competitive results because of the following shortcomings that have been identified: (i) a viable concept for a β-spectrometer with the required performance is missing; (ii) a factor of 10⁶ in the event rate is missing; and (iii) controlling spurious electromagnetic potentials to the level of 10⁻¹³ Tm and 10⁻⁹ V is hardly conceivable.

We discuss questions raised concerning the proposal of kinematically reconstructing the neutrino mass using an ultracold source of tritium atoms (Otten E W 2011 New J. Phys.13 078001). We provide further details about our two-dimensional fit and emphasize the importance of simultaneously utilizing information from both the neutrino mass squared peak and the β-spectrum. We also explain how the simulation evolved over various drafts of the paper, and we comment on future directions for additional simulation work, including more detailed simulations of spectrometers and electromagnetic field variations.