We propose and analyse a simple method to measure simultaneously the real and imaginary parts of the effective refractive index of a turbid suspension of particles. The method is based on measurements of the angle of refraction and transmittance of a laser beam that traverses a hollow glass prism filled with a colloidal suspension. We provide a comprehensive assessment of the method. It can offer high sensitivity while still being simple to interpret. We present results of experiments using an optically turbid suspension of polystyrene particles and compare them with theoretical predictions. We also report experimental evidence showing that the refractive behaviour of the diffuse component of light coming from a suspension depends on the volume fraction of the colloidal particles.

Quantum mechanics is an incredibly successful theory and yet the statistical nature of its predictions is hard to accept and has been the subject of numerous debates. The notion of inherent randomness, something that happens without any cause, goes against our rational understanding of reality. To add to the puzzle, randomness that appears in non-relativistic quantum theory tacitly respects relativity, for example, it makes instantaneous signaling impossible. Here, we argue that this is because the special theory of relativity can itself account for such a random behavior. We show that the full mathematical structure of the Lorentz transformation, the one which includes the superluminal part, implies the emergence of non-deterministic dynamics, together with complex probability amplitudes and multiple trajectories. This indicates that the connections between the two seemingly different theories are deeper and more subtle than previously thought.

The physical origins of negative refractive index are derived from a dilute microscopic model, producing a result that is generalized to the dense condensed phase limit. In particular, scattering from a thin sheet of electric and magnetic dipoles driven above resonance is used to form a fundamental description for negative refraction. Of practical significance, loss and dispersion are implicit in the microscopic model. While naturally occurring negative index materials are unavailable, ferromagnetic and ferroelectric materials provide device design opportunities.

An erratum page was added to the end of the published paper on 11 November 2005.

Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.

We have shown experimentally, in a real-world setting, that it is possible to use two beams of incoherent radio waves, transmitted on the same frequency but encoded in two different orbital angular momentum states, to simultaneously transmit two independent radio channels. This novel radio technique allows the implementation of, in principle, an infinite number of channels in a given, fixed bandwidth, even without using polarization, multiport or dense coding techniques. This paves the way for innovative techniques in radio science and entirely new paradigms in radio communication protocols that might offer a solution to the problem of radio-band congestion.

Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘the quantum variational eigensolver’ was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

The conical shape of a shuttlecock allows it to flip on impact. As a light and extended particle, it flies with a pure drag trajectory. We first study the flip phenomenon and the dynamics of the flight and then discuss the implications on the game. Lastly, a possible classification of different shots is proposed.

Within the last two decades, quantum technologies (QT) have made tremendous progress, moving from Nobel Prize award-winning experiments on quantum physics (1997: Chu, Cohen-Tanoudji, Phillips; 2001: Cornell, Ketterle, Wieman; 2005: Hall, Hänsch-, Glauber; 2012: Haroche, Wineland) into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the ‘strange’ quantum properties, such as superposition and entanglement. The field comprises four domains: quantum communication, where individual or entangled photons are used to transmit data in a provably secure way; quantum simulation, where well-controlled quantum systems are used to reproduce the behaviour of other, less accessible quantum systems; quantum computation, which employs quantum effects to dramatically speed up certain calculations, such as number factoring; and quantum sensing and metrology, where the high sensitivity of coherent quantum systems to external perturbations is exploited to enhance the performance of measurements of physical quantities. In Europe, the QT community has profited from several EC funded coordination projects, which, among other things, have coordinated the creation of a 150-page QT Roadmap ( http://qurope.eu/h2020/qtflagship/roadmap2016). This article presents an updated summary of this roadmap.

We explore the influence of contact interactions on a synthetically spin–orbit coupled system of two ultracold trapped atoms. Even though the system we consider is bosonic, we show that a regime exists in which the competition between the contact and spin–orbit interactions results in the emergence of a ground state that contains a significant contribution from the anti-symmetric spin state. This ground state is unique to few-particle systems and does not exist in the mean-field regime. The transition to this state is signalled by an inversion in the average momentum from being dominated by centre-of-mass momentum to relative momentum and also affects the global entanglement shared between the real- and pseudo-spin spaces. Indeed, competition between the interactions can also result in avoided crossings in the ground state which further enhances these correlations. However, we find that correlations shared between the pseudo-spin states are strongly depressed due to the spin–orbit coupling and therefore the system does not contain spin–spin entanglement.

We discuss the trajectory of a fast revolving solid ball moving in a fluid of comparable density. As the ball slows down owing to drag, its trajectory follows an exponential spiral as long as the rotation speed remains constant: at the characteristic distance where the ball speed is significantly affected by the drag, the bending of the trajectory increases, surprisingly. Later, the rotation speed decreases, which makes the ball follow a second kind of spiral, also described in the paper. Finally, the use of these highly curved trajectories is shown to be relevant to sports.

Within the last two decades, quantum technologies (QT) have made tremendous progress, moving from Nobel Prize award-winning experiments on quantum physics (1997: Chu, Cohen-Tanoudji, Phillips; 2001: Cornell, Ketterle, Wieman; 2005: Hall, Hänsch-, Glauber; 2012: Haroche, Wineland) into a cross-disciplinary field of applied research. Technologies are being developed now that explicitly address individual quantum states and make use of the ‘strange’ quantum properties, such as superposition and entanglement. The field comprises four domains: quantum communication, where individual or entangled photons are used to transmit data in a provably secure way; quantum simulation, where well-controlled quantum systems are used to reproduce the behaviour of other, less accessible quantum systems; quantum computation, which employs quantum effects to dramatically speed up certain calculations, such as number factoring; and quantum sensing and metrology, where the high sensitivity of coherent quantum systems to external perturbations is exploited to enhance the performance of measurements of physical quantities. In Europe, the QT community has profited from several EC funded coordination projects, which, among other things, have coordinated the creation of a 150-page QT Roadmap ( http://qurope.eu/h2020/qtflagship/roadmap2016). This article presents an updated summary of this roadmap.

We study the optomechanical behaviour of a driven Fabry–Pérot cavity containing two vibrating dielectric membranes. We characterize the cavity mode frequency shift as a function of the two-membrane positions, and report a ∼2.47 gain in the optomechanical coupling strength of the membrane relative motion with respect to the single membrane case. This is achieved when the two membranes are properly positioned to form an inner cavity which is resonant with the driving field. We also show that this two-membrane system has the capability to tune the single-photon optomechanical coupling on demand, and represents a promising platform for implementing cavity optomechanics with distinct oscillators. Such a configuration has the potential to enable cavity optomechanics in the strong single-photon coupling regime, and to study synchronization in optically linked mechanical resonators.

The studies of multiplex networks are increasingly popular in recent years. Modeling multiple complex systems as a multiplex network has refreshed our understanding about the structure and dynamics of various real-world systems. As an important variant of the voter models, belief formation dynamics such as the asynchronous belief percolation (ABP) model has attracted much attention from statistical physics and network science communities. Existing studies of the ABP model mainly focus on the applications to single networks, whereas how the structure of multiplex networks affects its dynamical behavior is still not well understood. To close this gap, we propose a multi-scale ABP model that takes into account the differential velocities of belief propagation at different subnetworks within the multiplex network. Using extensive computer simulations, we find that (i) increasing the degree correlation between subnetworks can promote nodes with minority belief to form stable clusters and (ii) minority nodes require less initial supports to survive in multiplex networks with respect to single networks. Our conclusion is robust against the detailed topology of the subnetworks that constitute the multiplex network.

Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal assumptions on the devices being tested. In this work, we address the question of which states can be self-tested. This has been answered recently in the bipartite case (Coladangelo et al 2017 Nat. Commun. 8 15485), while it is largely unexplored in the multipartite case, with only a few scattered results, using a variety of different methods: maximal violation of a Bell inequality, numerical SWAP method, stabiliser self-testing etc. In this work, we investigate a simple, and potentially unifying, approach: combining projections onto two-qubit spaces (projecting parties or degrees of freedom) and then using maximal violation of the tilted CHSH inequalities. This allows one to obtain self-testing of Dicke states and partially entangled GHZ states with two measurements per party, and also to recover self-testing of graph states (previously known only through stabiliser methods). Finally, we give the first self-test of a class of multipartite qudit states: we generalise the self-testing of partially entangled GHZ states by adapting techniques from (Coladangelo et al 2017 Nat. Commun. 8 15485), and show that all multipartite states which admit a Schmidt decomposition can be self-tested with few measurements.

Interdependent networks (IN) are collections of non-trivially interrelated graphs that are not physically connected, and provide a more realistic representation of real-world networked systems as compared to traditional isolated networks. In particular, they are an efficient tool to study the evolution of cooperative behavior from the viewpoint of statistical physics. Here, we consider a prisoner dilemma game taking place in IN, and introduce a simple rule for the calculation of fitness that incorporates individual popularity, which in its turn is represented by one parameter α. We show that interdependence between agents in different networks influences the cooperative behavior trait. Namely, intermediate α values guarantee an optimal environment for the evolution of cooperation, while too high or excessively low α values impede cooperation. These results originate from an enhanced synchronization of strategies in different networks, which is beneficial for the formation of giant cooperative clusters wherein cooperators are protected from exploitation by defectors.

The van der Waals dispersion interaction between two chiral molecules in the presence of arbitrary magnetoelectric media is derived using perturbation theory. To be general, the molecular polarisabilities are assumed to be of electric, paramagnetic and diamagnetic natures, and the material environment is considered to possess a chiral electromagnetic response. The derived expressions of electric dipole polarisable–chiral, magnetic dipole susceptible–chiral, and diamagnetic susceptible–chiral, and chiral–chiral interaction potentials when added to the previously obtained contributions in the literature, form a complete set of dispersion interaction formulas. We present them in a unified form making use of electric–magnetic duality. As an application, the case of two anisotropic molecules embedded in a bulk magnetoelectric medium is considered, where we derive the retarded and non-retarded limits with respect to intermolecular distance.

Ultra-intense lasers produce and manipulate plasmas, allowing to locally generate extremely high static and electromagnetic fields. This study presents a concept of an ultra-intense optical tweezer, where two counter-propagating circularly polarized intense lasers of different frequencies collide on a nano-foil. Interfering inside the foil, lasers produce a beat wave, which traps and moves plasma electrons as a thin sheet with an optically controlled velocity. The electron displacement creates a plasma micro-capacitor with an extremely strong electrostatic field, that efficiently generates narrow-energy-spread ion beams from the multi-species targets, e.g. protons from the hydrocarbon foils. The proposed ion accelerator concept is explored theoretically and demonstrated numerically with the multi-dimensional particle-in-cell simulations.

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic spinor representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.

A comprehensive analysis of the exact unitary dynamics of two-component mass-imbalanced fermions in a one-dimensional double-well potential is accomplished by considering the total number of particles maximum up to six. The simultaneous effect of mass imbalance between the flavors and their mutual interactions on the dynamics is scrutinized through the exact diagonalization. In particular, we investigate the occupation dynamics of such systems being initially prepared in experimentally accessible states in which opposite components occupy opposite wells. Moreover, to capture the role of interactions, we also inspect situations in which initial states contain an opposite-spin pair localized in a chosen well. Finally, to assess the amount of quantum correlations produced during the evolution, we analyze the behavior of the von Neumann entanglement entropy between components.

We study statistical properties of the process Y( t) of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion X( t) with the Hurst index H ∈ (0,1). We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time t limit in proportion to , which defines a family of anomalous super-diffusions. We evaluate the disorder-averaged Wigner–Ville spectrum of the advection process Y( t) and demonstrate that it has a rather unusual power-law form with a characteristic exponent which exceed the value 2. Our results also suggest that sample-to-sample fluctuations of the spectrum can be very important.

Topological edge states have crucial applications in nano spintronics and valleytronics devices, while topological inner-edge states have seldom been extensively researched in this field. Based on the inner-edge states of the hybridized zigzag silicene-like nanoribbons, we investigate their transport properties. We propose two types of spin–valley filters. The first type can generate two different spin–valley polarized currents in output leads, respectively. The second type outputs the specific spin–valley polarized current in only one of the output leads. All these inner-edge states have the spin–valley-momentum locking property. These types of filters can switch the output spin–valley polarizations by modulating the external fields. Besides, we also find that the device size plays a crucial role in designing these spin–valley filters. Moreover, the local current distributions are calculated to visualize the detailed transport process and understand the mechanism. The mechanism lies that the spin–valley polarized current can nearly freely pass through the system with the same momentum, spin and valley degrees of freedom. The small reflection of the current results from the inter-valley scattering. In particular, we also consider the realistic (disorder) effects on the performance of these filters to ensure the robustness of our systems. We believe these spin–valley current filtering effects have potential applications in the future spintronics and valleytronics device designs.

Microswimmers are encountered in a wide variety of biophysical settings. When interacting with flow fields, they show interesting dynamical features such as hydrodynamic trapping, clustering, and preferential orientation. One important step towards the understanding of such features is to clarify the interplay of hydrodynamic flows with microswimmer motility and shape. Here, we study the dynamics of ellipsoidal microswimmers in a two-dimensional axisymmetric vortex flow. Despite this simple setting, we find surprisingly rich dynamics, which can be comprehensively characterized in the framework of dynamical systems theory. By classifying the fixed-point structure of the underlying phase space as a function of motility and microswimmer shape, we uncover the topology of the phase space and determine the conditions under which microswimmers are trapped in the vortex. For spherical microswimmers, we identify Hamiltonian dynamics, which are broken for microswimmers of a different shape. We find that prolate ellipsoidal microswimmers tend to align parallel to the velocity field, while oblate microswimmers tend to remain perpendicular to it. Additionally, we find that rotational noise allows microswimmers to escape the vortex with an enhanced escape rate close to the system’s saddle point. Our results clarify the role of shape and motility on the occurrence of preferential concentration and clustering and provide a starting point to understand the dynamics in more complex flows.

We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called thermodynamic uncertainty relations (TURs). We not only strengthen the bounds but extend their realm of applicability and in many cases prove their optimality, without resorting to large deviation theory or information-theoretic techniques. In particular, we find the best TUR based on entropy production alone. We also derive a periodic uncertainty principle of which previous known bounds for periodic or stationary Markov chains known in the literature appear as limit cases. From it a novel bound for stationary Markov processes is derived, which surpasses previous known bounds. Our results exploit the non-invariance of the system under a symmetry which can be other than time reversal and thus open a wide new spectrum of applications.

The effective Hamiltonian method has recently received considerable attention due to its power to deal with finite-temperature problems and large-scale systems. In this work, we put forward a machine learning (ML) approach to generate realistic effective Hamiltonians. In order to find out the important interactions among many possible terms, we propose some new techniques. In particular, we suggest a new criterion to select models with less parameters using a penalty factor instead of the commonly-adopted additional penalty term, and we improve the efficiency of variable selection algorithms by estimating the importance of each possible parameter by its relative uncertainty and the error induced in the parameter reduction. We also employ a testing set and optionally a validation set to help prevent over-fitting problems. To verify the reliability and usefulness of our approach, we take two-dimensional MnO and three-dimensional TbMnO ₃ as examples. In the case of TbMnO ₃, our approach not only reproduces the known results that the Heisenberg, biquadratic, and ring exchange interactions are the major spin interactions, but also finds out that the next most important spin interactions are three-body fourth-order interactions. In both cases, we obtain effective spin Hamiltonians with high fitting accuracy. These tests suggest that our ML approach is powerful for identifying the effective spin Hamiltonians. Our ML approach is general so that it can be adopted to construct other effective Hamiltonians.

Quantum channels that break CHSH nonlocality on all input states are known as CHSH-breaking channels. In quantum networks, such channels are useless for distributing correlations that can violate the CHSH Inequality. Motivated by previous work on activation of nonlocality in quantum states, here we demonstrate an analogous activation of CHSH-breaking channels. That is, we show that certain pairs of CHSH-breaking channels are no longer CHSH-breaking when used in combination. We find that this type of activation can emerge in both uni-directional and bi-directional communication scenarios.