Showing papers in "Nature Physics in 2007"

Optical magnetometry - eScholarship

Abstract: Some of the most sensitive methods of measuring magnetic fields use interactions of resonant light with atomic vapour. Recent developments in this vibrant field have led to improvements in sensitivity and other characteristics of atomic magnetometers, benefiting their traditional applications for measurements of geomagnetic anomalies and magnetic fields in space, and opening many new areas previously accessible only to magnetometers based on superconducting quantum interference devices. We review basic principles of modern optical magnetometers, discuss fundamental limitations on their performance, and describe recently explored applications for dynamical measurements of biomagnetic fields, detecting signals in NMR and MRI, inertial rotation sensing, magnetic microscopy with cold atoms, and tests of fundamental symmetries of nature.

Challenges for semiconductor spintronics

Abstract: High-volume information-processing and communications devices are at present based on semiconductor devices, whereas information-storage devices rely on multilayers of magnetic metals and insulators. Switching within information-processing devices is performed by the controlled motion of small pools of charge, whereas in the magnetic storage devices information storage and retrieval is performed by reorienting magnetic domains (although charge motion is often used for the final stage of readout). Semiconductor spintronics offers a possible direction towards the development of hybrid devices that could perform all three of these operations, logic, communications and storage, within the same materials technology. By taking advantage of spin coherence it also may sidestep some limitations on information manipulation previously thought to be fundamental. This article focuses on advances towards these goals in the past decade, during which experimental progress has been extraordinary.

Valley filter and valley valve in graphene

Abstract: The potential of graphene for carbon electronics rests on the possibilities offered by its unusual band structure to create devices that have no analogue in silicon-based electronics1,2. Conduction and valence bands in graphene form conically shaped valleys, touching at a point called the Dirac point. There are two inequivalent Dirac points in the Brillouin zone, related by time-reversal symmetry. Intervalley scattering is suppressed in pure samples3,4,5. The independence and degeneracy of the valley degree of freedom suggests that it might be used to control an electronic device6, in much the same way as the electron spin is used in spintronics7 or quantum computing8. A key ingredient for ‘valleytronics’ would be a controllable way of occupying a single valley in graphene, thereby producing a valley polarization. Here we propose such a valley filter, based on a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled valley valve, representing a zero-magnetic-field counterpart to the familiar spin valve.

A single-photon transistor using nanoscale surface plasmons

Abstract: Photons rarely interact—which makes it challenging to build all-optical devices in which one light signal controls another. Even in nonlinear optical media, in which two beams can interact because of their influence on the medium’s refractive index, this interaction is weak at low light levels. Here, we propose a novel approach to realizing strong nonlinear interactions at the single-photon level, by exploiting the strong coupling between individual optical emitters and propagating surface plasmons confined to a conducting nanowire. We show that this system can act as a nonlinear two-photon switch for incident photons propagating along the nanowire, which can be coherently controlled using conventional quantum-optical techniques. Furthermore, we discuss how the interaction can be tailored to create a single-photon transistor, where the presence (or absence) of a single incident photon in a ‘gate’ field is sufficient to allow (or prevent) the propagation of subsequent ‘signal’ photons along the wire.

Entanglement-based quantum communication over 144km

Abstract: Quantum entanglement is the main resource to endow the field of quantum information processing with powers that exceed those of classical communication and computation. In view of applications such as quantum cryptography or quantum teleportation, extension of quantum-entanglement-based protocols to global distances is of considerable practical interest. Here we experimentally demonstrate entanglement-based quantum key distribution over 144 km. One photon is measured locally at the Canary Island of La Palma, whereas the other is sent over an optical free-space link to Tenerife, where the Optical Ground Station of the European Space Agency acts as the receiver. This exceeds previous free-space experiments by more than an order of magnitude in distance, and is an essential step towards future satellite-based quantum communication and experimental tests on quantum physics in space.

Quasiparticle dynamics in graphene

Abstract: The effectively massless, relativistic behaviour of graphene’s charge carriers—known as Dirac fermions—is a result of its unique electronic structure, characterized by conical valence and conduction bands that meet at a single point in momentum space (at the Dirac crossing energy). The study of many-body interactions amongst the charge carriers in graphene and related systems such as carbon nanotubes, fullerenes and graphite is of interest owing to their contribution to superconductivity and other exotic ground states in these systems. Here we show, using angle-resolved photoemission spectroscopy, that electron–plasmon coupling plays an unusually strong role in renormalizing the bands around the Dirac crossing energy—analogous to mass renormalization by electron–boson coupling in ordinary metals. Our results show that electron–electron, electron–plasmon and electron–phonon coupling must be considered on an equal footing in attempts to understand the dynamics of quasiparticles in graphene and related systems.

Spin qubits in graphene quantum dots

Abstract: The main characteristics of good qubits are long coherence times in combination with fast operating times. It is well known that carbon-based materials could increase the coherence times of spin qubits, which are among the most developed solid-state qubits. Here, we propose how to form spin qubits in graphene quantum dots. A crucial requirement to achieve this goal is to find quantum-dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with armchair boundaries. The most remarkable new feature of the proposed spin qubits is that, in an array of many qubits, it is possible to couple any two of them via Heisenberg exchange with the others being decoupled by detuning. This unique feature is a direct consequence of the quasi-relativistic spectrum of graphene.

Mapping surface plasmons on a single metallic nanoparticle

Abstract: Understanding how light interacts with matter at the nanometre scale is a fundamental issue in optoelectronics and nanophotonics. In particular, many applications (such as bio-sensing, cancer therapy and all-optical signal processing) rely on surface-bound optical excitations in metallic nanoparticles. However, so far no experimental technique has been capable of imaging localized optical excitations with sufficient resolution to reveal their dramatic spatial variation over one single nanoparticle. Here, we present a novel method applied on silver nanotriangles, achieving such resolution by recording maps of plasmons in the near-infrared/visible/ultraviolet domain using electron beams instead of photons. This method relies on the detection of plasmons as resonance peaks in the energy-loss spectra of subnanometre electron beams rastered on nanoparticles of well-defined geometrical parameters. This represents a significant improvement in the spatial resolution with which plasmonic modes can be imaged, and provides a powerful tool in the development of nanometre-level optics.

Reaction–diffusion processes and metapopulation models in heterogeneous networks

Abstract: Dynamical reaction–diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities—such as density, potentials and particles—diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction–diffusion process (given by the reaction steps B→A and B+A→2B) defined on networks with heterogeneous topology and no limit on the nodes’ occupation number. We investigate the effect of network topology on the basic properties of the system’s phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density-driven phase transitions, whereas phase transition and critical points independent of the particle density are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.

Electrical detection of spin transport in lateral ferromagnet–semiconductor devices

Abstract: The development of semiconductor spintronics requires a reliable electronic means for writing, processing and reading information using spin-polarized carriers. Here, we demonstrate a fully electrical scheme for achieving spin injection, transport and detection in a single device. Our device consists of a lateral semiconducting channel with two ferromagnetic contacts, one of which serves as a source of spin-polarized electrons and the other as a detector. Spin detection in the device is achieved through a non-local, spin-sensitive, Schottky-tunnel-barrier contact whose electrochemical potential depends on the relative magnetizations of the source and detector. We verify the effectiveness of this approach by showing that a transverse magnetic field suppresses the non-local signal at the detection contact by inducing spin precession and dephasing in the channel (the Hanle effect). The sign of the signal varies with the injection current and is correlated with the spin polarization in the channel as determined by optical Kerr rotation measurements.

Magnetic vortex oscillator driven by d.c. spin-polarized current

Abstract: Transfer of angular momentum from a spin-polarized current to a ferromagnet provides an efficient means to control the magnetization dynamics of nanomagnets. A peculiar consequence of this spin torque, the ability to induce persistent oscillations in a nanomagnet by applying a d.c. current, has previously been reported only for spatially uniform nanomagnets. Here, we demonstrate that a quintessentially non-uniform magnetic structure, a magnetic vortex, isolated within a nanoscale spin-valve structure, can be excited into persistent microwave-frequency oscillations by a spin-polarized d.c. current. Comparison with micromagnetic simulations leads to identification of the oscillations with a precession of the vortex core. The oscillations, which can be obtained in essentially zero magnetic field, exhibit linewidths that can be narrower than 300 kHz at ∼1.1 GHz, making these highly compact spin-torque vortex-oscillator devices potential candidates for microwave signal-processing applications, and a powerful new tool for fundamental studies of vortex dynamics in magnetic nanostructures.

Experimental entanglement of six photons in graph states

Abstract: Graph states1,2,3—multipartite entangled states that can be represented by mathematical graphs—are important resources for quantum computation4, quantum error correction3, studies of multiparticle entanglement1 and fundamental tests of non-locality5,6,7 and decoherence8. Here, we demonstrate the experimental entanglement of six photons and engineering of multiqubit graph states9,10,11. We have created two important examples of graph states, a six-photon Greenberger–Horne–Zeilinger state5, the largest photonic Schrodinger cat so far, and a six-photon cluster state2, a state-of-the-art ‘one-way quantum computer’4. With small modifications, our method allows us, in principle, to create various further graph states, and therefore could open the way to experimental tests of, for example, quantum algorithms4,12 or loss- and fault-tolerant one-way quantum computation13,14.

Dynamical synapses causing self-organized criticality in neural networks

Abstract: Self-organized criticality1 is one of the key concepts to describe the emergence of complexity in natural systems. The concept asserts that a system self-organizes into a critical state where system observables are distributed according to a power law. Prominent examples of self-organized critical dynamics include piling of granular media2, plate tectonics3 and stick–slip motion4. Critical behaviour has been shown to bring about optimal computational capabilities5, optimal transmission6, storage of information7 and sensitivity to sensory stimuli8,9,10. In neuronal systems, the existence of critical avalanches was predicted11 and later observed experimentally6,12,13. However, whereas in the experiments generic critical avalanches were found, in the model of ref. 11 they only show up if the set of parameters is fine-tuned externally to a critical transition state. Here, we demonstrate analytically and numerically that by assuming (biologically more realistic) dynamical synapses14 in a spiking neural network, the neuronal avalanches turn from an exceptional phenomenon into a typical and robust self-organized critical behaviour, if the total resources of neurotransmitter are sufficiently large.

Structure of phase III of solid hydrogen

Abstract: Hydrogen, being the first element in the periodic table, has the simplest electronic structure of any atom, and the hydrogen molecule contains the simplest covalent chemical bond. Nevertheless, the phase diagram of hydrogen is poorly understood. Determining the stable structures of solid hydrogen is a tremendous experimental challenge1,2,3, because hydrogen atoms scatter X-rays only weakly, leading to low-resolution diffraction patterns. Theoretical studies encounter major difficulties owing to the small energy differences between structures and the importance of the zero-point motion of the protons. We have systematically investigated the zero-temperature phase diagram of solid hydrogen using first-principles density functional theory (DFT) electronic-structure methods4, including the proton zero-point motion at the harmonic level. Our study leads to a radical revision of the DFT phase diagram of hydrogen up to nearly 400 GPa. That the most stable phases remain insulating to very high pressures eliminates a major discrepancy between theory5 and experiment6. One of our new phases is calculated to be stable over a wide range of pressures, and its vibrational properties agree with the available experimental data for phase III.

Efficient unidirectional nanoslit couplers for surface plasmons

Abstract: The emerging field of plasmonics is based on exploiting the coupling between light and collective electronic excitations within conducting materials known as surface plasmons. Because the so-called surface plasmon polariton (SPP) modes that arise from this coupling are not constrained by the optical diffraction limit, it is hoped that they could enable the construction of ultracompact optical components1,2. But in order that such potential can be realized, it is vital that the relatively poor light–SPP coupling be improved. This is made worse by the fact that the incident light that is conventionally used to launch SPPs in a metal film 3,4,5,6 is a significant source of noise, unless directed away from a region of interest, which then decreases the signal and increases the system’s size. Back-side illumination of subwavelength apertures in optically thick metal films7,8,9,10,11,12,13 eliminates this problem but does not ensure a unique propagation direction for the SPP. We propose a novel back-side slit-illumination method that incorporates a periodic array of grooves carved into the front side of a thick metal film. Bragg reflection enhances the propagation of SPPs away from the array, enabling them to be unidirectionally launched from, and focused to, a localized point.

Parallel and selective trapping in a patterned plasmonic landscape

Abstract: The implementation of optical tweezers1 at a surface opens a huge potential towards the elaboration of future lab-on-a-chip devices entirely operated with light2. The transition from conventional three-dimensional (3D) tweezers to 2D is made possible by exploiting evanescent fields bound at interfaces3,4,5. In particular, surface plasmons (SP) at metal/dielectric interfaces are expected to be excellent candidates to relax the requirements on incident power and to achieve subwavelength trapping volumes6,7. Here, we report on novel 2D SP-based optical tweezers formed by finite gold areas fabricated at a glass surface. We demonstrate that SP enable stable trapping of single dielectric beads under non-focused illumination with considerably reduced laser intensity compared with conventional optical tweezers. We show that the method can be extended to parallel trapping over any predefined pattern. Finally, we demonstrate how SP tweezers can be designed to selectively trap one type of particles out of a mixture, acting as an efficient optical sieve.

Plasma mirrors for ultrahigh-intensity optics

Abstract: Specular reflection is one of the most fundamental processes of optics. At moderate light intensities generated by conventional light sources this process is well understood. But at those capable of being produced by modern ultrahigh-intensity lasers, many new and potentially useful phenomena arise. When a pulse from such a laser hits an optically polished surface, it generates a dense plasma that itself acts as a mirror, known as a plasma mirror (PM). PMs do not just reflect the remainder of the incident beam, but can act as active optical elements. Using a set of three consecutive PMs in different regimes, we significantly improve the temporal contrast of femtosecond pulses, and demonstrate that high-order harmonics of the laser frequency can be generated through two distinct mechanisms. A better understanding of these processes should aid the development of laser-driven attosecond sources for use in fields from materials science to molecular biology.

Superradiance of quantum dots

Abstract: In 1954, Dicke pointed out that the description of a spontaneously radiating gas has to include the fact that all atoms or molecules interact with a common radiation field1. Consequently, the individual particles may not be considered as independent sources of radiation. In this regard, the question arises of whether quantum dot (QD) systems may also exhibit signatures of cooperative radiation and hence have to be considered as coupled quantum systems. Here, we present experimental evidence for a long-range electromagnetic interaction between laterally arranged QDs. The experimental results suggest that the QDs do not behave like independent objects as long as they form an ensemble of QDs. By removing QDs from the sample, we found that the coupling was reduced. The range of interaction is shown to be at least 150 nm. This may therefore provide a mechanism to couple discrete quantum objects on a large scale.

Classes of complex networks defined by role-to-role connectivity profiles

Abstract: In physical, biological, technological and social systems, interactions between units give rise to intricate networks. These-typically non-trivial-structures, in turn, critically affect the dynamics and properties of the system. The focus of most current research on complex networks is, still, on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes on the basis of their link type frequency. Importantly, we demonstrate that these structural features cannot be captured by means of often studied global properties.

In situ evidence of magnetic reconnection in turbulent plasma

Abstract: Magnetic reconnection is a universal process leading to energy conversion in plasmas1. It occurs in the Solar System2,3,4,5,6,7, in laboratory plasmas 8 and is important in astrophysics 9,10. Reconnection has been observed so far only at large-scale boundaries between different plasma environments 4,5,6,7,8. It is not known whether reconnection occurs and is important in turbulent plasmas where many small-scale boundaries can form. Solar11 and laboratory12 measurements as well as numerical simulations 13,14,15,16 indicate such possibility. Here we report, for the first time, in situ evidence of reconnection in a turbulent plasma. The turbulent environment is the solar wind downstream of the Earth’s bow shock. We show that reconnection is fast and electromagnetic energy is converted into heating and acceleration of particles. This has significant implications for laboratory and astrophysical plasmas where both turbulence and reconnection should be common.

Scaling of proton acceleration driven by petawatt-laser-plasma interactions

Abstract: The possibility of using high-power lasers to generate high-quality beams of energetic ions is attracting large global interest. The prospect of using laser-accelerated protons in medicine attracts particular interest, as these schemes may lead to compact and relatively low-cost sources. Among the challenges remaining before these sources can be used in medicine is to increase the numbers and energies of the ions accelerated. Here, we extend the energy and intensity range over which proton scaling is experimentally investigated, up to 400 J and 6×10^20 Wcm−2 respectively, and find a slower proton scaling than previously predicted. With the aid of plasma-expansion simulation tools, our results suggest the importance of time-dependent andmultidimensional effects in predicting the maximum proton energy in this ultrahigh-intensity regime. The implications of our new understanding of proton scaling for potential medical applications are discussed. (Less)

Electrical spin-injection into silicon from a ferromagnetic metal/tunnel barrier contact

Abstract: The electron’s spin angular momentum is one of several alternative state variables under consideration on the International Technology Roadmap for Semiconductors (ITRS) for processing information in the fundamentally new ways that will be required beyond the ultimate scaling limits of silicon-based complementary metal–oxide–semiconductor technology1. Electrical injection/transport of spin-polarized carriers is prerequisite for developing such an approach2,3. Although significant progress has been realized in GaAs (ref. 4), little progress has been made in Si, despite its overwhelming dominance of the semiconductor industry. Here, we report successful injection of spin-polarized electrons from an iron film through an Al2O3 tunnel barrier into Si(001). The circular polarization of the electroluminescence resulting from radiative recombination in Si and in GaAs (in Si/AlGaAs/GaAs structures) tracks the Fe magnetization, confirming that these spin-polarized electrons originate from the Fe contact. The polarization reflects Fe majority spin. We determine a lower bound for the Si electron spin polarization of 10%, and obtain an estimate of ∼30% at 5 K, with significant polarization extending to at least 125 K. We further demonstrate spin transport across the Si/AlGaAs interface.

Interferometric synthetic aperture microscopy

Abstract: State-of-the-art methods in high-resolution three-dimensional optical microscopy require that the focus be scanned through the entire region of interest. However, an analysis of the physics of the light–sample interaction reveals that the Fourier-space coverage is independent of depth. Here we show that, by solving the inverse scattering problem for interference microscopy, computed reconstruction yields volumes with a resolution in all planes that is equivalent to the resolution achieved only at the focal plane for conventional high-resolution microscopy. In short, the entire illuminated volume has spatially invariant resolution, thus eliminating the compromise between resolution and depth of field. We describe and demonstrate a novel computational image-formation technique called interferometric synthetic aperture microscopy (ISAM). ISAM has the potential to broadly impact real-time three-dimensional microscopy and analysis in the fields of cell and tumour biology, as well as in clinical diagnosis where in vivo imaging is preferable to biopsy.

Self-similarity in ultrafast nonlinear optics

Abstract: Recent developments in nonlinear optics have led to the discovery of a new class of ultrashort pulse, the `optical similariton'. Optical similaritons arise when the interaction of nonlinearity, dispersion and gain in a high-power fibre amplifier causes the shape of an arbitrary input pulse to converge asymptotically to a pulse whose shape is self-similar. In comparison with optical solitons, which rely on a delicate balance of nonlinearity and anomalous dispersion and which can become unstable with increasing intensity, similaritons are more robust at high pulse powers. The simplicity and widespread availability of the components needed to build a self-similar amplifier capable of producing optical similaritons provides a convenient experimental platform to explore the fundamental nature of dynamical self-similarity. Here, we provide an overview of self-similar pulse propagation and scaling in optical fibre amplifiers, and their use in the development of high-power ultrafast optical sources, pulse synthesis and all-optical pulse regeneration.

Gigahertz quantized charge pumping

Abstract: The high-speed, high-accuracy transport of single electrons in nanoscale devices is predicted to underpin future electronics. A key and topical application is the development of a fundamental standard of electrical current linking the ampere to the elementary charge and frequency. For a practical standard, currents at the nanoampere level are required, corresponding to gigahertz transport frequencies. Recent research has concentrated on transport using Coulomb blockade techniques. However, the tunnelling time of the electrons in such devices limits the operation to a few megahertz. We present a different pumping mechanism of single charges, whereby electrons ‘surf’ as particles on a time-dependent potential instead of tunnelling through the barriers as waves. This potential is created by two phase-shifted sinusoidal signals applied directly to metallic finger gates on an etched GaAs/AlGaAs quantum wire. Pumping accurate to better than 10−4, at a frequency up to 3.4 GHz, is reported with this approach.

Imaging single atoms in a three-dimensional array

Abstract: Asingle neutral atom trapped by light is a promising qubit. It has weak, well-understood interactions with the environment, its internal state can be precisely manipulated1, interactions that entangle atoms can be varied from negligible to strong2,3,4 and many single atoms can be trapped near each other in an optical lattice5. This collection of features would allow for a relatively large quantum computer6 if each neutral atom qubit could be independently detected and addressed7,8,9,10. A quantum computer with even 50 qubits would allow quantum simulations that are out of the reach of classical computers11,12. So far, fewer than ten single atoms have been simultaneously imaged13. Here we demonstrate trapping and imaging of 250 single atoms in a three-dimensional optical lattice and show that imaging is highly unlikely to change the pattern of site occupancy. Our lattice spacing is large enough that, in principle, individual atoms can be addressed, which in combination with reproducible imaging should allow for verifiable filling of vacancies, execution of site-specific quantum gates and measurement of each atom’s final quantum state14,15. The lattice we use can readily be scaled to include thousands of trapped atoms.

Breaking the delay-bandwidth limit in a photonic structure

Abstract: Storing light on-chip, which requires that the speed of light be significantly slowed down, is crucial for enabling photonic circuits on-chip. Ultraslow propagation1,2,3 and even stopping4,5 of light have been demonstrated using the electromagnetically induced transparency effect in atomic systems1,3,4,5 and the coherent population oscillation effect in solid-state systems2. The wavelengths and bandwidths of light in such devices are tightly constrained by the property of the material absorption lines, which limits their application in information technologies. Various slow-light devices based on photonic structures have also been demonstrated6,7,8,9,10; however, these devices suffer a fundamental trade-off between the transmission bandwidth and the optical delay. It has been shown theoretically11,12,13 that stopping light on-chip and thereby breaking the fundamental link between the delay and the bandwidth can be achieved by ultrafast tuning of photonic structures. Using this mechanism, here we report the first demonstration of storing light using photonic structures on-chip, with storage times longer than the bandwidth-determined photon lifetime of the static device. The release time of the pulse is externally controlled.

Observation of Landau levels of Dirac fermions in graphite

Abstract: The unique electronic behaviour of monolayer and bilayer graphene1,2 is a result of the unusual quantum-relativistic characteristics of the so-called ‘Dirac fermions’ (DFs) that carry charge in these materials. Although DFs in monolayer graphene move as if they were massless, and in bilayer graphene they do so with non-zero mass, all DFs show chirality, which gives rise to an unusual Landau level (LL) energy spectrum3,4,5,6,7,8,9,10,11 and the observation of an anomalous quantum Hall effect in both types of graphene4,5,8. Here we report low-temperature scanning tunnelling spectra of graphite subjected to a magnetic field of up to 12 T, which provide the first direct observations of the LLs that produce such behaviour. Unexpectedly, we find evidence for the coexistence of both massless and massive DFs in graphite, and confirm the quantum-relativistic nature of these quasiparticles through the appearance of a zero-energy LL.

Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material

Abstract: Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material

Making a splash with water repellency

Abstract: A splash is usually heard when a solid body enters water at large velocity. This phenomenon originates from the formation of an air cavity during the impact. The classical view of impacts on free surfaces relies solely on fluid inertia; therefore, surface properties and viscous effects should be negligible at sufficiently large velocities. In strong contrast to this large-scale hydrodynamic viewpoint, we demonstrate here that the wettability of the impacting body is a key factor in determining the degree of splashing. This unforeseen fact is further embodied in the dependence of the threshold velocity for air entrainment on the contact angle of the impacting body, as well as on the ratio between surface tension and fluid viscosity, thereby defining a critical capillary velocity. As a paradigm, superhydrophobic impactors make a big splash for any impact velocity.