Quantum tunneling is a ubiquitous phenomenon in nature and crucial for many technological applications. It allows quantum particles to reach regions in space which are energetically not accessible according to classical mechanics. In this "tunneling region," the particle density is known to decay exponentially. This behavior is universal across all energy scales from nuclear physics to chemistry and solid state systems. Although typically only a small fraction of a particle wavefunction extends into the tunneling region, we present here an extreme quantum system: a gigantic molecule consisting of two helium atoms, with an 80% probability that its two nuclei will be found in this classical forbidden region. This circumstance allows us to directly image the exponentially decaying density of a tunneling particle, which we achieved for over two orders of magnitude. Imaging a tunneling particle shows one of the few features of our world that is truly universal: the probability to find one of the constituents of bound matter far away is never zero but decreases exponentially. The results were obtained by Coulomb explosion imaging using a free electron laser and furthermore yielded He 2 's binding energy of 151.9 ± 13.3 neV, which is in agreement with most recent calculations.clusters | helium dimer | wavefunction | tunneling A ttractive forces allow particles to condense into stable bound systems such as molecules or nuclei with a ground state and (in most cases) energetically excited bound states, as shown in Fig. 1. Classical particles situated in such a binding potential oscillate back and forth between two turning points. The regions beyond these points are inaccessible for a classical particle due to a lack of energy. Quantum particles, however, can penetrate into the potential barrier by a phenomenon known as "tunneling." Tunneling is omnipresent in nature and occurs on all energy scales from megaelectron volts in nuclear physics to electron volts in molecules and solids and to nanoelectron volts in optical lattices. For bound matter, the fraction of the probability density distribution in this classically forbidden region is usually small. For shallow short-range potentials, this situation can change dramatically: upon decreasing the potential depth, excited states are expelled one after the other as they become unbound (transition from A to B in Fig. 1). A further decrease of the potential depth effects the ground state as well, as more and more of its wavefunction expands into the tunneling region ( Fig. 1 C and D). Consequently, at the threshold (i.e., in the limit of vanishing binding energy), the size of the quantum system expands to infinity. For short-range potentials, this expansion is accompanied by the fact that the system becomes less "classical" and more quantumlike. Systems existing near that threshold (and therefore being dominated by the tunneling part of their wavefunction) are called "quantum halo states" (1). These states are known, for example, from nuclear physics where 11 Be and 11 Li form ...

The fast evaporative cooling of micrometer-sized water droplets in a vacuum offers the appealing possibility to investigate supercooled water-below the melting point but still a liquid-at temperatures far beyond the state of the art. However, it is challenging to obtain a reliable value of the droplet temperature under such extreme experimental conditions. Here, the observation of morphology-dependent resonances in the Raman scattering from a train of perfectly uniform water droplets allows us to measure the variation in droplet size resulting from evaporative mass losses with an absolute precision of better than 0.2%. This finding proves crucial to an unambiguous determination of the droplet temperature. In particular, we find that a fraction of water droplets with an initial diameter of 6379±12  nm remain liquid down to 230.6±0.6  K. Our results question temperature estimates reported recently for larger supercooled water droplets and provide valuable information on the hydrogen-bond network in liquid water in the hard-to-access deeply supercooled regime.

Crystallization is a fundamental process in materials science, providing the primary route for the realization of a wide range of novel materials. Crystallization rates are considered also to be useful probes of glass-forming ability. [1][2][3]. At the microscopic level, crystallization is described by the classical crystal nucleation and growth theories [4, 5], yet in general solid formation is a far more complex process. Particularly the observation of apparently different crystal growth regimes in many binary liquid mixtures greatly challenges our understanding of crystallization [1, 6-12]. Here, we study by experiments, theory, and computer simulations the crystallization of supercooled mixtures of argon and krypton, showing that crystal growth rates in these systems can be reconciled with existing crystal growth models only by explicitly accounting for the non-ideality of the mixtures. Our results highlight the importance of thermodynamic aspects in describing the crystal growth kinetics, providing a major step towards a more sophisticated theory of crystal growth.The classical crystal nucleation and growth theories describe the microscopic steps by which a solid phase spontaneously forms in the supercooled liquid at some temperature T below melting.Homogeneous crystal nucleation is the process of the formation by thermal fluctuations of a small, localized nucleus of the newly ordered phase in the metastable liquid [4]. Once the nucleus has reached its critical size, it grows at a rate that within the kinetic theory of crystal growth is givenwhere f ≤ 1 is a geometrical factor representing the fraction of atomic collisions with the crystal surface that actually contribute to the growth, a(T ) is a characteristic interatomic spacing that can be identified with the lattice constant, ν(T ) is the crystal addition rate at the crystal/liquid interface, ∆S m is the molar entropy of fusion, R is the universal gas constant, and ∆G(T ) = G L (T ) − G C (T ) is the difference in liquid (L) and crystal (C) molar Gibbs free energies. In the Wilson-Frenkel (WF) theory [13], the crystal addition rate is proportional to the atomic diffusivity D(T ), ν WF (T ) = 6D(T )/Λ 2 (T ), and hence exhibits the strong temperature dependence associated with an activated process. Here, Λ(T ) = ca(T ) is an average atomic displacement that we assume to be proportional to a(T ), with c being a dimensionless parameter. In the collision-limited (CL) scenario [14], the crystal addition rate is proportional to the average thermal velocity of the particles, ν CL (T ) = 3k B T /m/Λ(T ), where k B is Boltzmann's constant and m is the particle's mass, and represents the extreme case in which there is no activation barrier for ordering.At the microscopic level, the WF and CL models can be characterized by limiting time scales

We present a cryogenic source of periodic streams of micrometer-sized hydrogen and argon droplets as ideal mass-limited target systems for fundamental intense laser-driven plasma applications. The highly compact design combined with a high temporal and spatial droplet stability makes our injector ideally suited for experiments using state-of-the-art high-power lasers in which a precise synchronization between the laser pulses and the droplets is mandatory. We show this by irradiating argon droplets with multi-Terawatt pulses.

This corrects the article DOI: 10.1103/PhysRevLett.120.015501.