Wave-particle duality is an inherent peculiarity of the quantum world. The double-slit experiment has been frequently used for understanding different aspects of this fundamental concept. The occurrence of interference rests on the lack of which-way information and on the absence of decoherence mechanisms, which could scramble the wave fronts. Here, we report on the observation of two-center interference in the molecular-frame photoelectron momentum distribution upon ionization of the neon dimer by a strong laser field. Postselection of ions, which are measured in coincidence with electrons, allows choosing the symmetry of the residual ion, leading to observation of both, gerade and ungerade, types of interference.

Quantum theory dictates that upon weakening the two-body interaction in a three-body system, an infinite number of three-body bound states of a huge spatial extent emerge just before these three-body states become unbound. Three helium atoms have been predicted to form a molecular system that manifests this peculiarity under natural conditions without artificial tuning of the attraction between particles by an external field. Here we report experimental observation of this long predicted but experimentally elusive Efimov state of 4 He3 by means of Coulomb explosion imaging. We show spatial images of an Efimov state, confirming the predicted size and a typical structure where two atoms are close to each other while the third is far away. One Sentence Summary:We report experimental discovery of a gigantic molecule that consists of three helium atoms and is bound solely by a universal feature of quantum mechanics called "Efimov effect".Ever since the early days of celestial mechanics, the three-body problem posed a major challenge to physicists. In the early 20th century the failure of finding a stable solution for the classical helium atom (2 electrons and a nucleus) heralded the demise of Niels Bohr's program of semiclassical atomic physics (1). Quantum mechanics then added yet another surprising twist to the three-body problem when in 1970 Vitaly Efimov predicted the appearance of an infinite series of stable three-body states of enormous spatial extents (2). These Efimov states are predicted to exist for short-range interactions like the van der Waals force between atoms or the strong force between nucleons. When the potential becomes so shallow that the last two-body bound state is at the verge of becoming unbound or is unbound, then three particles stick together to form Efimov states. Intriguingly, this three-body behavior does not depend on the details of the underlying two-body interactions. This makes the Efimov effect a universal phenomenon, with important applications in particle, nuclear (3, 4), atomic (4), condensed matter (5) and biological physics (6).Figure 1 summarizes two facets of Efimov's prediction, namely the energy spectrum and the structure of an Efimov state. Figure 1A shows how the two-and three-body binding energies (the binding energy of an atomic cluster is defined as the energy needed to separate all constituents of the cluster to infinite distances) change as the depth of the two-body potential is increased. As 2 indicated by the arrow above Figure 1A, the depth of the two-body potential increases along the horizontal axis. As the depth increases, the s-wave scattering length a changes from negative values to infinitely large values to positive values. Negative a values correspond to the domain where shallow two-body bound states do not exist. For positive a, a shallow two-body bound state, the dimer (see the blue solid line), exists. Bound three-body states (called trimers) exist in the green-shaded area. The extremely weakly-bound three-body states close to threshold (see...

Helium shows fascinating quantum phenomena unseen in any other element. In its liquid phase, it is the only known superfluid. The smallest aggregates of helium, the dimer (He 2 ) and the trimer (He 3 ) are, in their predicted structure, unique natural quantum objects. While one might intuitively expect the structure of 4 He 3 to be an equilateral triangle, a manifold of predictions on its shape have yielded an ongoing dispute for more than 20 years. These predictions range from 4 He 3 being mainly linear to being mainly an equilateral triangle. Here we show experimental images of the wave functions of 4 He 3 and 3 He 4 He 2 obtained by Coulomb explosion imaging of mass-selected clusters. We propose that 4 He 3 is a structureless random cloud and that 3 He 4 He 2 exists as a quantum halo state.

During the last 15 years a novel decay mechanism of excited atoms has been discovered and investigated. This so called "Interatomic Coulombic Decay" (ICD) involves the chemical environment of the electronically excited atom: the excitation energy is transferred (in many cases over long distances) to a neighbor of the initially excited particle usually ionizing that neighbor. It turned out that ICD is a very common decay route in nature as it occurs across van-der-Waals and hydrogen bonds. The time evolution of ICD is predicted to be highly complex, as its efficiency strongly depends on the distance of the atoms involved and this distance typically changes during the decay. Here we present the first direct measurement of the temporal evolution of ICD using a novel experimental approach.In 1997 Cederbaum and coworkers realized that the presence of loosely bound atomic or molecular neighbors opens a new relaxation pathway to an electronically excited atom or molecule. In the decay mechanism they proposed -termed Intermolecular Coulombic Decay (ICD) -the excited particle relaxes efficiently by transferring its excitation energy to a neighboring atom or molecule [1]. As a consequence the atom or molecule receiving the energy emits an electron of low kinetic energy. The occurrence of ICD was proven in experiments in the mid 2000s by means of electron spectroscopy [2] and multi-coincidence techniques [3]. Since that time a wealth of experimental and theoretical studies have shown that ICD is a rather common decay path in nature, as it occurs almost everywhere in loosely bound matter. It has been proven to occur after a manifold of initial excitation schemes such as innervalence shell ionization, after Auger cascades [4,5], resonant excitation [6,7], shakeup ionization [8] and resonant Auger decay. ICD has also been observed in many systems as rare gas clusters [9], even on surfaces [10] and small water droplets [11,12]. The latter suggested that ICD might play a role in radiation damage of living tissue [13], as it creates low energy electrons, which are known to be genotoxic [14,15]. More recently that scenario was reversed as it was suggested to employ ICD in treatment of tagged malignant cells [16]. Apart from these potential applications the elementary process of ICD is under investigation, as the decay is predicted to have a highly complex temporal * Electronic address: jahnke@atom.uni-frankfurt.de behavior. The efficiency and thus the decay times of ICD depend strongly on the size of the system, i.e. the number of neighboring particles and the distance between them and the excited particle. However, even for most simple possible model systems consisting of only two atoms the temporal evolution of the decay is non-trivial and predicted theoretically to exhibit exciting physics [17]: as ICD happens on a timescale that is fast compared to relaxation via photon emission, but comparable to the typical times of nuclear motion in the system, the dynamics of the decay is complicated and so far only theoretically explored...

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 ...