Imaging the He 2 quantum halo state using a free electron laser

In bound matter on all length scales, from nuclei to molecules to macroscopic solid objects, most of the density of the bound particles is within the range of the interaction potential which holds the system together. Quantum halos on the contrary are a type of matter where the particle density is mostly outside the range of the interaction potential in the tunneling region of the potential. Few examples of these fascinating systems are known in nuclear and molecular physics. The conceptually simplest halo system is made of only two particles. Here we experimentally image the wavefunction of the He 2 quantum halo. It shows the predicted exponential shape of a tunneling wavefunction. 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.