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Revealing the nature of mesoscopic molecular ions

Analyzing ions at zero temperature may provide deep insights into charge transport and may also allow for controlled state-to-state chemical reactions. A group of scientists around Prof. Peter Schmelcher (Universität Hamburg) has succeeded in calculating the potential size of mesoscopic molecular ion clusters at zero temperature. The scientists report the detailed simulations of the quantum state in the journal Physical Review Letters. They identified two regimes and in between the dissociation threshold at which the molecule reaches its maximal number of constituents.

At ultracold temperatures, a single ion is able to capture a neutral atom into a very loosely bound state with binding radii on the order of a micrometer. Hence, already the dimer crosses the border between the microscopic and the macroscopic world. In case of indistinguishable atoms which possess bosonic symmetry, multiple atoms can even be bound into the very same state. In this way, massive molecular charged clusters can form which may consist of up to hundreds of atoms and a single ion.

Fifteen years after the first theoretical predictions

Moreover, the atoms might arrange in a shell-like structure around the molecule being reminiscent of electrons around the atomic core. “Even fifteen years after their first theoretical prediction it is still under debate, how large these molecules can become and how stable they are. In addition, the experimental confirmation of their existence is so far missing. Due to our study, we could now answer some of the open questions,” says Johannes M. Schurer, who is the main author of the study.

The scientists computed for example the experimentally relevant spatial atomic densities and revealed the structure of the many-body bound state depending on the atom number and the inter-atomic interaction. The detailed simulations of the quantum many-body state of the molecules based on a microscopic theory became possible by the Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) which represents an ab-initio method to derive the many-body wave function including all correlations.

Two regimes and dissociation threshold identified

In their study, the scientists uncovered the zero-temperature phase-diagram of N atoms and a single ion in one spatial dimension. Thereby they found two regimes: one where all atoms are bound to the ion and another one where unbound atoms exist and form a bath-type background gas for the molecule.

Between these two regimes, the scientists were able to identify the dissociation threshold at which the molecule reaches its maximal number of constituents. Moreover, they found a pronounced interaction-induced self-localization of the ion for an increasing number of bound atoms which they explained by the generation of a huge effective mass for the ion.

Schurer: “In the near future, hybrid atom-ion technologies will enable analyzing such rather exotic states of matter possibly validating our predictions about the size and the self-localization behavior of mesoscopic molecular ions.”

Schematic view on a mesoscopic molecular ion formed by a single ion (red) and multiple atoms (blue) and its behavior for increasing atom number N. As long as the atom number is small enough, typically less than hundred (left), all atoms remain bound to the ion. When the critical atom number Nc is reached (center) no more atoms can be bound and the dissociation occurs. Increasing the atom number further (right) results in a free (unbound) fraction which forms a background gas for the molecular ion. Illustration: J. M. Schurer


J. M. Schurer, A. Negretti, and P. Schmelcher
„Unraveling the Structure of Ultracold Mesoscopic Collinear Molecular Ions“
Physical Review Letters 119, 063001 (2017)
DOI: 10.1103/PhysRevLett.119.063001