J. H. Sandoval | Searcharxiv

arXiv2017

Squeezing the Efimov effect

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.

cond-mat.quant-gas↗

arXiv2016

Mean-square radii in mixed-species systems in two dimensions

We calculate root-mean-square radii for a three-body system confined to two spatial dimensions and consisting of two identical bosons ($A$) and one distinguishable particle ($B$). We use zero-range two-body interactions between each of the pairs, and focus thereby directly on universal properties. We solve the Faddeev equations in momentum space and express the mean-square radii in terms of first-order derivatives of the Fourier transforms of densities. The strengths of the interactions are adjusted for each set of masses to produce equal two-body bound-state energies between different pairs. The mass ratio, ${\cal A}=m_B/m_A$, between particles $B$ and $A$ are varied from $0.01$ to $100$ providing a number of bound states decreasing from $8$ to $2$. Energies and mean-square radii of these states are analyzed for small ${\cal A}$ by use of the Born-Oppenheimer potential between the two heavy $A$-particles. For large ${\cal A}$ the radii of the two bound states are consistent with a slightly asymmetric three-body structure. When ${\cal A}$ approaches thresholds for binding of the three-body excited states, the corresponding mean-square radii diverge inversely proportional to the deviation of the three-body energy from the two-body thresholds. The structures at these three-body thresholds correspond to bound $AB$-dimers and one loosely bound $A$-particle.

physics.atom-ph↗