Semisuper Efimov Effect of Two-Dimensional Bosons at a Three-Body Resonance

Abstract

Wave-particle duality in quantum mechanics allows for a halo bound state whose spatial extension far exceeds a range of the interaction potential. What is even more striking is that such quantum halos can be arbitrarily large on special occasions. The two examples known so far are the Efimov effect and the super Efimov effect, which predict that spatial extensions of higher excited states grow exponentially and double exponentially, respectively. Here, we establish yet another new class of arbitrarily large quantum halos formed by spinless bosons with short-range interactions in two dimensions. When the two-body interaction is absent but the three-body interaction is resonant, four bosons exhibit an infinite tower of bound states whose spatial extensions scale as R_{n}∼e^{(πn)^{2}/27} for a large n. The emergent scaling law is universal and is termed a semisuper Efimov effect, which together with the Efimov and super Efimov effects constitutes a trio of few-body universality classes allowing for arbitrarily large quantum halos.

Universal few-body physics and cluster formation

“…(Massignan and Castin, 2006) This effect emerges from the combination of pure s-wave interactions and the fact that the two-body collisions take place in mixed-dimensions which couples the angular momenta of the A and B atomic species. The theoretical predictions (Nishida andTan, 2008, 2010) have apparently been observed by (Lamporesi et al, 2010), who created a mixed-dimensional confinement of two ultracold atomic species, namely 41 K and 87 Rb. The 41 K atoms are trapped in two-dimensions whereas the 87 Rb atoms move in three-dimensions, which is achieved by implementing species-selective dipole trapping techniques LeBlanc and Thywissen, 2007;Massignan and Castin, 2006).…”

“…Recently, a theoretical treatment by (Nishida, 2017) has introduced the "semi-super Efimov effect". This is in a system of four bosons in 2D, which exhibit a different scaling possible for an infinite pattern of energy levels and state sizes, in a scenario where the three-boson interactions are resonant but the two-body interactions are negligible.…”

Quantum droplet of one-dimensional bosons with a three-body attraction

“…Whether such novel systems without two-body but with tunable three-body interactions exhibit interesting physics remains largely unexplored and thus can be an important research frontier in ultracold atoms. One of the recent advances toward this direction was the discovery of the semisuper Efimov effect, where two-dimensional bosons at a threebody resonance form an infinite tower of four-body bound states with the universal scaling law in their binding energies [11].…”

Large-momentum tail of one-dimensional Fermi gases with spin-orbit coupling

“…These relations have already been successfully verified in experiments near the s-wave Feshbach resonance [8][9][10][11]. Furthermore, the universal relations were also studied in other atomic systems, such as the quantum gases with higher-partial-wave interactions [12][13][14][15][16][17][18][19], in one dimension [20][21][22][23][24] and two dimensions [25][26][27][28][29][30][31][32] with threebody correlations [33][34][35][36][37][38][39] near a Raman-dressed Feshbach resonance [40] and with ultracold polar molecules [41]. Besides, the contact tensor was predicted in the axisymmetry-* qinfang@ustc.edu.cn broken p-wave Fermi gases [42].…”