Threshold behavior of bosonic two-dimensional few-body systems

Abstract

Bosonic two-dimensional self-bound clusters consisting of N atoms interacting through additive van der Waals potentials become unbound at a critical mass m (N) * ; m (N) * has been predicted to be independent of the size of the system. Furthermore, it has been predicted that the ground state energy EN of the N -atom system varies exponentially as the atomic mass approaches m * . This paper reports accurate numerical many-body calculations that allow these predictions to be tested. We confirm the existence of a universal critical mass m * , and show that the near-threshold behavior can only be described properly if a previously neglected term is included. We comment on the universality of the energy ratio EN+1/EN near threshold. PACS numbers:Restricting the motion of particles to one or two dimensions can lead to properties that differ dramatically from those in three dimensions. The most prominent two-dimensional (2D) system is the surface of bulk matter. Another example are one-or two-atom layer thin films, e.g., atomic or molecular hydrogen films [1,2], grown on substrates. Neglecting the adatom-substrate interaction, many properties of such systems can be understood within a truly 2D framework. In addition to homogeneous 2D systems, it is interesting to consider 2D clusters (see, e.g., Refs. [3,4]). What happens when a finite number of atoms is restricted to 2D space? Inhomogeneous 2D systems can potentially be studied by placing a few atoms on the surface of a substrate or by confining atoms by external potentials. Effectively 2D atom traps have been realized recently [5,6]; extension to optical lattices with only a few atoms per lattice site is possible with today's technology. These systems are particularly interesting since Feshbach resonances allow the interaction strengths to be tuned through application of magnetic fields.Bosonic 2D systems interacting through short-range two-body potentials that support one zero angular momentum bound state are predicted to exhibit intriguing universal, that is, model-independent, behaviors [7,8,9,10,11,12,13,14,15,16,17,18]. i) 2D clusters with N particles [9,10,12] are predicted to become unbound when the mass m reaches a critical value m (N ) * [7]. This critical mass is predicted to be universal, i.e., m (N ) * = m * [10], and to be the same for the corresponding homogeneous system [8,19]. ii) For a given system size, the ground state energies E N near threshold are predicted to change exponentially as the atomic mass m decreases [7,11]. Similarly, for a given atomic mass, the ground state energies near threshold are predicted to change exponentially with varying system size [17]. iii) The ratio between the ground state energies of a 2D system with N +1 atoms and those of a system with N atoms reaches, in the limit of zero-range interactions, a constant. This constant has been determined analytically for small 2D systems: E δ 3 /E δ 2 = 16.52 [9,16] and E δ 4 /E δ 3 = 11.94 [18]. For large systems, the ratio E δ N +1 /E δ N has been predicted to approach 8.57 [17]...

Supercircle description of universal three-body states in two dimensions

“…The question of few-body states in equal mass two-dimensional systems has been addressed in a number of works. Bound states of three- [17][18][19][20][21][22], four- [21,23], and larger particle number droplets [24][25][26], as well as scattering [21] and recombination observables [27], have been addressed.…”

Ultracold three-body recombination in two dimensions

“…As shown in Refs. [19][20][21][22][23][24][25], for identical bosons in 2D there are always two three-body states associated with the weakly bound diatom state. Their energies are universally related to E 2b as…”

“…From the few-body perspective [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], when interatomic interactions are strong, i.e., when the s-wave 2D scattering length a greatly exceeds the van der Waals length r vdW or any other short-range length scale, the system acquires universal properties that are manifested in both its bound and scattering properties. Universal few-body states have been studied for homonuclear and heteronuclear bosonic systems with strong s-wave interactions [19][20][21][22][23][24][25][26][27][28][29] and represent a novel class of states that might be accessible in experiments in 2D ultracold gases.…”

“…Universal few-body states have been studied for homonuclear and heteronuclear bosonic systems with strong s-wave interactions [19][20][21][22][23][24][25][26][27][28][29] and represent a novel class of states that might be accessible in experiments in 2D ultracold gases. Their importance for many-body behavior is a question of much interest in the ultracold community.…”

QuantumN-boson states and quantized motion of solitonic droplets: Universal scaling properties in low dimensions

“…In two dimensions (2D), the limit o f A = 3,4, i.e., threeand four-body bound states have been studied previously [31][32][33][34][35][36][37], The authors o f Ref. [33] have also proposed a bound state for A bosons; we later identify it as a classical solution to the 2D quantum problem studied in the following.…”