We consider a two-dimensional Bose gas formed in a planar atomic trap in conditions where the two-dimensional scattering length exceeds all other microscopic length scales in the system and, accordingly, the gas parameter assumes relatively high values. We show that, unlike in the three-dimensional case, for sufficiently low areal densities the two-dimensional gas remains stable against collapse even in the resonant regime. Furthermore, we evaluate the three-body recombination rate that sets the upper limit for the lifetime of the two-dimensional resonant atomic condensate.
We consider a two-dimensional Bose gas formed in a planar atomic trap in conditions where the two-dimensional scattering length exceeds all other microscopic length scales in the system and, accordingly, the gas parameter assumes relatively high values. We show that, unlike in the three-dimensional case, for sufficiently low areal densities the two-dimensional gas remains stable against collapse even in the resonant regime. Furthermore, we evaluate the three-body recombination rate that sets the upper limit for the lifetime of the two-dimensional resonant atomic condensate.
We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e., the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length a(s)<0), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length a(s)*<0. For a(s)<a(s)*, the density consists of a core of upper branch bosons surrounded by an outer layer of equilibrium branch. The conditions of low three-body recombination require that the particle number N<1.024(T/ω)(5/2) in a harmonic trap with frequency ω.
Abstract The characterization of few-body interactions is fundamental for understanding the properties and collisional stability of ultracold quantum gases in reduced dimensions. In this work, we theoretically investigate the atom-dimer scattering and three-body recombination processes in a two-dimensional quantum gas. By generalizing the Skorniakov–Ter-Martirosian equations to two dimensions, we obtain the exact atom-dimer scattering amplitude and systematically evaluate the validity of common theoretical approximations, revealing a distinct feature of two-dimensional (2D) collisions: while mean-field theory fails rapidly with increasing interaction strength, the single-pole approximation remains remarkably accurate across a broad interaction regime. Furthermore, we extend our exact framework to non-zero incident momenta to calculate the three-body recombination rate. Our results demonstrate that the lifetime of the 2D quantum gas exhibits a power-law dependence on the 2D gas parameter n a 2D 2 with an exponent of approximately − 2.45 , showing a significant reduction in stability as interactions are enhanced. This study bridges the gap between exact few-body theory and practical many-body approximations, offering a robust benchmark for predicting the stability of cold atomic mixtures and guiding future experimental explorations of universal few-body physics in highly controllable 2D environments.
In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.
We perform accurate investigation of stability of localized vortices in an effectively two-dimensional (``pancake-shaped'') trapped Bose-Einstein condensate with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity S=1 are stable in a third of their existence region, 0<N<(1∕3)Nmax(S=1), where N is the number of atoms, and Nmax(S=1) is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, (1∕3)Nmax(S=1)<N<0.43Nmax(S=1), the unstable vortex periodically splits in twofragments and recombines. At N>0.43Nmax(S=1), the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full three-dimensional (3D) Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio 10, the stability interval of the S=1 vortices occupies $\ensuremath{\approx}40%$ of their existence region, hence the two-dimensional (2D) limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to 2. All vortices with $S\ensuremath{\geqslant}2$ are unstable.
In this paper, we explore the nature of three-dimensional Bose gases at large positive scattering lengths via resummation of dominating processes involving a minimum number of virtual atoms. We focus on the energetics of the nearly fermionized Bose gases beyond the usual dilute limit. We also find that an onset instability sets in at a critical scattering length, beyond which the near-resonance Bose gases become strongly coupled to molecules and lose the metastability. Near the point of instability, the chemical potential reaches a maximum, and the effect of the three-body forces can be estimated to be around a few percent.