Collapse of 2D Bose gases with two- and three-body interactions

Dinh-Thi Nguyen, Julien Ricaud

Mohammad Sadegh Mashayekhi, Jean-Sébastien Bernier, Dmitry Borzov +2 more

Anonymous

Deke Li, Yuan Li, Qingxuan Wang

We consider a system of $N$ interacting bosons in a rotating harmonic trap in $\mathbb{R}^2$, where the two-body interaction is attractive and scaled as $N^{2α}U(N^αx)$ with $0<α<1/12$, and the three-body interaction is repulsive and scaled as $N^{4β}W(N^βx,N^βy)$ with $0<β<1/24$. In the mean-field limit, the ground state energy is effectively described by a rotating cubic-quintic nonlinear Schrödinger functional. We analyze the collapse regime where the two-body coupling $a$ approaches the critical value $a_*$ and the three-body coupling $b$ tends to zero. The NLS ground states blow up with a universal profile given by the optimizer of the Gagliardo-Nirenberg inequality, and the energy satisfies $E^{\mathrm{NLS}} = (1-ζ/4+o(1))\mathcal{Q}{\rm{pot}}\ell_n^2$ with $ζ\geqslant0$ determined by the relative rates of $a_n\to a_*$ and $b_n\searrow0$. From the many-body theory, we rigorously justify this effective description: the quantum ground state energy converges to the NLS energy with the same asymptotic expansion in the collapse regime, and the many-body ground states exhibit complete Bose-Einstein condensation onto the universal blow-up profile.

Thomas Bourdel

Mohammad Sadegh Mashayekhi, Jean-Sébastien Bernier, Dmitry Borzov +2 more

We report in this Letter the results of our investigation of 2D Bose gases beyond the dilute limit emphasizing the role played by three-body scattering events. We demonstrate that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of 2D 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 here are universal, fully characterized by the effective 2D scattering length a(2D) (or the size of the 2D bound states) and are, in comparison to the 3D case, independent of three-body ultraviolet physics. We find, within our approach, the ratios of the contribution to the chemical potential due to three-body interactions to the one due to two-body to be 0.27 near the maximum of the chemical potential and 0.73 in the vicinity of the onset instability.