Universality in ultradilute liquid Bose-Bose mixtures

We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at T=0. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the s-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.Postprint (published version

The free energy of dilute Bose gases at low temperatures

We consider a low density Bose gas interacting through a repulsive potential in the thermodynamic limit. We justify, as a rigorous lower bound, a Lee--Huang--Yang type formula for the free energy at suitably low temperatures, where the modified excitation spectrum leads to a second order correction of the same order as the Lee--Huang--Yang correction to the ground state energy

The ground state energy of the weakly interacting Bose gas at high density

We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.Comment: RevTeX4, 16 page

The energy of dilute Bose gases

For a dilute system of non-relativistic bosons interacting through a positive $L^1$ potential $v$ with scattering length $a$ we prove that the ground state energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+ \frac{128}{15\sqrt{\pi}} \sqrt{\rho a^3} +o(\sqrt{\rho a^3}\,))$, thereby proving the Lee-Huang-Yang formula for the energy density.Comment: 64 pages, minor correction

Collective modes of a quasi two-dimensional Bose condensate in large gas parameter regime

We have theoretically studied the collective modes of a quasi two-dimensional (Q2D) Bose condensate in the large gas parameter regime by using a formalism which treats the interaction energy beyond the mean-field approximation. In the calculation we use the perturbative expansion for the interaction energy by incorporating the Lee, Huang and Yang (LHY) correction term. The results show that incorporation of this higher order term leads to detectable modifications in the mode frequencies.Comment: 10 pages, 2 figure

Effects of quantum fluctuations on macroscopic quantum tunneling and self-trapping of BEC in a double well trap

We study the influence of quantum fluctuations on the macroscopic quantum tunneling and self-trapping of a two-component Bose-Einstein condensate in a double-well trap. Quantum fluctuations are described by the Lee-Huang-Yang term in the modified Gross-Pitaevskii equation. Employing the modified Gross-Pitaevskii equation in scalar approximation, we derive the dimer model using a two-mode approximation. The frequencies of Josephson oscillations and self-trapping conditions under quantum fluctuations are found analytically and proven by numerical simulations of the modified Gross-Pitaevskii equation. The tunneling and localization phenomena are investigated also for the case of the Lee-Huang-Yang fluid loaded in the double-well potential.Comment: 14 pages, 9 figure

Self-consistent derivation of the modified Gross-Pitaevskii equation with Lee-Huang-Yang correction

We consider a dilute and ultracold bosonic gas of weakly-interacting atoms. Within the framework of quantum field theory we derive a zero-temperature modified Gross-Pitaevskii equation with beyond-mean-field corrections due to quantum depletion and anomalous density. This result is obtained from the stationary equation of the Bose-Einstein order parameter coupled to the Bogoliubov-de Gennes equations of the out-of-condensate field operator. We show that, in the presence of a generic external trapping potential, the key steps to get the modified Gross-Pitaevskii equation are the semiclassical approximation for the Bogoliubov-de Gennes equations, a slowly-varying order parameter, and a small quantum depletion. In the uniform case, from the modified Gross-Pitaevskii equation we get the familiar equation of state with Lee-Huang-Yang correction.Comment: 7 pages, invited contribution for the special issue "Optical Properties of Confined Quantum Systems" of the journal Applied Sciences, included the effect of anomalous densit