In these lecture notes, we discuss the physics of a two-dimensional binary mixture of Bose gases at zero temperature, close to the point where the two fluids tend to demix. We are interested in the case where one of the two fluids (the bath) fills the whole space, while the other one (the minority component) contains a finite number of atoms. We discuss under which condition the minority component can form a stable, localized wave packet, which we relate to the celebrated "Townes soliton". We discuss the formation of this soliton and the transition towards a droplet regime that occurs when the number of atoms in the minority component is increased. Our investigation is based on a macroscopic approach based on coupled Gross-Pitaevskii equations, and it is complemented by a microscopic analysis in terms of bath-mediated interactions between the particles of the minority component.In these lecture notes, we discuss the physics of a two-dimensional binary mixture of Bose gases at zero temperature, close to the point where the two fluids tend to demix. We are interested in the case where one of the two fluids (the bath) fills the whole space, while the other one (the minority component) contains a finite number of atoms. We discuss under which condition the minority component can form a stable, localized wave packet, which we relate to the celebrated "Townes soliton". We discuss the formation of this soliton and the transition towards a droplet regime that occurs when the number of atoms in the minority component is increased. Our investigation is based on a macroscopic approach based on coupled Gross-Pitaevskii equations, and it is complemented by a microscopic analysis in terms of bath-mediated interactions between the particles of the minority component.

arXiv:2210.14045Oct 25, 20223 citations

Universal quantum corrections of two-body correlation in a weakly interspecies interacting binary Bose mixture

Rui-Yan Chen, Zhaoxin Liang, Gao Xianlong

We investigate universal quantum corrections to two-body correlations in a zero-temperature binary Bose mixture using the Cornwall-Jackiw-Tomboulis two-particle-irreducible effective action formalism. In the weak interspecies-coupling regime, a saddle-point treatment based on Hubbard-Stratonovich transformations can be combined with a two-loop expansion and a gapless Hartree-Fock correction, thereby preserving the Goldstone theorem and reducing the coupled two-component problem to two analytically solvable single-component theories. Within this framework, we derive the ground-state energy density as a low-density expansion in the gas parameter, together with the quantum depletion and chemical potentials. The results exhibit a simple mapping to the single-component case: the universal quantum corrections of the mixture are obtained by evaluating the known single-component series at an effective scattering length $a_{σσ}-a_{12}$ for each species, where $a_{σσ}$ and $a_{12}$ are the intra- and interspecies $s$ -wave scattering lengths. This reproduces Petrov's equation of state at one-loop order in the weak-coupling limit and yields beyond-Lee-Huang-Yang corrections at two-loop order. We also analyze the role of mass imbalance, which enters the energy density through the exact rescaling factor $(1+m_{1}/m_{2})/2$ .We investigate universal quantum corrections to two-body correlations in a zero-temperature binary Bose mixture using the Cornwall-Jackiw-Tomboulis two-particle-irreducible effective action formalism. In the weak interspecies-coupling regime, a saddle-point treatment based on Hubbard-Stratonovich transformations can be combined with a two-loop expansion and a gapless Hartree-Fock correction, thereby preserving the Goldstone theorem and reducing the coupled two-component problem to two analytically solvable single-component theories. Within this framework, we derive the ground-state energy density as a low-density expansion in the gas parameter, together with the quantum depletion and chemical potentials. The results exhibit a simple mapping to the single-component case: the universal quantum corrections of the mixture are obtained by evaluating the known single-component series at an effective scattering length $a_{σσ}-a_{12}$ for each species, where $a_{σσ}$ and $a_{12}$ are the intra- and interspecies $s$-wave scattering lengths. This reproduces Petrov's equation of state at one-loop order in the weak-coupling limit and yields beyond-Lee-Huang-Yang corrections at two-loop order. We also analyze the role of mass imbalance, which enters the energy density through the exact rescaling factor $(1+m_{1}/m_{2})/2$.

arXiv:2608.17473Aug 18, 20260 citations

Mixtures of Bose liquids at finite temperature

William B. Colson, Alexander L. Fetter

Journal of Low Temperature PhysicsNov 1, 197857 citations

a_{σσ}-a_{12}

for each species, where

a_{σσ}

and

a_{12}

are the intra- and interspecies

s

-wave scattering lengths. This reproduces Petrov's equation of state at one-loop order in the weak-coupling limit and yields beyond-Lee-Huang-Yang corrections at two-loop order. We also analyze the role of mass imbalance, which enters the energy density through the exact rescaling factor

(1+m_{1}/m_{2})/2