Variational Bethe Ansatz approach for dipolar one-dimensional bosons

Understand

We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model.

• We apply our variational approximation to a gas of dipolar bosons in the single mode approximation and obtain its ground state energy per unit length.
• This allows for the calculation of the Tomonaga-Luttinger exponent as a function of density and the determination of the structure factor at small momenta.
• Moreover, in the case of attractive dipolar interaction, an instability is predicted at a critical density, which could be accessed in lanthanide atoms.