Variational Bethe ansatz approach for dipolar one-dimensional bosons

Abstract

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. PACS numbers:arXiv:1910.05965v2 [cond-mat.quant-gas]

Creating quantum many-body scars through topological pumping of a 1D dipolar gas

“…Accounting for corrections from the regularized 1D DDI provides a small shift from the nondipolar results, as shown in solid lines in panel (B) and (C). These lines are similar to that calculated in a recent perturbative treatment [68]. Regardless, these shifts are too small to be resolved by the experiment.…”

“…5, which are nearly indistinguishable from that derived by a perturbative calculation presented in Ref. [68]; and 2) determine the position of the vertical dotted line in Fig. 2C of the main text and in Supp.…”

“…Stimulated by our work, the authors of Ref. [68] considered the repulsive ground state of a Lieb-Liniger model with the DDI perturbatively added. They report R versus A 2 curves very similar to those presented as solid lines in Supp.…”

“…This contains the 1/r 3 divergence when two atoms approach one another. However, in a quasi-1D trap, this divergence is smoothed out by the transverse degrees of freedom; the interaction must be regularized by integrating out these transverse degrees of freedom [18,68,77,78]. This operation removes the divergence, replacing it with an extra delta function-like term while reducing the strength of the 1/r 3 term at short distances.…”

Quantum dynamics of few dipolar bosons in a double-well potential

“…The ground state properties of ultracold trapped bosons with dipolar interactions have been studied extensively both at mean-field level and in the one-dimensional limit [61][62][63][64][65][66][67] (see more refs. in [48,49]).…”