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In this letter we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound state and cause scattering resonances. This represents the dipole induced resonance in low-dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using asymptotic Bethe ansatz. Despite of long-range nature of dipolar interaction, we find that a behavior similar as short-range Lieb-Linger gas emerges at the resonance regime.
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We consider dipolar bosons in two tubes of one-dimensional lattices, where the dipoles are aligned to be maximally repulsive and the particle filling fraction is the same in each tube. In the classical limit of zero inter-site hopping, the particles arrange themselves into an ordered crystal for any rational filling fraction, forming a complete devils staircase like in the single tube case. Turning on hopping within each tube then gives rise to a competition between the crystalline Mott phases and a liquid of defects or solitons. However, for the two-tube case, we find that solitons from different tubes can bind into pairs for certain topologies of the filling fraction. This provides an intriguing example of pairing that is purely driven by correlations close to a Mott insulator.
Ultracold dipolar droplets have been realized in a series of ground-breaking experiments, where the stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang (LHY) correction. We scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions supporting quasi-one-dimensional droplet states. By applying an interaction quench to the droplet, a modulational instability is induced and multiple droplets are produced, along with bright solitons and atomic radiation. We also assess the droplets robustness to collisions, revealing population transfer and droplet fission.
The length scale separation in dilute quantum gases in quasi-one- or quasi-two-dimensional traps has spatially divided the system into two different regimes. Whereas universal relations defined in strictly one or two dimensions apply in a scale that is much larger than the characteristic length of the transverse confinements, physical observables in the short distances are inevitably governed by three-dimensional contacts. Here, we show that $p$-wave contacts defined in different length scales are intrinsically connected by a universal relation, which depends on a simple geometric factor of the transverse confinements. While this universal relation is derived for one of the $p$-wave contacts, it establishes a concrete example of how dimensional crossover interplays with contacts and universal relations for arbitrary partial wave scatterings.
One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically-bound nearest-neighbor dimers enhances the role of the $1/r^3$ dipolar tail, resulting, in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.
We investigate the effect of dipolar interactions in one-dimensional systems in connection with the possibility of observing exotic many-body effects with trapped atomic and molecular dipolar gases. By combining analytical and numerical methods, we show how the competition between short- and long-range interactions gives rise to frustrating effects which lead to the stabilization of spontaneously dimerized phases characterized by a bond-ordering. This genuine quantum order is sharply distinguished from Mott and spin-density wave phases, and can be unambiguously probed by measuring non local order parameters in-situ imaging techniques.
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