Abstract
We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole–dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as a function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three-, four- and five-body problems in two or more tubes. Our results indicate that in the weakly coupled limit the intertube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.
Highlights
We consider the setup depicted schematically in figure 1, i.e. an array of equidistant 1D tubes containing dipolar particles with dipole moments aligned by an external field that does not interfere with the tubular geometry
Is determined by the laser intensity. This can be translated into a Gaussian wave packet in the transverse direction that will be increasingly localized in space as the laser intensity increases
We have studied dipolar bosonic particles confined to a setup consisting of a number of 1D tubes
Summary
We consider the setup depicted schematically in figure 1, i.e. an array of equidistant 1D tubes containing dipolar particles with dipole moments aligned by an external field that does not interfere with the tubular geometry. For n = 0, experimental setups, arrays of 1D tubes are constructed by applying optical lattices to the dipolar gas [7, 8] In this case the tubes are not strictly 1D but will have some width along the transverse direction that. We will assume that the lattice is very strong so that the strict 1D expression above is valid for the interaction of particles in different tubes, which is accurate when the transverse width, l, is much smaller than the intertube distance, d. Corrections to this picture have been discussed in [24, 25]. We will only consider the regime where this quantity is positive, i.e. the case for which two dipoles in a single tube repel each other in order to avoid any collapsing states within the tubes
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