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arXiv:1104.4277 · Physical Review A

Two-dimensional dipolar scattering with a tilt

Christopher Ticknor

Published Sep 6, 2011• 17 citations
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Abstract

We study two-body dipolar scattering in two dimensions with a tilted polarization axis. This tilt reintroduces the anisotropic interaction in a controllable manner. As a function of this polarization angle, we present the scattering rates in both the threshold and semiclassical regimes. Additionally, we study the properties of the molecular bound states as a function of the polarization angle.

DOI
10.1103/physreva.84.032702

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We study two-body dipolar scattering in two dimensions with a tilted polarization axis. This tilt reintroduces the anisotropic interaction in a controllable manner. As a function of this polarization angle, we present the scattering rates in both the threshold and semiclassical regimes. Additionally, we study the properties of the molecular bound states as a function of the polarization angle.
We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.
We analyze the ground state of a system of dipolar bosons moving in the XYXYXY plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle $\ensuremath{\alpha}$ with respect to the ZZZ axis. We use the path-integral ground-state method to analyze the static properties of the system as both $\ensuremath{\alpha}$ and the density nnn vary over a wide range where the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them. We find that, in addition to a superfluid gas and a solid phase, the system reaches a stripe phase at large tilting angles that is entirely induced by the anisotropic character of the interaction. We also show that the quantum phase transition from the gas to the stripe phase is of second order and report approximate values for the critical exponents.
The impact of the short-range interaction on the resonances' occurrence in the anisotropic dipolar scattering in a plane is numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We reveal the strong dependence of the cross section of the two-dimensional (2D) dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We define the critical (magic) tilt angle of one of the dipoles, depending on the direction of the second dipole for arbitrarily oriented dipoles. We find that resonances arise only when this angle is exceeded. In contrast to the three-dimensional (3D) case, the energy dependencies of the boson (fermion) 2D scattering cross section grow (are reduced) with an energy decrease in the absence of the resonances. We show that the mutual orientation of dipoles strongly impacts the form of the energy dependencies, which begin to oscillate with the tilt angle increase, unlike the 3D dipolar scattering. The angular distributions of the differential cross section in the 2D dipolar scattering of both bosons and fermions are highly anisotropic at nonresonant points. The results of the accurate numerical calculations of the cross section agree well with the results obtained within the Born and eikonal approximations.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^d x = n a 0 d , with n n the density, d d the dimensionality of the space ( d=1,2,3 d = 1 , 2 , 3 ) and a_0 a 0 the s s -wave scattering length. The universal regime typically extends up to x\approx 0.001 x ≈ 0.001 , while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0 a 0 depend on the polarization angle \alpha α , so different combinations of n and \alpha α can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of x x that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.