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arXiv:0908.0155 · Physical Review A

Two-dimensional dipolar scattering

Christopher Ticknor

Published Nov 5, 2009• 50 citations
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Abstract

We characterize the long-range dipolar scattering in two dimensions. We use the analytic zero energy wave function including the dipolar interaction; this solution yields universal dipolar scattering properties in the threshold regime. We also study the semiclassical dipolar scattering and find universal dipolar scattering for this energy regime. For both energy regimes, we discuss the validity of the universality and give physical examples of the scattering.

DOI
10.1103/physreva.80.052702

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We characterize the long-range dipolar scattering in two dimensions. We use the analytic zero energy wave function including the dipolar interaction; this solution yields universal dipolar scattering properties in the threshold regime. We also study the semiclassical dipolar scattering and find universal dipolar scattering for this energy regime. For both energy regimes, we discuss the validity of the universality and give physical examples of the scattering.
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.
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.
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.
We establish that two-dimensional dipolar quantum gases admit a universal description, i.e., their thermodynamic properties are independent of details of the interaction at short distances.The only relevant parameters are the dipole length as well as the scattering length of the combined short-range plus dipolar interaction potential.We derive adiabatic relations that link the change in the thermodynamic potentials with respect to the scattering length and the dipole length to a generalized Tan contact parameter and a new dipolar contact, which involves an integral of a short-distance regularized pair distribution function.These two quantities determine the scale anomaly in the difference between pressure and energy density and also the internal energy in the presence of a harmonic confinement.For a weak transverse confinement, configurations with attractive interactions appear, which lead to a density-wave instability beyond a critical strength of the dipolar interaction.We show that this instability essentially coincides with the onset of a roton minimum in the excitation spectrum and may be understood in terms of a quantum analog of the Hansen-Verlet criterion for freezing of a classical fluid.
We explore the impact of the short-range interaction on the scattering of ground state polar molecules and study the transition from a weak to strong dipolar scattering over an experimentally reasonable range of energies and electric field values. In the strong dipolar limit, the scattering scales with respect to a dimensionless quantity defined by mass, induced dipole moment, and collision energy. The scaling has implications for all quantum mechanical dipolar scattering. Furthermore the universal scattering regime will readily be achieved with polar molecules at ultracold temperatures.