Two-dimensional dipolar scattering

Abstract

We characterize the long range dipolar scattering in 2-dimensions. We use the analytic zero energy wavefunction including the dipolar interaction; this solution yields universal dipolar scattering properties in the threshold regime. We also study the semi-classical 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. [3]. Such theories show dipolar systems will lead to exotic and highly correlated quantum systems. Reduced dimensionality also offers another level of control to exert over ultracold matter. In pursuit of such quantum systems, there has been exciting experimental progress in the production of polar molecules [4,5] and in the production of quasi-2 dimensional ultracold gases [6,7]. This makes it seem that the experimental production of 2D dipolar gases is at hand. However, there is no simple understanding of dipolar scattering in 2D, even for the case of the long range scattering. Such an understanding is an important first step in the study of these quantum systems. In this paper we study the properties of long range dipolar scattering in 2D and present estimates of the scattering cross section. We consider the scenario when the polarization of the molecules (d =ẑ) is perpendicular to the plane of motion (ρ = x 2 + y 2 , d ·ρ = 0). We do not consider the complications of transverse confinement. Under these simplifications the dipolar interaction is: V dd = d 2 /ρ 3 , where d is the magnitude of the induced dipole moment. The anisotropy of the interaction has been removed and the interaction is purely repulsive.To understand the scattering we use the dipolar length scale: D = µd 2 / 2 where µ is the reduced mass. In polar molecules this length scale can be quite large, orders of magnitude larger than the range of the short range interaction, ρ 0 . Using D to rescale the 2D radial Schrödinger equation and expanding in partial waves, ψ(ρ, ϕ) = m e imϕ φ m (ρ)/ √ρ , the result is:whereρ = ρ/D, k 2 = 2µE/ 2 , and E is the scattering energy. Ifρ = ρ 0 /D ≪ 1 then the only degree of freedom is Dk, so once Eq. (1) is solved for a given Dk the resulting scattering will apply to any quantum mechanical 2D dipolar system; this is universal dipolar scattering [8, 9, 10].We have analyzed Eq. (1) and characterized the long range 2D dipolar scattering. We present analytic estimates of the scattering in both the threshold and semiclassical limits. In contrast to 3D, there is a diagonal s-wave dipolar interaction, and this leads to universal dipolar scattering in the threshold regime. We refer to the isotropic m = 0 partial wave as s-wave. For threshold scattering in 3D, it is required that a s ≪ D to have universal dipolar scattering [9,10]. This is challenging because a s , the s-wave scattering length, depends sensitively on the details of the short range interaction. However in 2D, the repulsive dipolar interaction prevents ultracold particles from reaching the short rang...

Strong dependence of ultracold chemical rates on electric dipole moments

“…However, at large d, the numerical rate tends to the analytical d −4 behavior. The quenching rate decreases rapidly as the dipole moment increases and this may be promising for efficient evaporative cooling of polar molecules since the elastic rate is expected to grow with increasing dipole moment [41].…”

Quasi-two-dimensional dipolar scattering

“…The scattering on this potential is understood and has a universal form [19]. Thus it will be important to see when the adiabatic curves deviate from the pure 2D potential and this will offer an idea of when the scattering deviates from the pure 2D case.…”

Ground state properties and excitation spectrum of a two dimensional gas of bosonic dipoles

“…In particular, these trapping potentials can be tight enough to make the system effectively two-or onedimensional. Many interesting studies concerning two-or quasitwo dimensional dipolar quantum gases have been performed in recent years, including the analysis of two-body scattering properties [11,12,13], static properties of the many body trapped system [9,14] and homogeneous gas [15,16,17,18,19], and some works about the dynamic response [20,21,22].…”