Dipolar Confinement-Induced Resonances of Ultracold Gases in Waveguides

Abstract

We develop a non-perturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory allowing to include accurately long-range anisotropic interactions. Analyzing ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization e.g. Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases. In low-dimensional geometries due to tightly confining traps, ultracold atomic scattering undergoes crucial modifications yielding the effect of confinement-induced resonances (CIRs) [1,2]. A CIR is a Fano-Feshbach-type of resonance occurring when the scattering length a s and the length of the transversal confinement a ⊥ are comparable, namely a s /a ⊥ ≈ 0.68. Remarkably, the deepened theoretical understanding of CIR physics [3-10] has lead to major achievements in the experimental manipulation [11,12] of interacting gaseous atomic matter. Together with the extensive study of free-space dipolar collisions [13][14][15][16][17][18][19][20], confinement-induced resonant scattering introduces an intriguing perspective for the control of dipolar many-body phases [21,22]. Indeed, reduced dimensionality has lead to the prediction of dipolar crystals [23] and the control of internal and external degrees of freedom of molecules has allowed the realization of dense ultracold polar molecule gases [24]. In view of the substantial theoretical effort made on confined dipolar scattering [25][26][27][28][29][30], the need for a rigorous understanding of the role of anisotropic forces in CIRs becomes evident.In this letter, we analytically derive the resonance condition for s-wave dipolar CIR (DCIR), with explicit dependence on the dipole-dipole interaction (DDI) strength. This is done within an extended K-matrix formalism for harmonic quasi-one-dimensional (Q1D) geometries [10] which incorporates anisotropic forces, i.e. the DDI, and takes into account contributions from higher angular momentum states. These ℓ-wave states are firstly coupled due to the anisotropic nature of the DDI and secondly by the harmonic confinement, which leads to a rich resonance structure of the DCIRs. The ℓ-wave DCIRs appear in the vicinity of shape resonances which are properly taken into account within the K-matrix approach going beyond the effective onedimensional pseudopotential theory [27]. Interestingly, this interplay between the confinement and the DDI leads to an intricate dependence of the s-wave DCIRs positions...

Generalized local-frame-transformation theory for excited species in external fields

“…(12) is obtained by employing the relations in Eqs. (10) and (21). Then the quantity J ℓℓ ′ reads where U 0 αℓm (ǫ) (with α = β F or β) denotes the shortrange local frame transformation amplitudes that omit effects of the Stark barrier (see Eq.…”

“…Furthermore, the LFT theory gives a compact description of a variety of physical processes such as dielectronic recombination [12], negative-ion photodetachment in magnetic [13] or electric fields [14][15][16] or under generic external confinement [17], or ultracold atomic and/or * pgiannak@purdue.edu † chgreene@purdue.edu ‡ robichf@purdue.edu dipolar collisions in the presence of external trapping potentials [18][19][20][21]. In molecular applications frame transformation theory has been decisive in describing the rich rovibrational Rydberg spectra of diatomic molecules [22], and the dissociative recombination of H + 3 [23,24].…”

Energy-dependentℓ-wave confinement-induced resonances

“…Recent experimental advances allowed to explore the corresponding physics of CIRs in quasi-one-and quasi-two-dimensional (quasi-1D and quasi-2D) waveguide geometries [11][12][13][14][15] or in mixed dimensional scattering processes [16]. Complementing the experimental studies, substantial theoretical efforts exhibit a kaleidoscope of confinement-induced processes, such as dual [17] and higher partial wave CIRs [18,19], multichannel [20][21][22][23] or anharmonic CIRs [24][25][26] and CIR molecule formation [27] or dipolar CIRs [28][29][30]. Further studies on CIR effects focus on the impact of various confining geometries, such as quasi-2D either harmonic [31,32] or square well [33], and lattice potentials [34][35][36], or collisions in mixed dimensions [37].…”

“…The atoms are allowed to perform collisions with higher partial waves where we take into account that the total colliding energy is well above the threshold of the ground state of the transversal confinement. The theoretical conceptualization of the corresponding resonant phenomena is based on a fully analytical and non-perturbative framework of the K-matrix approach [19,28] including appropriate interatomic interactions with e.g. a van der Waals tail.…”

“…(2) interrelates the wave functions of the asymptotic and the inner region. Consequently, the corresponding K matrices are connected according to the relation 18,19,28,33], where the K 3D -Matrix is a diagonal matrix in the ℓ-wave representation with entries given by the tangent of the phase shifts.…”