Confinement-induced resonances in ultracold atom-ion systems

Abstract

We investigate confinement-induced resonances in a system composed by a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region -from the "long-wavelength" limit to the opposite case when the typical length scale of the atom-ion polarisation potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the "long-wavelength and zero-energy" limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semi-analytic formula for the resonance position in the "long-wavelength and zero-energy" limit and we investigate numerically how the position of the resonance is affected by a finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi one dimensional atomic quantum gas.

Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

“…is the relative variable between the colliding atoms [9][10][11][12][13] or the atom variable relative the heavy ion [18]. Here, f e (E) is the desired scattering amplitude, Φ 0 (x, y) is the wave function of the groundstate of the 2D harmonic oscillator [9][10][11][12][13] or the mass of atom colliding with heavy ion [18].…”

“…Here, f e (E) is the desired scattering amplitude, Φ 0 (x, y) is the wave function of the groundstate of the 2D harmonic oscillator [9][10][11][12][13] or the mass of atom colliding with heavy ion [18]. In the case of the atom-atom interaction a four-channel potentialV(r) describing three lowest magnetic Feshbach resonances in Cs [19] (with c = 1, 2, 3) was used in works [11,12].…”

“…Some of these resonances have been used in experimental investigation of the Cs confinement-induces resonances in anisotropic waveguide-like traps [8]. In the case of atom-ion confined scattering the problem (1, 2) was reduced to one channel scattering (α = e) with scalar atom-ion potentialV(r) → V(r) ∼ C 4 /r 4 [18].…”

“…However, to develop an efficient computational scheme for the integration of the problem (1, 2) in a confining trap (ω x 0, ω y 0) is a challenging task due to sharp jumps at the edge of the interaction in the diagonal terms V αα (r) chosen in the form of square-well potential [11,12]. In the case of atom-ion confined scattering the tensorial structure of the potentialV(r) is absent but the need arises to get accurate solution for the long-range scalar atom-ion interaction V(r) ∼ C 4 /r 4 [18].…”

Quantum States of Interacting Atoms in Quasi-One-Dimensional Ultracold Trapped Gases

“…In these approaches, the scattering amplitude is determined by means of the expansion of the scattering wave function [8] [15] [21] into the eigenstates of the transverse unperturbed (Huang's potential independent) Hamiltonian. As a result, it is possible to relate the effective 1D coupling strength to the s-wave scattering length (an experimentally accessible quantity, related to the Feshbach resonance interaction), showing the existence of phenomena such as CIRs [14] [22]- [29] and multiple CIRs [13] [30] [31] [32] [33] [34] and providing the connection between theoretical and experimental quantities in the study of ultracold gases.…”