Confinement-induced resonances in anharmonic waveguides

Abstract

We develop the theory of anharmonic confinement-induced resonances (ACIR). These are caused by anharmonic excitation of the transverse motion of the center of mass (COM) of two bound atoms in a waveguide. As the transverse confinement becomes anisotropic, we find that the COM resonant solutions split for a quasi-1D system, in agreement with recent experiments. This is not found in harmonic confinement theories. A new resonance appears for repulsive couplings (a3D > 0) for a quasi-2D system, which is also not seen with harmonic confinement. After inclusion of anharmonic energy corrections within perturbation theory, we find that these ACIR resonances agree extremely well with anomalous 1D and 2D confinement induced resonance positions observed in recent experiments. Multiple even and odd order transverse ACIR resonances are identified in experimental data, including up to N = 4 transverse COM quantum numbers.

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].…”

Theory of inelastic confinement-induced resonances due to the coupling of center-of-mass and relative motion

“…coupling can have a significant impact on an ultracold atomic quantum gas. In [5,6] it was revealed that the particle loss and heating observed in [7] was caused by inelastic confinement-induced resonances (CIR), i. e. resonances due to the c.m.-rel. coupling of a c.m.…”

Numerical Solution of the Time Dependent 3D Schrödinger Equation Describing Tunneling of Atoms from Anharmonic Traps

“…For β = 0.427471, this models an actual atom-trap interaction [1,11,12] in modern experiments [13] on ultracold atoms (figure 1). The atom-atom interaction is taken of Gaussian form:…”