Confinement-induced resonance with weak background interaction

Abstract

We studied the scattering problem of two atoms with unequal mass, where one atom (atom α) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom β) is localized by a 3D harmonic trap. We show that in such a system if atom α is much heavier than β, confinementinduced resonance (CIR) can appear when the 3D scattering length as of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either as > 0 or as < 0. This is quite different from the usual CIRs which occurs only when as is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough that can serve as a tool for the control of effective inter-atomic interaction. We further show the mechanism of these CIRs via the Born-Oppenheimer approximation. Our results can be used for the realization of stronglyinteracting systems with ultracold atoms with weak 3D background interaction (i.e., small as), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic field.

Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement

“…When E < E 0 , the Green's function G 0 (E, ze z ) (z > 0) can be expressed as the Laplace transform of the imaginary-time propagator [45][46][47][48][49],i.e.,…”

“…Nevertheless, this integration diverges in the limit z → 0. That is due to the behavior of the leading term e −z 2 /(4β) /(4πβ) 3 2 of the function K(z, E, β) in the limit β → 0 + [45][46][47][48][49].We can separate this divergence by re-expressing the integration as…”

Interacting two-mode model for ultracold quantum interferometers

“…This is particularly important since from one side one can obtain an improvement of the sensitivity taking advantage of interactions in the splitting process or to generate squeezed input states, but from the other side the presence of interactions in specific steps of the interferometric scheme may lead to a degradation of the sensitivity [2]. The effects of the presence of interactions and the connection with entanglement have been intensively studied [3,4,5,6,7,8,9,10,11,12], see as well the reviews [2,13,14].…”

Three ultracold fermions in a two-dimensional anisotropic harmonic confinement

“…the effective inter-atomic interaction intensity and the Viral coefficients [1][2][3][4]. One can also obtain basic understandings for the effects induced by inter-atomic interaction via the properties of few-body systems [5][6][7][8][9][10][11][12], or develop new techniques for the control of effective inter-atomic interaction via studying scattering problems of two ultracold atoms in various confinements [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], or under laser and magnetic fields [29][30][31][32][33][34][35][36]. On the other hand, the ultracold atom system is an excellent platform for the study of important few-body problems, e.g.…”