1. Universal energy-dependent pseudopotential for the two-body problem of confined ultracold atoms
- Author
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Da-Wu Xiao, Ren Zhang, and Peng Zhang
- Subjects
Physics ,QC1-999 - Abstract
The two-body scattering amplitude and energy spectrum of confined ultracold atoms are of fundamental importance for both theoretical and experimental studies of ultracold-atom physics. For many systems, one can efficiently calculate these quantities via the zero-range Huang-Yang pseudopotential (HYP), in which the interatomic interaction is characterized by the scattering length a. Furthermore, when the scattering length is dependent on the kinetic energy ɛ_{r} of two-atom relative motion, i.e., a=a(ɛ_{r}), the results are applicable for a broad energy region. However, when the free Hamiltonian of atomic internal state (e.g., the Zeeman Hamiltonian) does not commute with the interatomic interaction, or the center-of-mass (c.m.) motion is coupled to the relative motion, the generalization of this technique is still lacking. In this work we solve this problem and construct a reasonable energy-dependent multichannel HYP, which is characterized by a “scattering length operator” a[over ̂]_{eff}, for the above complicated cases. Here, a[over ̂]_{eff} is an operator for atomic internal states and c.m. motion, and depends on both the total two-atom energy and the external field as well as the trapping parameter. The effects from the internal-state or c.m.-relative motion coupling can be self-consistently taken into account by a[over ̂]_{eff}. We further show a method based on the quantum defect theory, with which a[over ̂]_{eff} can be analytically derived for systems with van der Waals interatomic interaction. To demonstrate our method, we calculate the spectrum of two ultracold fermionic alkaline-earth-like atoms [in electronic ^{1}S_{0} (|g〉) and ^{3}P_{0} (|e〉) states, respectively] confined in an optical lattice. By comparing our results with the recent experimental measurements for two ^{173}Yb atoms and two ^{171}Yb atoms, we calibrate the scattering lengths a_{±} with respect to antisymmetric and symmetric nuclear-spin states to be a_{+}=2012(19)a_{0} and a_{−}=193(4)a_{0} for ^{173}Yb, and a_{+}=232(3)a_{0} and a_{−}=372(1)a_{0} for ^{171}Yb.
- Published
- 2022
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