Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.
Collisions between tightly confined atoms can lead to ionization and hence to loss of atoms from the trap. We develop second-order perturbation theory for a tensorial perturbation of a spherically symmetric system and the theory is then applied to processes mediated by the spin-dipole interaction. Redistribution and loss mechanisms are studied for the case of spin-polarized metastable helium atoms and results obtained for the five lowest s states in the trap and trapping frequencies ranging from 1 kHz to 10 MHz.
We consider the problem of cold atomic collisions in tight traps, where the absolute scattering length may be larger than the trap size. As long as the size of the trap ground state is larger than a characteristic length of the van der Waals potential, the energy eigenvalues can be computed self-consistently from the scattering phase shift for untrapped atoms. By comparing with the exact numerical eigenvalues of the trapping plus interatomic potentials, we verify that our model gives accurate eigenvalues up to milliKelvin energies for single-channel s-wave scattering of
23Na atoms in an isotropic harmonic trap, even when outside the Wigner threshold regime. Our model works also for multichannel scattering, where the scattering length can be made large due to a magnetically tunable Feshbach resonance.
We compute the ground-state energy of two atoms in a one-dimensional geometry of a harmonic optical trap. We obtain a dependence of the energy on a one-dimensional scattering length, which corre-sponds to various strengths of the interaction potential V int (x) = V 0 exp {−2cx 2}. The calculation is performed by numerical and analytical methods. For the analytical method we choose the oscillator representation method (OR), which has been successfully applied to computations of bound states of various few-body systems. The main results of this paper are (1) a numerical investigation of the validity range of the previously used pseudopotential method and (2) an investigation of the validity range of the OR for the potential V(x) = V conf (x) + V int (x) = x 2/2 + V 0 exp {−2cx 2}.
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 ${\ensuremath{\varepsilon}}_{\mathrm{r}}$ of two-atom relative motion, i.e., $a=a({\ensuremath{\varepsilon}}_{\mathrm{r}})$, 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'' ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathrm{eff}}$, for the above complicated cases. Here, ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathrm{eff}}$ 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 ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathrm{eff}}$. We further show a method based on the quantum defect theory, with which ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{\mathrm{eff}}$ 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
1S0 $(|g\ensuremath{\rangle})$ and
3P0 $(|e\ensuremath{\rangle})$ states, respectively] confined in an optical lattice. By comparing our results with the recent experimental measurements for two
173Yb atoms and two
171Yb atoms, we calibrate the scattering lengths ${a}_{\ifmmode\pm\else\textpm\fi{}}$ with respect to antisymmetric and symmetric nuclear-spin states to be
a+=2012(19)a0 and ${a}_{\ensuremath{-}}=193(4){a}_{0}$ for
173Yb, and
a+=232(3)a0 and ${a}_{\ensuremath{-}}=372(1){a}_{0}$ for
171Yb.
We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in
p wave and confined in an axially symmetric harmonic trap. To this end we utilize
p-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a
p-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the
p-wave Feshbach resonance.