Effects of anisotropy in control of ultracold atom-atom collisions by a light field

Vladimir Melezhik

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia

We analyze possible controlling at ultralow temperatures the atom-atom interaction by a nonresonant optocal laser.

Including into consideration the finiteness of the laser wavelength $\lambda_{L}$ or the alteration of the laser polarization makes the problem of ultracold atom-atom collisions in the laser field nonseparable over both angular variables $\theta$ and $\phi$ (scattering angles). It leads to essentially anisotropic scattering. For treating this problem we developed an approach without usual partial-wave expansion [1]. Here the angular part of the scattering wave-function is approximated in the spirit of the discrete-variable representation [2] or Lagrange-mesh [3]. The method was suggested in [4] for solving nonseparable two-dimensional scattering problem and extended to three-dimensional atoms in strong fields [5,6].

With this approach we find considerable influence of a nonresonant optical laser of intensity $I\geq 10^{5} W/cm^{2}$ on the Cs-Cs ultracold collisions:

1) In such field the scattering becomes strongly anisotropic even in the region of ulralow colliding energies where the $s$-wave dominates at $I=0$. I.e. the usual scattering length approach $f(k,\hat{\bf k_{i}},\hat{\bf k_{f}}) = -a_{0}$ does not work and one has to analyze the stability of BEC for unusual behavior of the amplitude $f(k,\hat{\bf k_{i}},\hat{\bf k_{f}}) =f(\hat{\bf k_{i}},\hat{\bf k_{f}})$ at $k\rightarrow 0$. At that the amplitude may be strongly dependent on the $\lambda_{L}$, on the relative atom-atom orientation with respect to the field $\hat{\bf k_{i}}$ and on the scattering angle $\hat{\bf k_{f}}$, even changes the sign at some $\hat{\bf k_{i}}$ and $\hat{\bf k_{f}}$.

2) The maximum anisotropy is developed for the linear laser polarization. The differential cross section may change from zero at some angles up to hundreds a.u. in the direction of polarization.

3) Strong dependence on the laser wavelength $\lambda_{L}$ is shown at the optical region as $\lambda_{L}$ becomes shorter than the critical value $\lambda_{0} \sim 3000$ nm (of the de Broglie wave $\lambda$) defining the region $\lambda\geq \lambda_{0}$ of the $s$-wave domination at $I=0$.

It would be interesting to include the considered effects of anysotropy in ulralow collisions into the theoretical models for BEC and to test experimentally.

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[3] D. Baye and P.-H. Heenen, J. Phys. A19, 2041 (1986)
[4] V.S. Melezhik, J. Comput. Phys. 92, 67 (1991)
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[6] P. Fassbinder and W. Schweizer, Phys. Rev. A53, 2135 (1996)