Magnetic Trapping of Ultracold Rydberg Atoms

We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-$n$-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.

Figure 1

Intersection through the adiabatic potential curves of the $n=3$ multiplet for $Z=0$. Three regimes can be distinguished. The angular momentum barrier dominated regime with a visible ${\rho }^{-2}$ dependence, the regime dominated by the electronic energy, and for large $\rho$ the Zeeman-splitting indicating the onset of the local homogeneity limit can be observed.

Figure 2

Uppermost energy surface in the $n=35$ multiplet with $m_T=64.5$ and $\gamma =1.586\times {10}^{-10}$. This value of $\gamma$ corresponds to a ${}^{87}\mathrm{Rb}$ atom in a quadrupole field with a gradient of $b=4.45{\mathrm{Tm}}^{-1}$. The energy surface exhibits a well-pronounced minimum in the $\rho \mathrm{\text{−}}Z$ plane; i.e., the c.m. wave functions form concentric rings with a diameter of about $1.2\mu \mathrm{m}$ around the $z$ axis of the quadrupole trap.