TIME-ORBITING-POTENTIAL QUADRUPOLE MAGNETIC TRAP FOR COLD ATOMS

An analytical theory of the time-orbiting-potential quadrupole magneti c trap for cold atoms is developed. It is shown that the rotating magn etic field used to create the time-averaged harmonic potential is resp onsible for the formation of quasienergy states of an atom in the trap . It is found that the motion of an atom near the origin of the trap c an be represented as consisting of slow motion in the time-averaged po tential and fast oscillations with small amplitude. Eigenstates and ei genfunctions for the motion are found. The eigenfunctions are used to calculate the coordinate and momentum distributions for a single atom. It is concluded that at low temperature the quantum-statistical momen tum distribution for a single atom exhibits a ring shaped structure du e to the fast oscillations in the atomic linear momentum. [S1050-2947( 98)00310-2].