Magnetic trapping of neutral particles: Classical and Quantum-mechanical study of a Ioffe-Pritchard type trap

Recently, we developed a method for calculating the lifetime of a particle inside a magnetic trap with respect to spin flips, as a first step in our efforts to understand the quantum-mechanics of magnetic traps. The 1D toy model that was used in this study was physically unrealistic because the magnetic field was not curl-free. Here, we study, both classically and quantum-mechanically, the problem of a neutral particle with spin S, mass m and magnetic moment μ, moving in 3D in an inhomogeneous magnetic field corresponding to traps of the IoffePritchard, ‘clover-leaf’ and ‘baseball’ type. Defining by ωp, ωz and ωr the precessional, the axial and the lateral vibrational frequencies, respectively, of the particle in the adiabatic potential Veff = μ |B|, ∗Also with the Center for Technological Education Holon, 52 Golomb St., P.O.B 305, Holon 58102, Israel. †Also with the Department of Physics, University of California, San Diego, La Jolla, 92093 CA, USA.