Penning trap from the phase space quantum mechanics point of view

Y S Kim, Marilyn E. Noz

G. Horváth, Richard Claude Thompson

We present a phase-space picture of laser cooling of the radial motion of ions in a Penning trap. This picture enables a particularly simple derivation of the condition for simultaneous cooling of all degrees of freedom of a single ion to be obtained. It also allows a physically intuitive approach to be taken to the cooling process. Using this approach, we discuss different aspects of the cooling of a single ion in a Penning trap, including the formation of ``trapped'' states where the steady-state motion amplitude is nonzero for either the magnetron or modified cyclotron motion. We use an analytical approach where the approximation of small-amplitude motions can be made, and we use numerical calculations for larger-amplitude motions. The best procedure to use for effective laser cooling is derived. A similar approach is then used to treat the laser cooling of two ions in the Penning trap. We show that the use of the phase-space approach allows new insights into many aspects of the laser-cooling process to be gained, and we indicate how these insights may be applied in experimental investigations.

J C David Fernández

We explain the meaning of dynamical manipulation, and we illustrate its mechanism by using a system composed of a charged particle in a Penning trap. It is shown that by means of appropriate electric shocks (delta-like pulses) applied to the trap walls one can induce the squeezing transformation. The geometric phases associated to some cyclic evolutions, induced either by the standard fields of the Penning trap or by the superposition of these plus a rotating magnetic field, are analysed.

James A. Brooke, Franklin E. Schroeck

Franklin E. Schroeck

Michael Genkin, Eva Lindroth

We study the time evolution of a charged particle in a Penning trap in the framework of open quantum systems. The interaction with the environment is taken into account by imposing Lindblad operators which are linear in the canonical variables. For the special case of a proton in an asymmetric Penning trap, we compare the dynamics with earlier results obtained from the unitary time-dependent Schrödinger equation. A possibility of estimating the spatial decoherence time of the system is discussed, and approximate decoherence time scales are given for different ions.