Stability of the RF paul trap revisited: A state space approach

In this paper, we analyze the stability of a ring radio frequency Paul trap in the Lyapunov sense, using the state space approach. This involves constructing a state-space model based on the relevant statistical moments of the quantum system. This formulation enables the application of state-space control techniques to assess the trap’s stability. We also establish a double implication between the dynamics of the mean values and uncertainties. This provides a theoretical basis for neglecting uncertainties in a first-order stability analysis. Additionally, we present an alternative method for computing the trap’s stability diagram in terms of the system’s parameters. This method benefits practical trap design. Simulations illustrating the main results are given.