Quantum control of a Paul-trapped ion via double radio-frequency driving

Due to an infinite series solution of the classical Mathieu equation, using single-radio-frequency (rf) driving makes it difficult to manipulate motional states of a Paul-trapped ion. Here, we apply double-rf driving consisting of two external fields to generate the squeezed coherent states of simple forms. Stability parameter regions of the system are found in which both the first and second rf fields may be very strong but only the latter can be weak. Based on exact solutions, we investigate the time evolutions of expectation energies and controllable transitions between not only two stationary states, but also two nonstationary states. Such a quantum-control scenario may be tested experimentally.