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

Abstract

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.

Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

“…The gates are then driven by electric fields in the radio frequency (rf ) range. 70 This scheme becomes analog to the control of the vibrational states of a diatomic molecule but in a completely different spectral range. Wang and Babikov 69 have recently numerically simulated a four-qubit Shor's algorithm driven by rf pulses obtained by multi-target optimal control theory (MTOCT).…”

Propagator for the general time-dependent harmonic oscillator with application to an ion trap

“…In particular, timedependent frequency is encountered in ion traps; this is due to the fact that the electric potential can have no local minima; thus, in order to trap an ion one must push-pull the ion, resulting in time-dependent frequency (see, e.g., Refs. [5,6]). Using such traps, a number of coherent and squeezed states have been prepared in the vibrational motion of ions [7,8].…”