Quantum Dynamics of a Single Trapped Ion Interacting with Standing Laser Pulses

Li Fei, Hai Wen-Hua, Chong Gui-Shu +1 more

A classically chaotic system consisting of a Paul trapped ion and a sequences of standing laser pulses is treated quantum-mechanically. Under the circumstance of time-dependence, we derive the transition probability from the ion's motional state to ', and find, in the first-order approximation, the classically chaotic character disappears. Theoretical analysis and numerical calculations show that by regulating the phase parameter we can control the transition probability. When reaches some specific values, the transition from the state to ' is forbidden and, for some laser periods, resonance occurs, which leads to the corresponding transitions between different motional states. The time-evolution of an initial motional state just over one period is also studied in detail.

Rasim Dermez, Bekir Deveci, Durdu Ö. Güney

Randall G. Hulet, Jonas Bergquist, David J. Wineland

Yang Mei-Rong, Hai Wen-Hua, Gengbiao Lu +2 more

We investigate the secular motion of a single Paul-trapped ion in the Lamb-Dicke regime, which interacts with a sequence of standing laser pulses. By using the ansatz method, we get an exact quantum solution of the system. Based on the wave-packet trains described by the exact solution, we find that: i) The center, height and width of the wave-packet trains depend on the strength of laser pulses, the deformation and spread of the wave-packet trains can be controlled by adjusting the strength of laser. ii) Energy expectation values of the ion show jumps at the instantaneous switching on of the laser pulses. In the time intervals when the laser pulses are switched off some narrow energy bands are generated. iii) When the strength of laser pulses reaches a critical value, the system changes its stability.

J. K. Breslin, Catherine A. Holmes, Gerard J Milburn

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C. A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Wayne M. Itano, Jonas Bergquist, F. Diedrich +1 more