Coherence of states in trapped ions

C. J. Myatt, B. E. King, Q. A. Turchet

Shih-Chuan Gou, Jörg Steinbach, P. L. Knight

We propose a scheme for generating vibrational pair coherent states of the motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is excited bichromatically by three laser beams along different directions in the $X\ensuremath{-}Y$ plane of the ion trap. We show that if the initial vibrational state is given by a two-mode Fock state, the final steady state, indicated by the extinction of the fluorescence emitted by the ion, is a pure state. The motional state of the ion in the equilibrium realizes that of the highly correlated pair coherent state.

D. J. Wineland, Christopher R. Monroe, W. M. Itano +4 more

Coherent manipulations involving the quantized motional and internal states of a single trapped ion can be used to simulate the dynamics of other systems. We consider some examples, including the action of a Mach Zehnder interferometer which uses entangled input states. Coherent manipulations can also be used to create entangled states of multiple trapped ions; such states can be used to demonstrate fundamental quantum correlations.

Marcelo Terra Cunha, Maria Carolina Nemes

Wayne M. Itano, James C Bergquist, J. J. Bollinger +5 more

Olga V. Man’ko

Simplectic tomography of the one-mode problem of an ion in a Paul trap, and of the two-mode problem of an ion in a Penning trap is discussed. The marginal distribution of quadrature for nonlinear coherent states of a trapped ion is studied. The N-mode tomography for nonlinear coherent states and Schrodinger cat states is considered.