Ba An Nguyen

We introduce a novel class of higher-order, three-mode states called K-dimensional trio coherent states. We study their mathematical properties and prove that they form a complete set in a truncated Fock space. We also study their physical content by explicitly showing that they exhibit nonclassical features such as oscillatory number distribution, sub-poissonian statistics, Cauchy-Schwarz inequality violation and phase-space quantum interferences. Finally, we propose an experimental scheme to realize the state with K=2 in the quantized vibronic motion of a trapped ion.

We study the Hillery-type, i.e. $N$-th power, amplitude squeezing in the fan-state $| ξ;2k,f>_{F}$ characterized by $ξ\in \mathcal{C}$, $k=1,2,3,...$ and $f$ a nonlinear operator-valued function. We show that for a given $k$ there exists a critical $ξ_c$ such that for $0<|ξ|\leq|ξ_c|$ squeezing occurs simultaneously in $2k$ directions for the powers $N$ which are a multiple of $2k$. This result does not depend on the concrete form of $f$, i.e. it holds true for both $f\equiv 1$ and $f\neq 1$. However, for $f\neq 1$, which is realized here in the ion trap context, the squeezing directions as well as the magnitude of $ξ$ can be controlled by adjusting the system driving parameters.

We improve a previously proposed scheme (Phys. Rev. A 66 (2002) 065401) for generating vibrational trio coherent states of a trapped ion. The improved version is shown to gain a double advantage: (i) it uses only five, instead of eight, lasers and (ii) the generation process can be made remarkably faster.