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Physical Review A

Generation of three-mode nonclassical vibrational states of ions

Nguyen Ba An, Truong Minh Duc

Published Dec 6, 2002• 10 citations
Publisher

Abstract

We propose using eight lasers with appropriate orientations and conditions to generate stable trio coherent states of an ion in a three-dimensional isotropic trap. Seven lasers whose orientations are important should be detuned to the third lower sideband of the ion vibrational motion. The eighth laser whose direction is not important should be in resonance with the ionic transition.

DOI
10.1103/physreva.66.065401

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We propose using eight lasers with appropriate orientations and conditions to generate stable trio coherent states of an ion in a three-dimensional isotropic trap. Seven lasers whose orientations are important should be detuned to the third lower sideband of the ion vibrational motion. The eighth laser whose direction is not important should be in resonance with the ionic transition.
We present a scheme to generate an arbitrary two-dimensional quantum state of motion of a trapped ion. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on the sidebands of two modes of vibration. Not more than (M+1)(N+1)(M+1)(N+1)(M+1)(N+1) laser pulses are needed to generate a pure state with a phonon number limit M and N.
We propose a scheme for preparation of entangled coherent states for the motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion is driven by four laser beams along different directions in the ion trap plane, resulting in carrier excitation and couplings between the internal and external degrees of freedom. When the total quantum number of the vibrational modes initially has a definite parity, the competition between the unitary dynamics and spontaneous emission will force the system to evolve to a steady state, where the vibrational modes are in a two-mode cat state. We show that the method can be extended to realization of entangled coherent states for three vibrational modes of an ion in a three-dimensional anisotropic trap.
Using the nonlinear coherent states approach, a general formalism for the construction of various classes of nonlinear trio coherent states in the context of multi-mode quantum states has been proposed. In particular, taking into account the most popular nonlinearity function associated with f -deformed coherent states, i.e. the nonlinearity function of the centre-of-mass motion of a trapped ion, it is illustrated that the corresponding trio coherent state possesses some interesting nonclassical properties. To establish this observation, sub-Poissonian statistics, three-mode squeezing, the behaviour of Vogel's characteristic function and the existence of entanglement are investigated. Due to the intrinsic non-classicality nature of the considered three-mode states, their physical production may be of high interest in the quantum optics field. Thus, we have finally demonstrated how nonlinear motional trio coherent states can be generated in three-dimensional anisotropic traps, appropriately.
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.