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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Generation of two-mode squeezed pair-coherent states of the motion of a trapped ion

Shi‐Biao Zheng, Guang‐Can Guo

Published Apr 1, 1998• 10 citations
Publisher

Abstract

We propose a scheme for generating motional two-mode squeezed pair-coherent states of an ion trapped in a three-dimensional isotropic trap. It is based on the multichromatic excitation of the ion by six lasers in the x - y plane, and one in the z -axis. Under certain conditions, the system finally reaches the steady state, in which the vibrational motions in the x and y axes are in the two-mode squeezed pair-coherent state and the motion in the z -axis is in the vacuum state.

DOI
10.1088/1355-5111/10/2/015

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Acta Sinica Quantum Optica•Jan 1, 2003•0 citations
We propose a scheme for generating motional two-mode squeezed pair-coherent states of an ion trapped in a three-dimensional isotropic trap. It is based on the multichromatic excitation of the ion by six lasers in the x - y plane, and one in the z -axis. Under certain conditions, the system finally reaches the steady state, in which the vibrational motions in the x and y axes are in the two-mode squeezed pair-coherent state and the motion in the z -axis is in the vacuum state.
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.
We propose a scheme to generate mesoscopic superpositions of two squeezed states of motion using a highly anisotropic two-dimensional trap in which the ion's motion is tightly bound in the Y direction. In our scheme, the ion is driven multichromatically by three codirectional laser beams along the X axis, as well as a resonant laser beam along the Y axis. We show that, with the appropriate chosen initial states, the desired states of motion are realized in the X direction when the system reaches its steady state, which is indicated by the extinction of the fluorescence from the ion.
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.