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arXiv:quant-ph/9708008 · Physical Review A

Engineering two-mode interactions in ion traps

Jörg Steinbach, Jason Twamley, P. L. Knight

Published Dec 1, 1997• 101 citations
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Abstract

We describe how two vibrational degrees of freedom of a single trapped ion can be coupled through the action of suitably chosen laser excitation. We concentrate on a two-dimensional ion trap with dissimilar vibrational frequencies in the $x$ and $y$ directions of motion and derive from first principles a variety of quantized two-mode couplings, concentrating on a linear coupling that takes excitations from one mode to another. We demonstrate how this can result in a state rotation, in which it is possible to transfer the motional state of the ion from, say, the $x$ direction to the $y$ direction without prior knowledge of that motional state.

DOI
10.1103/physreva.56.4815

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We describe how two vibrational degrees of freedom of a single trapped ion can be coupled through the action of suitably chosen laser excitation. We concentrate on a two-dimensional ion trap with dissimilar vibrational frequencies in the xxx and yyy directions of motion and derive from first principles a variety of quantized two-mode couplings, concentrating on a linear coupling that takes excitations from one mode to another. We demonstrate how this can result in a state rotation, in which it is possible to transfer the motional state of the ion from, say, the xxx direction to the yyy direction without prior knowledge of that motional state.
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.
We propose a scheme for generating mesoscopic superpositions of two distinguishable pair coherent states of motion in a two-dimensional ion trap. In our scheme, the trapped ion is excited bichromatically by five laser beams along different directions in the X-Y plane of the ion trap. Four of these have the same frequency and can be derived from the same source, reducing the demands on the experimentalist. We show that if the initial vibrational state is given by a two-mode Fock state, as demonstrated in recent experiments, these highly correlated two-mode ``Schr\"odinger cat'' states are realized when the system reaches its steady state, which is indicated by the extinction of the fluorescence emitted by the ion. \textcopyright{} 1996 The American Physical Society.
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.