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Physical Review A

Macroscopic quantum states of a trapped ion

Heping Zeng, Sing Tang

Published Sep 1, 2000• 0 citations
Publisher

Abstract

The second-sideband Raman excitation of the motional ground state of a single ion trapped in a harmonic potential is analyzed in the strong Raman coupling regime. Appropriate Raman motional excitations driven by strong standing-wave lasers can be used to split the motional ground state to a macroscopic motional wave-packet state with spatial separation between the split parts comparable to the dimension of the involved ionic transition wavelengths. A spatial flat wave-packet with coherence persisting in a wide spatial range can also be excited. The spatial spread of such a spatial flat macroscopic motional wave-packet oscillates periodically during the free-time evolution in the harmonic trap, with a spatial flat distribution persisting at most of the oscillating times.

DOI
10.1103/physreva.62.045402

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Journal of Physics B Atomic Molecular and Optical Physics•Jan 1, 1999•0 citations
The second-sideband Raman excitation of the motional ground state of a single ion trapped in a harmonic potential is analyzed in the strong Raman coupling regime. Appropriate Raman motional excitations driven by strong standing-wave lasers can be used to split the motional ground state to a macroscopic motional wave-packet state with spatial separation between the split parts comparable to the dimension of the involved ionic transition wavelengths. A spatial flat wave-packet with coherence persisting in a wide spatial range can also be excited. The spatial spread of such a spatial flat macroscopic motional wave-packet oscillates periodically during the free-time evolution in the harmonic trap, with a spatial flat distribution persisting at most of the oscillating times.
For a single ion trapped in a harmonic potential under localization conditions beyond the Lamb-Dicke region, a motional wave packet can be coherently split by irradiating the trapped ion with appropriate counterpropagating traveling-wave laser pulses tuned to the second-sideband Raman resonance. Quantum interference between the split wave packets gives rise to interference fringes in the spatial probability distribution when the wave packets spatially overlap at a certain time during a periodic oscillation. An ion-trap interferometer is proposed on the basis of the wave-packet splitter in combination with quantum tomographic determination of the spatial interference fringes.
We consider the first-sideband Raman excitations of a trapped ion in the strong Raman coupling regime on the basis of the splitting approximation. It is demonstrated that not only weak but strong Raman excitations can be used to displace the motional ground state to some well-localized motional states under appropriate conditions. Nonlinear and nonresonant effects are taken into account for the Raman sideband transitions. The condition and limitation for the Raman vibrational excitations to be used for preparing Schr\"odinger cat motional states are analyzed. Quantum interference between the displaced motional states is discussed.
Raman sideband excitations driven by counterpropagating Raman beams are analyzed for the trapped ion under the localization conditions in and beyond the Lamb-Dicke regime. Multiquantum vibrational couplings are demonstrated to produce significant effects on the Raman sideband transitions and the relevant Raman excitations of the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by exciting the motional ground state are closely associated with the nonlinear vibronic couplings, Raman excitation, and localization conditions. Quantum entanglement and quantum interference are discussed for the trapped ion under various Raman excitation and localization conditions. The results are compared with the recent experiments. Further experimental attempts are proposed to use the single trapped 25Mg+{}^{25}{\mathrm{Mg}}^{+}25Mg+ ion in a linear ion trap.
A scheme is presented for the generation of macroscopic quantum-interference states for the motion of a trapped ion. In the scheme the ion is driven by a standing-wave laser beam whose carrier frequency is tuned to the ion transition. The distinct feature of the scheme is that the time required to generate the desired state is limited only by the available laser intensity, not by inherent mechanisms such as off-resonant excitations. Therefore, our scheme may allow the generation of the desired state at a high speed, which is important in view of decoherence. In the two-dimension case, entangled coherent states can be obtained. The scheme can also be used to generate entangled states for multiple modes of NNN trapped ions with a single strong standing-wave laser pulse.
The first sideband Raman excitations driven by counter-propagating Raman beams are analysed for the trapped ion under the localization condition in or beyond the Lamb-Dicke regime. It is demonstrated that multiquantum processes in the vibrational couplings produce significant effects on the the first sideband Raman transitions and the relevant Raman displacements for the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by displacing the motional ground state are demonstrated to be closely associated with the nonlinear vibronic couplings. Quantum entanglement, and quantum interference as well, are discussed for ion traps with various Raman excitation and localization conditions. The results are compared with the recent experiment reported by Monroe C et al in 1996 Science 272 1131-5.