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Physical Review A

Raman motional displacements of a trapped ion in the strong excitation regime

Heping Zeng, Fucheng Lin, Yuzhu Wang, Yusaburo Segawa

Published Jun 1, 1999• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.59.4589

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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.
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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.
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.
The interaction of a cold trapped ion with a strong laser field is studied in a configuration in which quasienergetic levels become important but heating of the system is unessential. Absorption spectroscopy of the quasienergetic states of a strongly confined and laser-driven trapped ion is analyzed by probing vibrational transitions. Calculations are carried out analytically by using the master equation in quasienergetic state representation. We consider a V\mathsf{V}V-level scheme for the ion with a resonant strong pump field and a weak probe field. The steady-state and time-evolution behavior of the system is discussed and the probe-field absorption spectrum for various initial population distributions of the motional state is calculated. It is found that the absorption spectrum displays vibrational sidebands with multipeak splitting due to the nonlinear dependence of the Rabi frequencies on both the Lamb-Dicke parameter and the trap occupation number. This multipeak splitting has interesting consequences and can be useful for the measurement of the initial trap number population distribution.
Raman interaction between two internal levels and its sideband cooling of a trapped ion or atom are investigated in copropagating traveling-wave light fields for localization beyond the Lamb-Dicke limit. Under certain conditions, only the first-order sideband excitations (\ensuremath{\Vert}n〉\ensuremath{\rightarrow}\ensuremath{\Vert}n\ifmmode\pm\else\textpm\fi{}1〉 with \ensuremath{\Vert}n〉 being a Fock state) may play a significant role. This provides an experimental realization of the Jaynes-Cummings model with quantized center-of-mass motion beyond the Lamb-Dicke regime, which can be used to measure the statistics of the quantized motion, and thus to detect nonclassical states of motion. Moreover, the multichromatic two-photon Raman excitations of the trapped particle can be used for the preparation of coherent squeezed states of motion.