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Raman sideband transitions and quantum manipulating vibrational motion of a trapped ion

Heping Zeng, Fei Lin

Published Jul 14, 1996• 0 citations
OpenAlex

Abstract

It is well known that electronic transitions driven by nearly resonant travelling- or standing- wave lasers are often accompanied with vibrational sideband transitions of a single trapped ion undergoing quantized center-of-mass motion [1], Our previous studies showed that quantum statistics of radiation fields can be used to manipulate the vibronic motion of a trapped ion localised within the Lamb-Dicke limit (LDL) [2]. The present paper addresses quantum manipulating vibronic motion of an ion trapped far beyond the LDL.

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It is well known that electronic transitions driven by nearly resonant travelling- or standing- wave lasers are often accompanied with vibrational sideband transitions of a single trapped ion undergoing quantized center-of-mass motion [1], Our previous studies showed that quantum statistics of radiation fields can be used to manipulate the vibronic motion of a trapped ion localised within the Lamb-Dicke limit (LDL) [2]. The present paper addresses quantum manipulating vibronic motion of an ion trapped far beyond the LDL.
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.
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.
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.
We propose a model for a single-trapped-ion vibronic Raman laser and study its dynamics by using quantum-trajectory methods. In our treatment, it is essential that both the cavity field of the high-finesse optical cavity and the center-of-mass vibrational motion of the trapped ion be quantized. A transition from a super-Poissonian light source to a Poissonian lasing regime is obtained by increasing the Raman coupling constant. Furthermore, we demonstrate that a nonclassical regime can be realized, where the photon statistics becomes sub-Poissonian and the photons leak out of the cavity in an antibunched manner. This is achieved by exploiting nonlinear Stark shifts inherent in the model, which depend on both the number of cavity photons and the number of vibrational quanta.
We propose a scheme to implement two-qubit controlled quantum phase gate(CQPG) via a single trapped two-level ion located in the standing wave field of a quantum cavity, in which the trap works beyond the Lamb–Dicke limit. When the light field is resonant with the atomic transition |g > ↔ |e> of the ion located at the antinode of the standing wave, we can perform CQPG between the internal and external states of the trapped ion; while the frequency of the light field is chosen to be resonant with the first red sideband of the collective vibrational mode of the ion located at the node of the standing wave, we can perform CQPG between the cavity mode and the collective vibrational mode of the trapped ion. Neither the Lamb–Dicke approximation nor the assistant classical laser is needed. Also we can generate a GHZ state if assisted with a classical laser.