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Physical Review A

Motional wave-packet splitting and ion-trap interferometry

Heping Zeng

Published Jan 1, 1998• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.57.388

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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.
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.
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 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.
Abstract A single 40Ca ion is confined in the harmonic potential of a Paul trap and cooled to a temperature of a few mK, with a wave packet of sub-μm spatial and sub-m s−1 velocity uncertainty. Deterministically extracted from the Paul trap, the single ion is propagating over a distance of 0.27 m and detected. By engineering the ion extraction process on the initial wave packet, theoretically modeling the ion trajectories, and studying experimentally the time-of-flight distribution, we directly infer the state of the previously trapped ion. This analysis allows for accurate remote sensing of the previous motional excitation in the trap potential, both coherently or incoherently. Our method paves a way to extract, manipulate and design quantum wave packets also outside of the Paul trap.