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Physical Review A

Quantum conversion between the cavity fields and the center-of-mass motion of ions in a quantized trap

Heping Zeng, Fucheng Lin

Published Nov 1, 1994• 68 citations
Publisher

Abstract

We propose a technique to generate nonclassical vibrational states of the quantized center-of-mass motion of an ion in a harmonic trap, based on the quantum conversion between the quantum cavity field and the quantized center-of-mass motion. It is shown that when an ion trap system interacts with the eigenmode of a single-mode Fabry-P\'erot cavity, where the trap is set in, and with an external classical driving electromagnetic field through Raman transitions, the interchange of the quantum features between the quantum cavity field and the quantized trap occurs. This kind of quantum conversion can be used to prepare some nonclassical trap states for the ion trap as well as to measure the quantum statistics of an initial nonclassical vibrational state.

DOI
10.1103/physreva.50.r3589

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We propose a technique to generate nonclassical vibrational states of the quantized center-of-mass motion of an ion in a harmonic trap, based on the quantum conversion between the quantum cavity field and the quantized center-of-mass motion. It is shown that when an ion trap system interacts with the eigenmode of a single-mode Fabry-P'erot cavity, where the trap is set in, and with an external classical driving electromagnetic field through Raman transitions, the interchange of the quantum features between the quantum cavity field and the quantized trap occurs. This kind of quantum conversion can be used to prepare some nonclassical trap states for the ion trap as well as to measure the quantum statistics of an initial nonclassical vibrational state.
A novel recipe is proposed to generate nonclassical vibrational states of the center-of-mass motions of ions in a quantized trap, based on the quantum conversion between the quantum cavity fields and the quantized trap. It is shown that, when an ion trap system interacts with the eigen mode of a single-mode Fabry-Pérot cavity where the trap was set in, and a particularly selected external laser pulse through Raman transitions, the interchange of the quantum features between the quantum light states and the quantized trap states occurs. This kind of quantum conversion can be used to prepare some nonclassical trap states in an ion trap as well as to measure the properties of initial nonclassical vibrational states.
The quantized center-of-mass (c.m.) motions of a single two-level atom or ion confined into a one-dimensional harmonic potential and interacting with a single-mode classical traveling-wave laser field are examined. We demonstrate that trap quantum states with remarkable nonclassical properties such as quadrature and amplitude-squared squeezing and sub-Poissonian statistics can be generated in this simple trap model when the c.m. motion is initially in certain coherent trap states. Our analyses also indicate that there exist some time regions where the production of nonclassical vibrational states is possible even if squeezing or sub-Poissonian statistics do not appear.
We consider a trapped ion with a quantized center-of-mass motion in 2D trap potential. With external laser fields the effective (non)linear coupling of two orthogonal vibrational modes can be established via stimulated Raman transition. Nonclassical vibrational states such as squeezed states or two-mode entangled states (Schroedinger cat-like states) can be generated. When the vibrational modes are entangled with internal energy levels the Greenberger-Horne-Zeilinger (GHZ) states can be prepared.
We propose a generation method of Bell-type states involving light and the vibrational motion of a single trapped ion. The trap itself is supposed to be placed inside a high-QQQ cavity sustaining a single mode, quantized electromagnetic field. Entangled light-motional states may be readily generated if a conditional measurement of the ion's internal electronic state is made after an appropriate interaction time and a suitable preparation of the initial state. We show that all four Bell states may be generated using different motional sidebands (either blue or red), as well as adequate ionic relative phases.