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International Journal of Optics and Photonics

Generation of Nonclassical States of the Radiation Field in the System of a Single Trapped Atom in a Cavity within the First Order of the Lamb-Dicke Approximation

M. H. Naderi, somayeh salimian rizi

Published Jan 15, 2014• 0 citations
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Investigation of generation of non-classical states for the radiation field in the system of a trapped atom in a cavity within the first order of the Lamb-Dicke approximation

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ENGINEERING MACROSCOPIC QUANTUM STATES OF A SINGLE TRAPPED ION: HIGHER-ORDER LAMB–DICKE APPROXIMATIONS

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The effects of higher-order Lamb–Dicke approximations (LDAs), on engineering motional quantum states of a single trapped cold ion, are discussed. By measuring the internally electronic states of a single trapped cold ion, which is driven by two classical laser beams tuning respectively to the first upper and lower sidebands, we show that the externally macroscopic vibrational states superposed by either even or odd number states are generated. Under the LDA (i.e., only the first order effect of LD parameter η is considered), these states just are the usual even and odd coherent states. For relative large values of η, we showed that the effects of higher-order LDAs, i.e., terms relating to ηk, k ≥ 2, are not negligible. They might significantly enhance certain nonclassical properties, e.g., squeezing and antibunching effects of the generated macroscopic quantum states.

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A scheme of quantum phase gate for trapped ion

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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.

Chinese Physics•Jun 1, 2007•6 citations
The effects of higher-order Lamb–Dicke approximations (LDAs), on engineering motional quantum states of a single trapped cold ion, are discussed. By measuring the internally electronic states of a single trapped cold ion, which is driven by two classical laser beams tuning respectively to the first upper and lower sidebands, we show that the externally macroscopic vibrational states superposed by either even or odd number states are generated. Under the LDA (i.e., only the first order effect of LD parameter η is considered), these states just are the usual even and odd coherent states. For relative large values of η, we showed that the effects of higher-order LDAs, i.e., terms relating to ηk, k ≥ 2, are not negligible. They might significantly enhance certain nonclassical properties, e.g., squeezing and antibunching effects of the generated macroscopic quantum states.
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 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.