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Chinese Physics B

Generation of Schrödinger cat state of a single trapped cold ion

Miao Zhang, Jia Huan-Yu, Ji Xiao-Hui, Si Kun

Published Mar 1, 2009• 0 citations
Publisher

Abstract

The fidelity of the generated Schrodinger Cat state (SCS) of a single trapped ion in the Lamb–Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb–Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb–Dike approximation in laser–ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb–Dicke parameters.

DOI
10.1088/1674-1056/18/3/035

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The fidelity of the generated Schrodinger Cat state (SCS) of a single trapped ion in the Lamb–Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb–Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb–Dike approximation in laser–ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb–Dicke parameters.
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.
Based on the conditional quantum dynamics of laser-ion interactions, we propose an efficient theoretical scheme to deterministically generate quantum pure states of a single trapped cold ion without performing the Lamb-Dicke approximation. An arbitrary quantum state can be created by sequentially using a series of classical laser pulses with selected frequencies, initial phases and durations. As special examples, we further show how to create or approximate several typical macroscopic quantum states, such as the phase state and the even/odd coherent states. Unlike previous schemes operating in the Lamb-Dicke regime, the present one does well for an arbitrary-strength coupling between the internal and external degrees of freedom of the ion. The experimental realizability of this approach is also discussed.