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Journal of Optics B Quantum and Semiclassical Optics

Generations of macroscopic quantum states of a single trapped ion beyond the Lamb–Dicke limit

Qinghong Yang, L. F. Wei, Liangyu Ding

Published Nov 18, 2004• 3 citations
Publisher

Abstract

On the basis of the quantum dynamics of laser–ion interaction beyond the Lamb–Dicke limit, we show how the macroscopic quantum states, typically, e.g., the even/odd coherent states, of a single trapped cold ion can be effectively approached via the superpositions of motional Fock states generated from the motional ground state. The fidelity and experimental realizability of this approach are discussed.

DOI
10.1088/1464-4266/7/1/002

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On the basis of the quantum dynamics of laser–ion interaction beyond the Lamb–Dicke limit, we show how the macroscopic quantum states, typically, e.g., the even/odd coherent states, of a single trapped cold ion can be effectively approached via the superpositions of motional Fock states generated from the motional ground state. The fidelity and experimental realizability of this approach are discussed.
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.
Based on the quantum dynamics of laser-ion interaction beyond the Lamb-Dicke limit，we discuss how to superpose a series of vibrational number states from motional ground state by sequentially applying laser beams. The Q function，Wigner distribution function，and the nonclassical properties such as squeezing effect and anti-bunching effect of the generated superposition states are investigated in detail by numerical method. It is shown that，by controlling the durations of the applied laser pulses，these quantum states could well approach to the well-known coherent states.
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 quantum dynamics of laser-ion interaction beyond the Lamd_Dicke limit, we discuss how to superpose a series of vibrational number states of a single trapped ion from the motional ground state. It is shown that, by controlling the durations and phases of the sequentially applied laser pulses, these superposed quantum states could well approach to the various target quantum states, e.g., squeezed coherent states, squeezed odd/even coherent states and squeezed vacuum states, etc.Their experimental realizabilities are also discussed.
Trapping ions outside the Lamb–Dicke limit have been proven to be useful for the laser-cooling and quantum computing. Under the supposition of the Rabi frequency much smaller than the Lamb–Dicke parameter, we can use a simple method to analytically solve the system with a single cold ion trapped and radiated beyond the Lamb– Dicke limit, in the absence of the rotating-wave approximation (RWA). Discussion has been made for the limitation of our approach and the comparison of our results with the solutions under the RWA.
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.