Symplectic tomography of nonlinear coherent states of a trapped ion

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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Even and Odd Coherent States of the Motion of a Trapped Ion

Physical Review Letters ◽

10.1103/physrevlett.76.608 ◽

1996 ◽

Vol 76 (4) ◽

pp. 608-611 ◽

Cited By ~ 198

Author(s):

R. L. de Matos Filho ◽

W. Vogel

Keyword(s):

Coherent States ◽

Trapped Ion

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Dark pair coherent states of the motion of a trapped ion

Physical Review A ◽

10.1103/physreva.54.r1014 ◽

1996 ◽

Vol 54 (2) ◽

pp. R1014-R1017 ◽

Cited By ~ 101

Author(s):

S. -C. Gou ◽

J. Steinbach ◽

P. L. Knight

Keyword(s):

Coherent States ◽

Trapped Ion

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Collapses and revivals of the coherence of a mesoscopic superposition of motional states.

Australian Journal of Physics ◽

10.1071/ph99056 ◽

2000 ◽

Vol 53 (3) ◽

pp. 413 ◽

Cited By ~ 1

Author(s):

Shi-Biao Zheng

Keyword(s):

Coherent States ◽

Quantum Coherence ◽

Vibrational Excitation ◽

Ion Motion ◽

Trapped Ion ◽

Schrödinger Cat ◽

Excitation Exchange ◽

Schrodinger Cat State

A scheme is proposed to observe the collapses and revivals of a mesoscopic superposition of coherent states in the motion of a trapped ion. In the scheme the ion motion in the x-axis is first prepared in a Schrödinger cat state, and then coupled to the motion in the z-axis. With the vibrational excitation exchange between the two modes, the mesoscopic quantum coherence collapses and revives periodically, providing an example for complementarity.

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