Generation of Pair Coherent States in Two-dimensional Trapped Ion

A scheme is presented for the generation of superpositions of two two-mode SU(2) coherent states of the motion for a trapped ion. In the scheme an ion is trapped in a two-dimensional isotropic harmonic potential and driven by two resonant laser beams. Under certain conditions, the motional two-mode SU(2) cat state can be generated after a conditional measurement on the internal state following the ion-laser interaction.

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Scalable loading of a two-dimensional trapped-ion array

Nature Communications ◽

10.1038/ncomms13005 ◽

2016 ◽

Vol 7 (1) ◽

Cited By ~ 20

Author(s):

Colin D. Bruzewicz ◽

Robert McConnell ◽

John Chiaverini ◽

Jeremy M. Sage

Keyword(s):

Two Dimensional ◽

Trapped Ion

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Generation of arbitrary two-dimensional motional states of a trapped ion

Physical Review A ◽

10.1103/physreva.65.045801 ◽

2002 ◽

Vol 65 (4) ◽

Cited By ~ 5

Author(s):

XuBo Zou ◽

K. Pahlke ◽

W. Mathis

Keyword(s):

Two Dimensional ◽

Trapped Ion

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Probabilistic aspects of the SU(2)-harmonic oscillator

Journal of Applied Probability ◽

10.1239/jap/1014842289 ◽

2000 ◽

Vol 37 (1) ◽

pp. 306-314

Author(s):

Shunlong Luo

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Probability Distributions ◽

Quantum Probability ◽

Dimensional Sphere ◽

Large Radius ◽

Two Dimensional ◽

Bargmann Transform ◽

Gaussian Distributions ◽

Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

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Coherent states for Smorodinsky-Winternitz potentials

Open Physics ◽

10.2478/s11534-009-0039-3 ◽

2009 ◽

Vol 7 (4) ◽

Cited By ~ 4

Author(s):

Nuri Ünal

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Wave Packets ◽

Harmonic Oscillators ◽

Polar Coordinates ◽

Two Dimensional ◽

Cartesian Coordinates ◽

Physical Time ◽

First Case

AbstractIn this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.

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Probabilistic aspects of the SU(2)-harmonic oscillator

Journal of Applied Probability ◽

10.1017/s0021900200015461 ◽

2000 ◽

Vol 37 (01) ◽

pp. 306-314

Author(s):

Shunlong Luo

Keyword(s):

Harmonic Oscillator ◽

Coherent States ◽

Probability Distributions ◽

Quantum Probability ◽

Dimensional Sphere ◽

Large Radius ◽

Two Dimensional ◽

Bargmann Transform ◽

Gaussian Distributions ◽

Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Download Full-text