Exact solution of the ion‐laser interaction in all regimes

Zúñiga-Segundo, Arturo; Juárez-Amaro, R.; Vargas-Martínez, J.M.; Moya‐Cessa, H.

doi:10.1002/andp.201100067

Cited by 6 publications

(5 citation statements)

References 24 publications

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“…It has been shown already that for low intensities it is possible also to consider the ion micromotion [26], and by using Ermakov-Lewis invariant methods [30,31,32] it was possible to linearize the ionlaser Hamiltonian when the micromotion was included [44]. Here, we follow Zúñiga et al [45] and show how it is possible to solve the ion-laser interaction in different regimes, including high intensity and medium intensity.…”

Section: Solution In Different Regimes: Dispersive Hamiltoniansmentioning

confidence: 97%

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Ion–laser interactions: The most complete solution

Moya‐Cessa¹,

Soto‐Eguibar²,

Vargas-Martínez³

et al. 2012

Physics Reports

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Trapped ions are considered one of the best candidates to perform quantum information processing. By interacting them with laser beams they are, somehow, easy to manipulate, which makes them an excellent choice for the production of nonclassical states of their vibrational motion, the reconstruction of quasiprobability distribution functions, the production of quantum gates, etc. However, most of these effects have been produced in the so-called low intensity regime, this is, when the Rabi frequency (laser intensity) is much smaller than the trap frequency. Because of the possibility to produce faster quantum gates in other regimes it is of importance to study this system in a more complete manner, which is the motivation for this contribution. We start by studying the way ions are trapped in Paul traps in and review the basic mechanisms of trapping. Then we show how the problem may be completely solved for trapping states; i.e., we find (exact) eigenstates of the full Hamiltonian. We show how in the low intensity regime Jaynes-Cummings and anti-Jaynes-Cummings interactions may be obtained, without using the rotating wave approximation and analyze the medium and high intensity regimes were dispersive Hamiltonians are produced. The traditional approach (low intensity regime) is also studied and used for the generation of non-classical states of the vibrational of the vibrational wavefunction. In particular, we show how to add and subtract vibrational quanta to an initial state, how to produce specific superpositions of number states and how to generate NOON states for the two-dimensional vibration of the ion. It is also shown how squeezing may be measured. The time dependent problem is studied by using Lewis-Ermakov methods, we give a solution to the problem when the time dependence of the trap is considered and also analyze an specific (artificial) time dependence that produces squeezing of the initial vibrational wave function. A way to mimic the ion-laser interaction via classical optics is also introduced.

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Section: Solution In Different Regimes: Dispersive Hamiltoniansmentioning

confidence: 97%

“…In Section 3.1, we showed that the ion-laser Hamiltonian (45) can be casted in the form given by expression (48) by means of the similarity transformation (46). Therefore, we have linearized the ionlaser interaction in an exact way, by means of a unitary transformation; i.e., both Hamiltonians,Ĥ ion andĤ ion are equivalent.…”

Section: Different Regimesmentioning

confidence: 99%

Ion–laser interactions: The most complete solution

Moya‐Cessa¹,

Soto‐Eguibar²,

Vargas-Martínez³

et al. 2012

Physics Reports

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show abstract

“…(4.20b). For practical purpose, let us consider the initial condition | (0) = | | , then, the solution at second order is given by | ( ) , = (2) , cos( taken from Eq.16 and Eq.18 of reference [36], which is the small rotation approximation solution for this system and where high = − 2 2 /2 in the case of high intensity regime. Hence, using Eq.…”

Section: Second Order Correctionmentioning

confidence: 99%

Approximate Solutions for the Ion-Laser Interaction in the High Intensity Regime: Matrix Method Perturbative Analysis

Martínez

Moya‐Cessa²,

Eguibar³

2021

Preprint

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“…taken from Eq.16 and Eq.18 of reference [36], which is the small rotation approximation solution for this system and where high = − 2 2 /2 in the case of high intensity regime. Hence, using Eq.…”

Section: Comparison Of the Perturbative Solution With The Small Rotat...mentioning

confidence: 99%