A family of exact eigenstates for a single trapped ion interacting with a laser field

Moya‐Cessa, H.; Jonathan, Daniel; Knight, P. L.

doi:10.1080/09500340210149633

“…We should stress that if we had considered a detuning, an extra term would have to be added to Equation 17 that would represent an extra static electric field interacting with an atomic dipole28.…”

Section: Fast Quantum Rabi Hamiltonianmentioning

confidence: 99%

Fast Quantum Rabi Model with Trapped Ions

Moya‐Cessa

¹

2016

Sci Rep

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“…With the tools we have developed up to here we can study the two-level atom-field interaction [3] or equivalently the ion-laser interaction [4,5] and construct atom and field entropy operators. In the off-resonant atom-field interaction, i.e.…”

Section: Atomic Entropy Operatormentioning

confidence: 99%

Entropy Operator and Associated Wigner Function

Moya‐Cessa

¹

2007

Int. J. Quantum Inform.

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“…Exact eigenstates of the ion-laser Hamiltonian, i.e. trapping states for this system have been found [18], but because they do not form a basis, a complete (exact) solution may be found only for such states (eigenstates).In this contribution we consider the complete Hamiltonian for the ion-laser interaction, linearise it as in [16] and further unitarily transform it, without performing the RWA to obtain an effective Hamiltonian that can be easily solved . This is an extension of a method of small rotations recently applied by to the Dicke model and other systems (they apply small rotations on the atomic basis).…”

mentioning

confidence: 99%

“…Exact eigenstates of the ion-laser Hamiltonian, i.e. trapping states for this system have been found [18], but because they do not form a basis, a complete (exact) solution may be found only for such states (eigenstates).…”

mentioning

confidence: 99%

Generalized qubits of the vibrational motion of a trapped ion

Aguilar

¹

,

Moya‐Cessa

²

2002

Self Cite

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We present a method to generate qubits of the vibrational motion of an ion. The method is developed in the non-rotating wave approximation regime, therefore we consider regimes where the dynamics has not been studied. Because the solutions are valid for a more extended range of parameters we call them generalized qubits.PACS numbers: 32.80.Qk, 42.50.Vk Nonclassical states of the center-of-mass motion of a trapped ion have played an important role because of the potential practical applications such as precision spectroscopy [1] [6,7], number states, specific superpositions of them, and in particular, robust to noise (spontaneous emmision) qubits have been proposed [8]. In theoretical and experimental studies of a laser interacting with a single trapped ion it has been usually considered the case in which it may be modeled as a Jaynes-Cummings interaction [5,9,10], then exhibiting the peculiar features of this model like collapses and revivals [11], and the generation of nonclassical states common to such a model or (multi-photon) generalizations of it [12][13][14]. In treating this system usually two rotating wave approximations (RWA's) are done (the first related to the laser [optical] frequency and the second to the vibrational frequency of the ion), to remove counter-propagating terms of the Hamiltonian (that can not be treated analytically). Approximations on the Lamb-Dickke parameter, η, are usually done, considering it much smaller than unity. Additionaly, other approximations are done, based on the intensity of the laser shining on the trapped ion: the low-excitation regime Ω ≪ ν and the strong-excitation regime Ω ≫ ν [15], with Ω being the intensity of the field, and ν the vibrational frequency of the ion.Recently there has been an alternative approach to the study of this dynamics [16]. In this approach a unitary transformation is used in order to linearise the ion-laser Hamiltonian. This transformation has been also used to propose schemes for realising faster logic gates for quantum information processing [3]. Under this unitary transformation the Hamiltonian takes exactly the form (note that not an effective form) of the Jaynes-Cummings Hamiltonian plus an extra term (an atomic driving term). In such a case a RWA may be done [16] in order to have an analytical solution for this problem, but it brings with it a new condition: Ω of the order of 2ν (note however that this is a new regime) and η still much less than unity. Later, another transformation [17] was used to diagonalize the linearized ion-laser Hamiltonian, without further conditions on Ω or η. This allowed the diagonalization of the Hamiltonian only in the ion basis. Exact eigenstates of the ion-laser Hamiltonian, i.e. trapping states for this system have been found [18], but because they do not form a basis, a complete (exact) solution may be found only for such states (eigenstates).In this contribution we consider the complete Hamiltonian for the ion-laser interaction, linearise it as in [16] and further unitarily transform it, witho...

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A family of exact eigenstates for a single trapped ion interacting with a laser field

Cited by 14 publications

References 18 publications

Fast Quantum Rabi Model with Trapped Ions

Fast Quantum Rabi Model with Trapped Ions

Entropy Operator and Associated Wigner Function

Generalized qubits of the vibrational motion of a trapped ion

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