Trapped ions in the strong-excitation regime: Ion interferometry and nonclassical states

Poyatos, Juan F.; Cirac, J. I.; Blatt, R.; Zoller, P.

doi:10.1103/physreva.54.1532

Cited by 109 publications

(82 citation statements)

References 32 publications

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“…Interferometers based on SDKs have been proposed [10] to measure the Sagnac effect, and have recently been implemented in a 1D non-Sagnac geometry to measure temperature over a wide dynamic range [9]. However, for a Sagnac gyroscope, the second displacement need not be spin-dependent and can therefore be implemented as a simple trap center shift.…”

Section: Phase-space Displacementsmentioning

confidence: 99%

Rotation sensing with trapped ions

Campbell

Hamilton

2017

J. Phys. B: At. Mol. Opt. Phys.

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We present a protocol for rotation measurement via matter-wave Sagnac interferometry using trapped ions. The ion trap based interferometer encloses a large area in a compact apparatus through repeated round-trips in a Sagnac geometry. We show how a uniform magnetic field can be used to close the interferometer over a large dynamic range in rotation speed and measurement bandwidth without contrast loss. Since this technique does not require the ions to be confined in the Lamb-Dicke regime, Doppler laser cooling should be sufficient to reach a sensitivity of

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Section: Phase-space Displacementsmentioning

confidence: 99%

Rotation sensing with trapped ions

Campbell

Hamilton

2017

J. Phys. B: At. Mol. Opt. Phys.

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“…Many schemes have been proposed for the purpose of engineering various quantum states [1][2][3][4][5][6][7][8], especially the superpositions of coherent states on a circle or superpositions of coherent states on a line in the field of cavity and trapped ions [9][10][11][12]. Because discrete superpositions of coherent states on a circle or on a line may approximate many quantum states [9], such as number states, amplitude-squeezed states and quadrature squeezed states, which provides a new way for quantum-state engineering.…”

Section: Introductionmentioning

confidence: 99%

“…The transition between these two internal states is dipole forbidden, but we can drive it by irradiating the ion with a pulsed laser that tuned to the frequency of the transition. In order to measuring the internal stated, we then employ the third auxiliary electric level |2 of the ion [5,13,14] which is a strong electric transition to the ground state |0 . By directing a laser resonant with the transition |0 → |2 on the ion, and then probing for the occurrence of fluorescence light, the electric quantum state is projected either into the ground or excited state, conditioned on the observation of fluorescence or of no-fluorescence event.…”

Section: Introductionmentioning

confidence: 99%

Quantum-State Engineering of Multiple Trapped Ions for Center-of-Mass Mode

Zeng

Kuang

Zhu

et al. 2001

Commun. Theor. Phys.

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We propose a scheme to generate a superposition with arbitrary coefficients on a line in phase space for the center-of-mass vibrational mode of N ions by means of isolating all other spectator vibrational modes from the centerof-mass mode. It can be viewed as the generation of previous methods for preparing motional states of one ion. For large number of ions we need only one cyclic operation to generate such a superposition of many coherent states.

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“…We apply this solution to a simple initial state and show that qubits may be produced. Because may be produced with less constrains on the parameters, we call them generalized qubits.We consider the Hamiltonian that describes the interaction of a single two-level trapped ion with a laser beam (we set = 1) [9,15]wheren =â †â , withâ † (â ) the ion vibratonial creation (anihilation) operator, andσ + = |e g| (σ − = |g e| ) is the electronic raising (lowering) operator, |e (|g ) denoting the excited (ground) state of the ion. The detuning δ is defined as the difference between the atomic transition frequency (ω 0 ) and the frequency of laser(ω L ).…”

mentioning

confidence: 99%

“…We consider the Hamiltonian that describes the interaction of a single two-level trapped ion with a laser beam (we set = 1) [9,15]…”

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confidence: 99%

Generalized qubits of the vibrational motion of a trapped ion

Aguilar

Moya‐Cessa

2002

Phys. Rev. A

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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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Trapped ions in the strong-excitation regime: Ion interferometry and nonclassical states

Cited by 109 publications

References 32 publications

Rotation sensing with trapped ions

Rotation sensing with trapped ions

Quantum-State Engineering of Multiple Trapped Ions for Center-of-Mass Mode

Generalized qubits of the vibrational motion of a trapped ion

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