Motional quantum states of a trapped ion: Measurement and its back action

Wallentowitz, S.; Vogel, W.

doi:10.1103/physreva.54.3322

Cited by 32 publications

(16 citation statements)

References 41 publications

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“…We consider an interaction proposed previously in the reconstruction of the quantum mechanical state of a trapped ion [33] and that has been used in the preparation of coherent superpositions of arbitrary quantum states such as Schrödinger cats [34]. A weak electronic transition of the ion is irradiated by two laser fields detuned to the first lower and first upper vibrational sidebands of the transition, respectively.…”

Section: Superpositions Of Equidistant Squeezed Statesmentioning

confidence: 99%

Generation of quasi-rectangle-states of the vibrational motion of an ion

Ramos-Prieto¹,

Rincon²,

Arrizón³

et al. 2020

Phys. Scr.

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We show how to generate quasi-rectangle-states of the vibrational motion of an ion, this is, states that have the same probability in a given position interval. We produce those states by repeated ionlaser interactions followed by conditional measurements that generate a superposition of squeezed states. The squeeze parameter of the initial state may be tuned in order to obtain such highly localized rectangle states. I. INTRODUCTIONThe early papers of Roy Glauber [1, 2] on coherence, marked a course on how to define nonclassical states, a first good approximation was: Those states that have less fluctuations in a given observable than that of a coherent state [2]. Since then, a myriad of ways of generating nonclassical states, theoretically and experimentally, have been proposed [3][4][5][6][7][8][9][10][11].Nonclassical states of the centre-of-mass motion of a trapped ion have played an important role because of fundamental problems in quantum mechanics and for their potential practical applications such as precision spectroscopy [3] and quantum computation [4,5]. By exhibiting less fluctuations than that of a coherent state, the so-called standard quantum limit they are of great importance.Ways of generating squeezed states [6], superpositions of coherent states [7,8], nonlinear coherent states [9-11], number states and some specific superpositions of them have been proposed [12]. In experimental and theoretical studies of single trapped ions interacting with laser beams it has been usually considered the case in which such interaction may be modeled as a Jaynes-Cummings interaction [6,13,14], therefore exhibiting collapses and revivals [15] and the generation of nonclassical states, peculiar of such a model, or its multiphotonic generalizations [16][17][18]. It should be noted also that, via a similarity transformation that does not need of any approximations, the ion-laser interaction may be taken to a two-level atom interacting with a quantized field, i.e., the Rabi interaction [19][20][21]. In fact multiphonon Rabi models may be realized via such transformation [22].When studying ion-laser interactions, usually two rotating wave approximations are performed, the first related to the laser optical frequency and the second to the vibrational frequency of the ion, in order to remove counterpropagating terms of the Hamiltonian, difficult to be treated analytically. Approximations on the Lamb-Dicke parameter, η, are usually done, considering it much smaller than unity. In order to perform the rotating wave approximation, the laser intensity, Ω, is considered much smaller than the trapping frequency, ν, namely Ω ν [23]. As mentioned above, cavity fields and trapped ions share several common features as in both topics the possibility to realize Jaynes-Cummings [24,25] and anti-Jaynes-Cummings [26] interactions, are feasible. In cavities interacting with atoms this model describes the resonant or slightly non-resonant interaction of an atom with the cavity mode [27]. On the other hand, for a trapped ion in the Lamb...

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Section: Superpositions Of Equidistant Squeezed Statesmentioning

confidence: 99%

Generation of quasi-rectangle-states of the vibrational motion of an ion

Ramos-Prieto¹,

Rincon²,

Arrizón³

et al. 2020

Phys. Scr.

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“…When η √n + 1 1, the so-called "Lamb-Dicke limit" (n is the average phonon number), the ion is well localized with respect to the wavelength of the laser, and we can expand the exponentials in Eq. (22) to first order in η, which is equivalent to first order in k cos θ q m (ζ), giving H (m)…”

Section: B Laser-induced Coupling Of Vibrational and Electronic Statesmentioning

confidence: 99%

Simulating quantum effects of cosmological expansion using a static ion trap

2010

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We propose a new experimental testbed that uses ions in the collective ground state of a static trap for studying the analog of quantum-field effects in cosmological spacetimes, including the Gibbons-Hawking effect for a single detector in de Sitter spacetime, as well as the possibility of modeling inflationary structure formation and the entanglement signature of de Sitter spacetime. To date, proposals for using trapped ions in analog gravity experiments have simulated the effect of gravity on the field modes by directly manipulating the ions' motion. In contrast, by associating laboratory time with conformal time in the simulated universe, we can encode the full effect of curvature in the modulation of the laser used to couple the ions' vibrational motion and electronic states. This model simplifies the experimental requirements for modeling the analog of an expanding universe using trapped ions and enlarges the validity of the ion-trap analogy to a wide range of interesting cases.

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“…Then we illuminate both the two ions simultaneously with two lasers , i.e., performing the propagator (4) with N = 2 on the above initial state (13), for an interaction time ∆t, following by a measurement on the internal state of two ions. If we detect the two ions both in excited state |1 , then the conditioned state for the system reads…”

Section: The Case For Two Ions (N=2)mentioning

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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Motional quantum states of a trapped ion: Measurement and its back action

Cited by 32 publications

References 41 publications

Generation of quasi-rectangle-states of the vibrational motion of an ion

Generation of quasi-rectangle-states of the vibrational motion of an ion

Simulating quantum effects of cosmological expansion using a static ion trap

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

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