Determination of entangled quantum states of a trapped atom

Wallentowitz, S.; Filho, R. L. de Matos; Vogel, W.

doi:10.1103/physreva.56.1205

Cited by 43 publications

(47 citation statements)

References 36 publications

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“…(1) is categorized as a discrete-variable-like hybrid entanglement. This type of entanglement was also characterized by a matrix Wigner function in the context of trapped ions [34].…”

Section: Generation Schemementioning

confidence: 99%

Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state

Kwon

Jeong

2015

Phys. Rev. A

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We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off detectors with low efficiencies and available resource states under current technology.

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“…(1) is categorized as a discrete-variable-like hybrid entanglement. This type of entanglement was also characterized by a matrix Wigner function in the context of trapped ions [34].…”

Section: Generation Schemementioning

confidence: 99%

Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state

Kwon

Jeong

2015

Phys. Rev. A

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“…The phase-space description corresponding to (7) is given by the Wigner-function matrix [18,19] whose elements arẽ…”

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confidence: 99%

Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron

et al. 2000

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We propose a scheme for the generation and reconstruction of entangled states between the internal and external (motional) degrees of freedom of a trapped electron. Such states also exhibit quantum coherence at a mesoscopic level.PACS numbers: 03.65. Bz, 42.50.Vk, 42.50.Dv A single electron trapped in a Penning trap [1] is one of the most fundamental quantum systems. Among its peculiar features, it allows the measurement of fundamental physical constants with striking accuracy. Recently, for instance, the electron cyclotron degree of freedom has been cooled to its ground state, where the electron may stay for hours, and quantum jumps between adjacent Fock states have been observed [2]. It is therefore evident that the manipulation and the characterization of the state of a trapped electron is an important issue, with implications in the very foundations of quantum mechanics. Earlier works [3,4] have dealt with this problem for one (motional) degree of freedom. On the other hand, entanglement [5] has been recognized as one of the most puzzling features of quantum mechanics, being also the basis of quantum information processing [6]. A striking achievement in this rapidly expanding field has been the recent entanglement of four trapped ions [7]. However, it is also possible (and conceptually equivalent) to entangle different degrees of freedom of the same particle [8].In the present work we propose to generate entangled states (combined cyclotron and spin states) of an electron in a Penning trap by using suitable applied fields. The complete structure of the cyclotron-spin quantum state is then obtained with the help of a tomographic reconstruction from the measured data.In a Penning trap an electron is confined by the combination of a homogeneous magnetic field along the positive z axis and an electrostatic quadrupole potential in the xy plane [1]. The spatial part of the electronic wave function consists of three degrees of freedom, but neglecting the slow magnetron motion (whose characteristic frequency lies in the kHz region), here we only consider the axial and cyclotron motions, which are two harmonic oscillators radiating in the MHz and GHz regions, respectively. On the other hand, the spin dynamics results from the interaction between the magnetic moment of the electron and the static magnetic field, so that the free Hamiltonian reads as [1]where the indices z, c, and s refer to the axial, cyclotron and spin motions, respectively.Here, in addition to the usual trapping fields, we consider an external radiation field as a standing wave along the z direction and rotating, i.e. circularly polarized, in the xy plane with frequency Ω [9]. To be more specific, we consider a standing wave within the cylindrical cavity configuration [10] with the (dimensionless) wave vector κ. Then, the interaction Hamiltonian reads [9] H int =hǫ â c e iΩt +â † c e −iΩt cos(κẑ + φ) +hζ σ − e iΩt +σ + e −iΩt sin(κẑ + φ) ,whereσ ± = (σ x ± iσ y )/2, andẑ =â z +â † z . The phase φ defines the position of the center of the axial mo...

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“…Quantum jumps have been extensively discussed in connection to the preparation and measuring of the quantum state of a trapped atom [5,11,14,18]. In a suitable setup their analysis can provide information on the dynamics and the state of the atomic center of mass degree of freedom.…”

Section: Introductionmentioning

confidence: 99%

“…Quantum jumps have inspired theoretical descriptions and methods in quantum optics, such as quantum trajectories [6,[8][9][10], and are at the basis of several theoretical proposals for post-selected quantum state preparation, some examples are found in Ref. [11][12][13], and for detecting the quantum state of trapped atoms [13,14]. Most recent experiments used quantum jumps in order to demonstrate single photon absorption by single trapped atoms [15], and analyzed their statistics in order to demonstrate quantum correlations between the absorbed photon and a second, entangled photon revealed at a detector [16].…”

Section: Introductionmentioning

confidence: 99%

Quantum jumps induced by the center-of-mass motion of a trapped atom

Torres¹,

Bienert²,

Zippilli³

et al. 2010

Eur. Phys. J. D

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We theoretically study the occurrence of quantum jumps in the resonance fluorescence of a trapped atom. Here, the atom is laser cooled in a configuration of level such that the occurrence of a quantum jump is associated to a change of the vibrational center-of-mass motion by one phonon. The statistics of the occurrence of the dark fluorescence period is studied as a function of the physical parameters and the corresponding features in the spectrum of resonance fluorescence are identified. We discuss the information which can be extracted on the atomic motion from the observation of a quantum jump in the considered setup.

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Determination of entangled quantum states of a trapped atom

Cited by 43 publications

References 36 publications

Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state

Generation of hybrid entanglement between a single-photon polarization qubit and a coherent state

Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron

Quantum jumps induced by the center-of-mass motion of a trapped atom

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