Ordered Expansions in Boson Amplitude Operators

Cahill, Kévin; Glauber, Roy J.

doi:10.1103/physrev.177.1857

Cited by 1,077 publications

(750 citation statements)

References 14 publications

Supporting

Mentioning

727

Contrasting

Unclassified

Order By: Relevance

“…The most popular example of informationally complete measurement is given by the coherent-state POVM for a single-mode of the radiation field, whose probability distribution is the so-called Q-function (or Husimi function) [5,6,7]. Another example, though of completely different kind, is the case of quantum tomography [8], in which one measures an observable randomly selected from an informationally complete set-a "quorum".…”

Section: Introductionmentioning

confidence: 99%

Informationally complete measurements and group representation

D’Ariano¹,

Perinotti²,

Sacchi

2004

J. Opt. B: Quantum Semiclass. Opt.

105

View full text Add to dashboard Cite

Abstract. Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM's) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.

show abstract

Section: Introductionmentioning

confidence: 99%

Informationally complete measurements and group representation

D’Ariano¹,

Perinotti²,

Sacchi

2004

J. Opt. B: Quantum Semiclass. Opt.

105

View full text Add to dashboard Cite

show abstract

“…[23]. Let us now consider, for a given value of |γ|, P (i) (n, γ) as a function of ϕ = arg[γ] [24] and calculate the coefficients of the Fourier expansion…”

mentioning

confidence: 99%

Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron

et al. 2000

View full text Add to dashboard Cite

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...

show abstract

“…This equivalence becomes clear if we recall the normally ordered definition of the generalized s-ordered quasidistribution functions [27]:…”

Section: B Modal Decompositionmentioning

confidence: 99%

“…The parameters that can be freely adjusted in a practical setup are the values of the four coherent displacementsα 1 ,α 2 ,β 1 , andβ 2 used to construct the Clauser-Horne combination given in Eq. (27). We shall therefore optimize them for a specified set ofη, ξ, and p D in order to find the maximum possible violation of the Clauser-Horne under given experimental constraints.…”

Section: Single Photon Statementioning

confidence: 99%

Direct measurement of optical quasidistribution functions: Multimode theory and homodyne tests of Bell’s inequalities

et al. 2002

View full text Add to dashboard Cite

We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as non-unit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's inequalities by measuring joint two-mode quasidistribution functions by photon counting under locality conditions. We determine the range of parameters of the experimental setup that enable violation of Bell's inequalities for two states exhibiting entanglement in the Fock basis: a one-photon Fock state divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced in the process of non-degenerate parametric down-conversion.

show abstract

Ordered Expansions in Boson Amplitude Operators

Cited by 1,077 publications

References 14 publications

Informationally complete measurements and group representation

Informationally complete measurements and group representation

Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron

Direct measurement of optical quasidistribution functions: Multimode theory and homodyne tests of Bell’s inequalities

Contact Info

Product

Resources

About