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Christopher C Gerry - One of the best experts on this subject based on the ideXlab platform.

  • SU(1,1) Parity and strong violations of a Bell inequality by entangled Barut–Girardello coherent states
    Journal of The Optical Society of America B-optical Physics, 2018
    Co-Authors: Edwin E. Hach, Richard Birrittella, Paul M. Alsing, Christopher C Gerry
    Abstract:

    We study the violations of the Bell–Clauser–Horne–Shimony–Holt inequality for entangled SU(1,1) Barut–Girardello coherent states. As in a previous paper where violations of the inequality were studied for entangled SU(1,1) coherent states of the Perelomov form [Phys. Rev. A.93, 042104 (2016)PLRAAN1050-294710.1103/PhysRevA.93.042104], we choose as our observable the SU(1,1) Parity Operator, though here we discuss the physical meaning of the Operator for single-mode and two-mode bosonic realizations of the su(1,1) Lie algebra. We show that the SU(1,1) Parity Operator is not the same as the usual photon number Parity Operator but rather is a form of higher-order photon number Parity. Distant observers Alice and Bob perform on each of their subsystems non-compact SU(1,1) transformations characterized by hyperbolic angles, followed by measurements of the SU(1,1) Parity Operators. We find strong violations of the inequality over a wide range of parameters, and these violations are stronger than those that can be obtained by the entangled Perelomov SU(1,1) coherent state.

  • the Parity Operator in quantum optical metrology
    Contemporary Physics, 2010
    Co-Authors: Christopher C Gerry, Jihane Mimih
    Abstract:

    Photon number states are assigned a Parity of +1 if their photon number is even and a Parity of −1 if odd. The Parity Operator, which is minus one to the power of the photon number Operator, is a Hermitian Operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the Parity Operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of Parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenber...

  • Single-mode squeezed vacuum states as approximate Schrödinger phase cats: relation to SU(1, 1) phase Operators
    Journal of Optics B-quantum and Semiclassical Optics, 2003
    Co-Authors: Christopher C Gerry, Adil Benmoussa, Kimberley M. Bruno
    Abstract:

    We study the eigenstates of the square of the phase Operator for a single-mode field, and show that they are given as superpositions of macroscopically distinguishable phase states, which we call Schrodinger phase cats, the phase states being eigenstates of the phase Operator. Those solutions that are also eigenstates of the Parity Operator with even Parity are shown to be very similar to the squeezed vacuum states over a range of relevant parameters. Thus, it is possible to consider some squeezed vacuum states as approximate Schrodinger phase-cat states. We discuss the connections to the phase states of the SU(1, 1) phase Operators for various realizations and representations.

Jihane Mimih - One of the best experts on this subject based on the ideXlab platform.

  • the Parity Operator in quantum optical metrology
    Contemporary Physics, 2010
    Co-Authors: Christopher C Gerry, Jihane Mimih
    Abstract:

    Photon number states are assigned a Parity of +1 if their photon number is even and a Parity of −1 if odd. The Parity Operator, which is minus one to the power of the photon number Operator, is a Hermitian Operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the Parity Operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of Parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenber...

Amir Karimi - One of the best experts on this subject based on the ideXlab platform.

Joris Van Der Jeugt - One of the best experts on this subject based on the ideXlab platform.

  • The u(2)α and su(2)α Hahn harmonic oscillators
    2020
    Co-Authors: E. I. Jafarov, N. I. Stoilova, Joris Van Der Jeugt
    Abstract:

    New models for the finite one-dimensional harmonic oscillator are proposed based upon the algebras u(2)_alpha and su(2)_alpha. These algebras are deformations of the Lie algebras u(2) and su(2) extended by a Parity Operator, with deformation parameter alpha. Classes of irreducible unitary representations of u(2)_alpha and su(2)_alpha are constructed. It turns out that in these models the spectrum of the position Operator can be computed explicitly, and that the corresponding (discrete) wavefunctions can be determined in terms of Hahn polynomials.

  • A finite oscillator model with equidistant position spectrum based on an extension of {\mathfrak{su}}(2)
    Journal of Physics A, 2016
    Co-Authors: Roy Oste, Joris Van Der Jeugt
    Abstract:

    We consider an extension of the real Lie algebra su(2) by introducing a Parity Operator P and a parameter c. This extended algebra is isomorphic to the Bannai-Ito algebra with two parameters equal to zero. For this algebra we classify all unitary finite-dimensional representations and show their relation with known representations of su(2). Moreover, we present a model for a one-dimensional finite oscillator based on the odd-dimensional representations of this algebra. For this model, the spectrum of the position Operator is equidistant and coincides with the spectrum of the known su(2) oscillator. In particular the spectrum is independent of the parameter c while the discrete position wavefunctions, which are given in terms of certain dual Hahn polynomials, do depend on this parameter.

  • Finite oscillator models: the Hahn oscillator
    Journal of Physics A, 2011
    Co-Authors: E. I. Jafarov, N. I. Stoilova, Joris Van Der Jeugt
    Abstract:

    A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra . This algebra is a deformation of the Lie algebra extended by a Parity Operator, with the deformation parameter α. A class of irreducible unitary representations of is constructed. In the finite oscillator model, the (discrete) spectrum of the position Operator is determined, and the position wavefunctions are shown to be dual Hahn polynomials. Plots of these discrete wavefunctions display interesting properties, similar to those of the parabose oscillator. We show indeed that in the limit, when the dimension of the representations goes to infinity, the discrete wavefunctions tend to the continuous wavefunctions of the parabose oscillator.

Mohammad Kazem Tavassoly - One of the best experts on this subject based on the ideXlab platform.