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Bloch Vector

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Hiroo Azuma – 1st expert on this subject based on the ideXlab platform

  • Quasiperiodicity in time evolution of the Bloch Vector under the thermal Jaynes–Cummings model
    Physica D: Nonlinear Phenomena, 2020
    Co-Authors: Hiroo Azuma

    Abstract:

    We study a quasiperiodic structure in the time evolution of the Bloch Vector,
    whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting
    the two-level atom into a certain pure state and the cavity field into a mixed
    state in thermal equilibrium at initial time, we let the whole system evolve
    according to the JCM Hamiltonian. During this time evolution, motion of the
    Bloch Vector seems to be in disorder. Because of the thermal photon
    distribution, both a norm and a direction of the Bloch Vector change hard at
    random. In this paper, taking a different viewpoint compared with ones that we
    have been used to, we investigate quasiperiodicity of the Bloch Vector‘s
    trajectories. Introducing the concept of the quasiperiodic motion, we can
    explain the confused behaviour of the system as an intermediate state between
    periodic and chaotic motions. More specifically, we discuss the following two
    facts: (1) If we adjust the time interval $\Delta t$ properly, figures
    consisting of plotted dots at the constant time interval acquire scale
    invariance under replacement of $\Delta t$ by $s\Delta t$, where $s(>1)$ is an
    arbitrary real but not transcendental number. (2) We can compute values of the
    time variable $t$, which let $|S_{z}(t)|$ (the absolute value of the
    $z$-component of the Bloch Vector) be very small, with the Diophantine
    approximation (a rational approximation of an irrational number).Comment: v3: 41 pages, 15 eps figures. Because the manuscript
    arXiv:1205:4308v2 was too long, it has been divided into two parts. The
    present paper is the first part of the original one. In this manuscript, the
    discussions focus on the quasiperiodicity in the thermal Jaynes-Cummings
    mode

  • equivalence of a compressible inviscid flow and the Bloch Vector under the thermal jaynes cummings model
    Physica D: Nonlinear Phenomena, 2015
    Co-Authors: Hiroo Azuma

    Abstract:

    Abstract In this paper, we show that the time evolution of the Bloch Vector governed by the thermal Jaynes–Cummings model is equivalent to a compressible inviscid flow with zero vorticity. Because of its quasiperiodicity, the dynamics of the Bloch Vector includes countably infinite angular momenta as integrals of motion. Moreover, to derive the Bloch Vector, we trace out the Hilbert space of the cavity field and remove entanglement between the single atom and the cavity mode. These facts indicate that the dynamics of the Bloch Vector can be described with a hidden-variable model that has local determinism and a countably infinite number of degrees of freedom. Our results fit these considerations.

  • quasiperiodicity in time evolution of the Bloch Vector under the thermal jaynes cummings model
    Physica D: Nonlinear Phenomena, 2014
    Co-Authors: Hiroo Azuma

    Abstract:

    Abstract We study a quasiperiodic structure in the time evolution of the Bloch Vector, whose dynamics is governed by the thermal Jaynes–Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, motion of the Bloch Vector seems to be in disorder. Because of the thermal photon distribution, both a norm and a direction of the Bloch Vector change hard at random. In this paper, taking a different viewpoint compared with ones that we have been used to, we investigate quasiperiodicity of the Bloch Vector’s trajectories. Introducing the concept of the quasiperiodic motion, we can explain the confused behaviour of the system as an intermediate state between periodic and chaotic motions. More specifically, we discuss the following two facts: (1) If we adjust the time interval Δ t properly, figures consisting of plotted dots at the constant time interval acquire scale invariance under replacement of Δ t by s Δ t , where s ( > 1 ) is an arbitrary real but not transcendental number. (2) We can compute values of the time variable t , which let | S z ( t ) | (the absolute value of the z -component of the Bloch Vector) be very small, with the Diophantine approximation (a rational approximation of an irrational number).

Atsuo Morinaga – 2nd expert on this subject based on the ideXlab platform

  • Complete geometric universal single qubit operation of cold two-level atoms
    2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science, 2008
    Co-Authors: Hiromitsu Imai, Atsuo Morinaga

    Abstract:

    A complete geometric manipulation of universal single qubit operation on a two-level cold ensemble of sodium atoms was demonstrated using a combination of geometric rotations of the Bloch Vector around axes 2 and 3.

  • Demonstration of pure geometric universal single-qubit operation on two-level atoms
    Physical Review A – Atomic, Molecular, and Optical Physics, 2008
    Co-Authors: Hiromitsu Imai, Atsuo Morinaga

    Abstract:

    With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch Vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.

Hiromitsu Imai – 3rd expert on this subject based on the ideXlab platform

  • Complete geometric universal single qubit operation of cold two-level atoms
    2008 Conference on Lasers and Electro-Optics and 2008 Conference on Quantum Electronics and Laser Science, 2008
    Co-Authors: Hiromitsu Imai, Atsuo Morinaga

    Abstract:

    A complete geometric manipulation of universal single qubit operation on a two-level cold ensemble of sodium atoms was demonstrated using a combination of geometric rotations of the Bloch Vector around axes 2 and 3.

  • Demonstration of pure geometric universal single-qubit operation on two-level atoms
    Physical Review A – Atomic, Molecular, and Optical Physics, 2008
    Co-Authors: Hiromitsu Imai, Atsuo Morinaga

    Abstract:

    With carefully prepared resonant laser-controlled pulses, the two quantum states of a cold ensemble of sodium atoms were manipulated by pure geometric rotations of the Bloch Vector around axes 2 and 3 on the Bloch sphere. The fidelity for two geometric rotations was improved to be 90%. A universal single-qubit operation on the ground-state wave function was demonstrated by a pure geometric operation and the phase shift due to the rotation around axis 3 was measured using a geometric atom interferometer.