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Hiroo Azuma - One of the best experts on this subject based on the ideXlab platform.
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Quasiperiodicity in time evolution of the Bloch Vector under the thermal Jaynes–Cummings model
Physica D: Nonlinear Phenomena, 2020Co-Authors: Hiroo AzumaAbstract: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
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equivalence of a compressible inviscid flow and the Bloch Vector under the thermal jaynes cummings model
Physica D: Nonlinear Phenomena, 2015Co-Authors: Hiroo AzumaAbstract: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.
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quasiperiodicity in time evolution of the Bloch Vector under the thermal jaynes cummings model
Physica D: Nonlinear Phenomena, 2014Co-Authors: Hiroo AzumaAbstract: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).
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Quasiperiodicity in time evolution of the Bloch Vector under the thermal Jaynes–Cummings model
Physica D: Nonlinear Phenomena, 2014Co-Authors: Hiroo AzumaAbstract: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).
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dynamics of the Bloch Vector in the thermal jaynes cummings model
Physical Review A, 2008Co-Authors: Hiroo AzumaAbstract:In this paper, we investigate the dynamics of the Bloch Vector of a single two-level atom which interacts with a single quantized electromagnetic field mode according to the Jaynes-Cummings model, where the field is initially prepared in a thermal state. The time evolution of the Bloch Vector $\mathbit{S}(t)$ seems to be in complete disorder because of the thermal distribution of the initial state of the field. Both the norm and the direction of $\mathbit{S}(t)$ oscillate hard and their periods seem infinite. We observe that the trajectory of the time evolution of $\mathbit{S}(t)$ in the two- or three-dimensional space does not form a closed path. To remove the fast frequency oscillation from the trajectory, we take the time average of the Bloch Vector $\mathbit{S}(t)$. We examine the histogram of ${\phantom{|}{S}_{z}(n\ensuremath{\Delta}t)|n=0,1,\dots{},N}$ for small $\ensuremath{\Delta}t$ and large $N$. It represents an absolute value of a derivative of the inverse function of ${S}_{z}(t)$. [When the inverse function of $y={S}_{z}(t)$ is a multivalued function, the histogram represents a summation of the absolute values of its derivatives at points whose real parts are equal to $y$ on the Riemann surface.] We examine the dependence of the variance of the histogram on the temperature of the field. We estimate the lower bound of the entanglement between the atom and the field.
Atsuo Morinaga - One of the best experts on this subject based on the ideXlab platform.
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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, 2008Co-Authors: Hiromitsu Imai, Atsuo MorinagaAbstract: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.
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Demonstration of pure geometric universal single-qubit operation on two-level atoms
Physical Review A - Atomic, Molecular, and Optical Physics, 2008Co-Authors: Hiromitsu Imai, Atsuo MorinagaAbstract: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 - One of the best experts on this subject based on the ideXlab platform.
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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, 2008Co-Authors: Hiromitsu Imai, Atsuo MorinagaAbstract: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.
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Demonstration of pure geometric universal single-qubit operation on two-level atoms
Physical Review A - Atomic, Molecular, and Optical Physics, 2008Co-Authors: Hiromitsu Imai, Atsuo MorinagaAbstract: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.
Gen Kimura - One of the best experts on this subject based on the ideXlab platform.
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The Bloch Vector for N-level systems
Physics Letters A, 2020Co-Authors: Gen KimuraAbstract:We determine the set of the Bloch Vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.Comment: REVTeX4, 16 pages, 2 EPS figures, add some references, correct some typo
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The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View
Open Systems & Information Dynamics, 2005Co-Authors: Gen Kimura, Andrzej KossakowskiAbstract:Bloch-Vector spaces for N -level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We present a characterization of the space by using the spectra of (orthogonal) generators of SU( N ). As an application, we find a dual property of the space which provides an overall picture of the space. We also provide three classes of quantum-state representations based on actual measurements and discuss their state-spaces.
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the Bloch Vector space for n level systems the spherical coordinate point of view
arXiv: Quantum Physics, 2004Co-Authors: Gen Kimura, Andrzej KossakowskiAbstract:Bloch-Vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We show that the maximum radius in each direction, which is due to the construction of the Bloch-Vector space, is determined by the minimum eigenvalue of the corresponding observable (orthogonal generator of SU(N)). From this fact, we reveal the dual property of the structure of the Bloch-Vector space; if in some direction the space reachs the large sphere (pure state), then in the opposite direction the space can only get to the small sphere, and vice versa. Another application is a parameterization with simple ranges of density operators. We also provide three classes of quantum-state representation based on actual measurements beyond the Bloch Vector and discuss their state-spaces.
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the Bloch Vector for n level systems
Physics Letters A, 2003Co-Authors: Gen KimuraAbstract:We determine the set of the Bloch Vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.
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the Bloch Vector for n level systems
Journal of the Physical Society of Japan, 2003Co-Authors: Gen KimuraAbstract:We explicitly determine the Bloch-Vector space for arbitrary N -level systems, which generalizes a familiar Bloch ball in 2-level systems.
Andrzej Kossakowski - One of the best experts on this subject based on the ideXlab platform.
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The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View
Open Systems & Information Dynamics, 2005Co-Authors: Gen Kimura, Andrzej KossakowskiAbstract:Bloch-Vector spaces for N -level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We present a characterization of the space by using the spectra of (orthogonal) generators of SU( N ). As an application, we find a dual property of the space which provides an overall picture of the space. We also provide three classes of quantum-state representations based on actual measurements and discuss their state-spaces.
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the Bloch Vector space for n level systems the spherical coordinate point of view
arXiv: Quantum Physics, 2004Co-Authors: Gen Kimura, Andrzej KossakowskiAbstract:Bloch-Vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We show that the maximum radius in each direction, which is due to the construction of the Bloch-Vector space, is determined by the minimum eigenvalue of the corresponding observable (orthogonal generator of SU(N)). From this fact, we reveal the dual property of the structure of the Bloch-Vector space; if in some direction the space reachs the large sphere (pure state), then in the opposite direction the space can only get to the small sphere, and vice versa. Another application is a parameterization with simple ranges of density operators. We also provide three classes of quantum-state representation based on actual measurements beyond the Bloch Vector and discuss their state-spaces.