Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

数理解析研究所講究録

A model of a cavity and a beam of harmonic atoms (Mathematical aspects of quantum fields and related topics)

博志 田村

Published Oct 1, 2014• 0 citations
OpenAlex

Abstract

We consider a simplified mathematical model for the physical system consists of a cavity and a beam of atoms which pass the cavity successively.The Hamiltonian contains time-dependent (piecewise constant) term de- scribing interaction between the cavity and the atom in the beam which is passing the cavity at the prescribed moment.We suppose that the radiation

Related papers

A Calculable Model for a Cavity and an Atomic Beam (Applications of Renormalization Group Methods in Mathematical Sciences)

博志 田村

We consider a simple model for the physical system consists of a cavity and a beam of atoms which pass the cavity successively.The Hamiltonian contains time-dependent (piecewise constant) term de- scribing interaction between the cavity and the atom in the beam which is passing the cavity at the prescribed moment.We deal with the model in which the radiation field inside the cavity and each atoms of the beam is modeled by simple harmonic oscillators.We calculate the time evolution of the density matrix of the system and the asymptotic behavior of the cavity, both in the Hamiltonian dynamics and the Markovian dynamics of Kossakowski-Lindblad-Davies type.We also dis-

数理解析研究所講究録•Jul 1, 2014•0 citations

A model of a cavity and a beam of harmonic atoms (Mathematical aspects of quantum fields and related topics)

Hiroshi Tamura

•Oct 1, 2014•0 citations

Generation of states maximally entanglement (EPR states) by passing two atoms through two coupled cavities

B. F. C. Yabu-uti, Fabiano Kenji Nohama, José Antonio Roversi +2 more

We present the results of the interaction of identical two‐level atoms with a system formed by two identical coupled cavities via evanescent field. With new bosonic operators (normal nodes), the interaction Hamiltonian between the cavities can be diagonalized. In a particular case, we can eliminate the interaction of the atoms with the nonresonant normal modes reducing the system to the interaction of the atom with a single‐mode (like JCM). As an application of this interaction, we analyze the entanglement between distant atoms. We present two related simple procedures to generate two atoms maximally entangled state (EPR pair) interacting (i)successively (atoms passing through the cavities at different moments) and (ii) simultaneously (at the same time) with the coupled cavities system. Moreover, in contrast with other schemes, we can use identical atoms which simplifies in a experiment point of view.

AIP conference proceedings•Jan 1, 2008•0 citations

INTERACTION OF AN ATOM WITH A CAVITY RADIATION FIELD

Fam Le Kien, A.S. Shumovsky

We review the dynamical statistical theory of the interaction of an atom with a cavity radiation field in the framework of exactly solvable Jaynes-Cummings type models.

International Journal of Modern Physics B•Aug 20, 1991•23 citations

Atoms in cavities

A. M. Fox

Abstract Before studying the interaction between atoms and cavities, it is helpful to remind ourselves of some of the basic properties of optical cavities. We shall restrict our attention here to the simplest case, namely a planar cavity. This will be sufficient to illustrate the chief points, and the results can then be generalized to other types of cavity.

•Apr 27, 2006•0 citations

A Model of Interacting Radiation and Matter

C. R. Willis

We investigate the long-time behavior of a model consisting of N two-level atoms in a lossless cavity. The Hamiltonian of our system contains the radiation oscillators in addition to the matter Hamiltonian and the usual ∫j·Adv interaction term. In order to treat the system perturbatively, it would be necessary to remove the tremendous degeneracy of the system. Since this is prohibitively difficult, and since we are interested in the long-time behavior of the system, we solve the quantum mechanical Liouville equation directly for a wide class of physically important initial distribution functions. We show the effective expansion parameter is γ̃Nγ̃ where γ̃ is a dimensionless atomic dipole moment and N is the number of atoms. In the lowest order we find the self-consistent field approximation. In the next order, particle-field correlations appear. We explicitly solve the equations of motion for the particle-field correlations in terms of the average quantities that appear in the self-consistent field approximation. We show the self-consistent field approximation consists of five first-order differential equations. Next we show the equations of motion for the density matrix of the system correct to order (γ̃Nγ̃)2 are equivalent to eight first-order differential equations. The three additional equations are needed to describe the three second moments of the density matrix of the electromagnetic field that appear in second order. Our lowest-order microscopic equations are equivalent to semiphenomenological theories and our higher-order equations contain only the measurable second-order moments of the electromagnetic field in addition to the variables that appear in semi-phenomenological theories.

Journal of Mathematical Physics•Sep 1, 1964•26 citations
We consider a simplified mathematical model for the physical system consists of a cavity and a beam of atoms which pass the cavity successively.The Hamiltonian contains time-dependent (piecewise constant) term de- scribing interaction between the cavity and the atom in the beam which is passing the cavity at the prescribed moment.We suppose that the radiation
We consider a simple model for the physical system consists of a cavity and a beam of atoms which pass the cavity successively.The Hamiltonian contains time-dependent (piecewise constant) term de- scribing interaction between the cavity and the atom in the beam which is passing the cavity at the prescribed moment.We deal with the model in which the radiation field inside the cavity and each atoms of the beam is modeled by simple harmonic oscillators.We calculate the time evolution of the density matrix of the system and the asymptotic behavior of the cavity, both in the Hamiltonian dynamics and the Markovian dynamics of Kossakowski-Lindblad-Davies type.We also dis-
We present the results of the interaction of identical two‐level atoms with a system formed by two identical coupled cavities via evanescent field. With new bosonic operators (normal nodes), the interaction Hamiltonian between the cavities can be diagonalized. In a particular case, we can eliminate the interaction of the atoms with the nonresonant normal modes reducing the system to the interaction of the atom with a single‐mode (like JCM). As an application of this interaction, we analyze the entanglement between distant atoms. We present two related simple procedures to generate two atoms maximally entangled state (EPR pair) interacting (i)successively (atoms passing through the cavities at different moments) and (ii) simultaneously (at the same time) with the coupled cavities system. Moreover, in contrast with other schemes, we can use identical atoms which simplifies in a experiment point of view.
We investigate the long-time behavior of a model consisting of N two-level atoms in a lossless cavity. The Hamiltonian of our system contains the radiation oscillators in addition to the matter Hamiltonian and the usual ∫j·Adv interaction term. In order to treat the system perturbatively, it would be necessary to remove the tremendous degeneracy of the system. Since this is prohibitively difficult, and since we are interested in the long-time behavior of the system, we solve the quantum mechanical Liouville equation directly for a wide class of physically important initial distribution functions. We show the effective expansion parameter is γ̃Nγ̃ where γ̃ is a dimensionless atomic dipole moment and N is the number of atoms. In the lowest order we find the self-consistent field approximation. In the next order, particle-field correlations appear. We explicitly solve the equations of motion for the particle-field correlations in terms of the average quantities that appear in the self-consistent field approximation. We show the self-consistent field approximation consists of five first-order differential equations. Next we show the equations of motion for the density matrix of the system correct to order (γ̃Nγ̃)2 are equivalent to eight first-order differential equations. The three additional equations are needed to describe the three second moments of the density matrix of the electromagnetic field that appear in second order. Our lowest-order microscopic equations are equivalent to semiphenomenological theories and our higher-order equations contain only the measurable second-order moments of the electromagnetic field in addition to the variables that appear in semi-phenomenological theories.