An algebraic approach to the Tavis-Cummings problem

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.Comment: 13 pages, 7 figure

Entanglement Sharing in the Two-Atom Tavis-Cummings Model

Individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. We investigate how this type of multipartite entanglement is generated in the context of a system consisting of two two-level atoms resonantly coupled to a single mode of the electromagnetic field. The dynamical evolution is studied in terms of the entanglements in the different bipartite partitions of the system, as quantified by the I-tangle. We also propose a generalization of the so-called residual tangle that quantifies the inherent three-body correlations in our tripartite system. This enables us to completely characterize the phenomenon of entanglement sharing in the case of the two-atom Tavis-Cummings model, a system of both theoretical and experimental interest.Comment: 11 pages, 4 figures, submitted to PRA, v3 contains corrections to small error

The social representation that adolescents from Jalisco, Mexico have of early detection of breast cancer [Representación social que los adolescentes de Jalisco, México, tienen de la detección precoz del cáncer de mama]

We consider a new exactly solvable nonlinear quantum model as a Hamiltonian defined in terms of the generators of the suq(2) algebra. The corresponding matrix elements of finite rotations (the q-deformed Wigner d functions) are introduced. It is shown that the quantum optical model of the three-wave interaction has an approximate suq(2) dynamical symmetry given by this Hamiltonian. Such q symmetry allows us to investigate the spectral and dynamical properties of the three wave model through new perturbation techniques. " 2001 MAIK "Nauka/Interperiodica".",,,,,,"10.1134/1.1432904",,,"http://hdl.handle.net/20.500.12104/45297","http://www.scopus.com/inward/record.url?eid=2-s2.0-0035562287&partnerID=40&md5=ce1aefa21bf31ef099081d8b7db172f3",,,,,,"12",,"Physics of Atomic Nuclei",,"209

The suq(2) algebra in the off-diagonal basis and applications to quantum optics

We consider a new exactly solvable nonlinear quantum model as a Hamiltonian defined in terms of the generators of the suq(2) algebra. The corresponding matrix elements of finite rotations (the q-deformed Wigner d functions) are introduced. It is shown that the quantum optical model of the three-wave interaction has an approximate suq(2) dynamical symmetry given by this Hamiltonian. Such q symmetry allows us to investigate the spectral and dynamical properties of the three wave model through new perturbation techniques. © 2001 MAIK "Nauka/Interperiodica"

Gaussians on the circle and quantum phase

We show that the phase distribution function for a strong quantum radiation field can be represented in terms of the Jacobi elliptic function ?3(z | q). This representation simplifies calculation of phase properties of the field. � 1997 Elsevier Science B.V

A Group-Theoretical Approach to Quantum Optics: Models of Atom-Field Interactions

Written by major contributors to the field who are well known within the community, this is the first comprehensive summary of the many results generated by this approach to quantum optics to date. As such, the book analyses selected topics of quantum optics, focusing on atom-field interactions from a group-theoretical perspective, while discussing the principal quantum optics models using algebraic language. The overall result is a clear demonstration of the advantages of applying algebraic methods to quantum optics problems, illustrated by a number of end-of-chapter problems. An invaluable source for atomic physicists, graduates and students in physics. © 2009 Wiley-VCH Verlag GmbH & Co. KGaA

Semiclassical quantization of the evolution operator for a class of optical models

We consider an arbitrary atomic system (n-level atom or many such atoms) interacting with a strong resonant quantum field. The approximate evolution operator for a quantum field case can be obtained from the atomic evolution operator in an external classical field by a "quantization prescription", passing the operator arguments to Wigner D-functions. Some applications are discussed. © 1995

On the SU(2) Wigner function dynamics

We study the quantum dynamics of the SU(2) quasiprobability distribution ("Wigner function") for the simple nonlinear Hamiltonian (finite analog of the Kerr medium, H = Sz 2). The quasiclassical approximation for the Wigner function and the corresponding evolution of mean values are considered and compared with the exact and classical solutions

Gaussians on the circle and quantum phase

We show that the phase distribution function for a strong quantum radiation field can be represented in terms of the Jacobi elliptic function Θ3(z | q). This representation simplifies calculation of phase properties of the field. © 1997 Elsevier Science B.V

Cavity quantum electrodynamics in a strong-field limit

Many n-level atoms with arbitrary degeneracy of levels placed in a perfect cavity are described by the Hamiltonian H = ω(a†a + H) + g(aX+ + a†X-), where a†, a are cavity-mode operators, h is the bare atomic Hamiltonian, and X+, X- are atomic-transition operators obeying commutation relations [h, H±] = ± x±, which implies RWA and excitation-number conservation. The fact that we do not impose any conditions on the commutator [X+, X-] gives a freedom in atomic system specification. For simplicity, we adopt the exact resonance condition: transition frequencies between neighboring levels equal to the field frequency ω. Consider initial coherent field state |α〉, α ≡ √n̄eiφ, with a large photon number. In the classical-field limit, the interaction Hamiltonian becomes proportional to Hcl = eiφX+ + e-iφX-. We determined the semiclassical eigenvectors (SE) to be Hcl|p〉at = λp o|p〉at. Now, let the initial atomic state be a SE. Then the system wave function is approximately factorized for times up to gt approx. n̄ and has the form |Ψ(t)〉 ≅ |Φp(t)〉f ⊗ |Ap(t)〉at, |Φp(t)〉f = ∑n pn exp[-igtλ(p)(0)√n-C+ 1/2 ] | n〉f, |Ap(t)〉at = exp(-iδt)exp(-itωph)|p〉 at, ω-p$/ ≡ gλp 0/(2√n̄ - C + 1/2 ), (1) where pn are the initial coherent-state amplitudes, C is the energy ground level of the bare atomic system, and exp(-iδt) is a phase factor, which we do not specify here. Equations (1) imply that as the field and atomic subsystems evolve, they remain approximately in pure states in spite of their interation. The mean atomic energy 〈h(t)〉 is constant, i.e., the SEs are trapping states. An arbitrary initial atomic state can be expanded in the SE basis. Therefore Eqs. (1) contain all the dynamical information; e.g., they imply atomic energy oscillations, collapses, and revivals. Our solution provides explicit calculation of any physical quantities for the systems under study