356,996 research outputs found
Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
We introduce two generalizations of the Jaynes-Cummings (JC) model for two
modes of oscillation. The first model is formed by two Jaynes-Cummings
interactions, while the second model is written as a simultaneous
Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of
its properties and obtain the energy spectrum and eigenfunctions of these
models by using the tilting transformation and the Perelomov number coherent
states of the two-dimensional harmonic oscillator. Moreover, as physical
applications, we connect these new models with two important and novelty
problems: The relativistic non-degenerate parametric amplifier and the
relativistic problem of two coupled oscillators.Comment: 16 page
Some remarks on 'superradiant' phase transitions in light-matter systems
In this paper we analyze properties of the phase transition that appears in a
set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally
the Jaynes-Cummings model. As the light-matter coupling is increased into the
deep strong coupling regime, the ground state turns from vacuum to become a
superradiant state characterized by both atomic and photonic excitations. It is
pointed out that all four transitions are of the mean-field type, that quantum
fluctuations are negligible, and hence these fluctuations cannot be responsible
for the corresponding vacuum instability. In this respect, these are not
quantum phase transitions. In the case of the Tavis-Cummings and
Jaynes-Cummings models, the continuous symmetry of these models implies that
quantum fluctuations are not only negligible, but strictly zero. However, all
models possess a non-analyticity in the ground state in agreement with a
continuous quantum phase transition. As such, it is a matter of taste whether
the transitions should be termed quantum or not. In addition, we also consider
the modifications of the transitions when photon losses are present. For the
Dicke and Rabi models these non-equilibrium steady states remain critical,
while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is
completely lost, i.e. in realistic settings one cannot expect a true critical
behaviour for the two last models.Comment: 25 pages (single column), 6 figure
Bound entanglement in the Jaynes-Cummings model
We study in detail entanglement properties of the Jaynes-Cummings model
assuming a two-level atom (qubit) interacting with the first levels of an
electromagnetic field mode (qudit) in a cavity. In the Jaynes-Cummings model,
the number operator is the conserved quantity that allows for the exact
diagonalization of the Hamiltonian and thus we study states that commute with
this conserved quantity and whose structure is preserved under the
Jaynes-Cummings dynamics. Contrary to the common belief, we show that there are
bound entangled states that satisfy the symmetries imposed by the conservation
of the number of excitations when . Furthermore we show that \emph{the
Jaynes-Cummings interaction can be used to generate bound-entanglement} between
the atom and the mode.Comment: Improved abstract, references and new section on the generation of
bound entanglement using the JC interactio
A Molecular Micromaser
We show that photoassociation of fermionic atoms into bosonic molecules
inside an optical lattice can be described using a Jaynes-Cummings Hamiltonian
with a nonlinear detuning. Using this equivalence to the Jaynes-Cummings
dynamics, we show how one can construct a micromaser for the molecular field in
each lattice site
Strong coupling expansion for the Bose-Hubbard and the Jaynes-Cummings lattice model
A strong coupling expansion, based on the Kato-Bloch perturbation theory,
which has recently been proposed by Eckardt et al. [Phys. Rev. B 79, 195131]
and Teichmann et al. [Phys. Rev. B 79, 224515] is implemented in order to study
various aspects of the Bose-Hubbard and the Jaynes-Cummings lattice model. The
approach, which allows to generate numerically all diagrams up to a desired
order in the interaction strength is generalized for disordered systems and for
the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and the
Jaynes-Cummings lattice model will be presented and compared with results from
VCA and DMRG. Our focus will be on the Mott insulator to superfluid transition.Comment: 29 pages, 21 figure
An approach to exact solutions of the time-dependent supersymmetric two-level three-photon Jaynes-Cummings model
By utilizing the property of the supersymmetric structure in the two-level
multiphoton Jaynes-Cummings model, an invariant is constructed in terms of the
supersymmetric generators by working in the sub-Hilbert-space corresponding to
a particular eigenvalue of the conserved supersymmetric generators. We obtain
the exact solutions of the time-dependent Schr\"{o}dinger equation which
describes the time-dependent supersymmetric two-level three-photon
Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary
transformation formulation. The case under the adiabatic approximation is also
discussed.
Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant
theory; geometric phase factor; adiabatic approximationComment: 7 pages, Late
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