2,375 research outputs found
The Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model
The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically
Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
We study a model describing identical bosonic atoms trapped in a
double-well potential together with a single impurity atom, comparing and
contrasting it throughout with the Dicke model. As the boson-impurity coupling
strength is varied, there is a symmetry-breaking pitchfork bifurcation which is
analogous to the quantum phase transition occurring in the Dicke model. Through
stability analysis around the bifurcation point, we show that the critical
value of the coupling strength has the same dependence on the parameters as the
critical coupling value in the Dicke model. We also show that, like the Dicke
model, the mean-field dynamics go from being regular to chaotic above the
bifurcation and macroscopic excitations of the bosons are observed. Overall,
the boson-impurity system behaves like a poor man's version of the Dicke model.Comment: 17 pages, 16 figure
Entanglement in the Dicke model
We show how an ion trap, configured for the coherent manipulation of external
and internal quantum states, can be used to simulate the irreversible dynamics
of a collective angular momentum model known as the Dicke model. In the special
case of two ions, we show that entanglement is created in the coherently driven
steady state with linear driving. For the case of more than two ions we
calculate the entanglement between two ions in the steady state of the Dicke
model by tracing over all the other ions. The entanglement in the steady state
is a maximum for the parameter values corresponding roughly to a bifurcation of
a fixed point in the corresponding semiclassical dynamics. We conjecture that
this is a general mechanism for entanglement creation in driven dissipative
quantum systems.Comment: Minor changes: Reference added and references correcte
Approximated integrability of the Dicke model
A very approximate second integral of motion of the Dicke model is identified
within a broad region above the ground state, and for a wide range of values of
the external parameters. This second integral, obtained from a Born Oppenheimer
approximation, classifies the whole regular part of the spectrum in bands
labelled by its corresponding eigenvalues. Results obtained from this
approximation are compared with exact numerical diagonalization for finite
systems in the superradiant phase, obtaining a remarkable accord. The region of
validity of our approach in the parameter space, which includes the resonant
case, is unveiled. The energy range of validity goes from the ground state up
to a certain upper energy where chaos sets in, and extends far beyond the range
of applicability of a simple harmonic approximation around the minimal energy
configuration. The upper energy validity limit increases for larger values of
the coupling constant and the ratio between the level splitting and the
frequency of the field. These results show that the Dicke model behaves like a
two-degree of freedom integrable model for a wide range of energies and values
of the external parameters.Comment: 6 pages, 3 figures. Second version with added text, references and
some new figure
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