Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model

Chaichian, M.; Ellinas, Demosthenes; Kulish, P. P.

doi:10.1103/physrevlett.65.980

Cited by 357 publications

(238 citation statements)

References 21 publications

Supporting

Mentioning

235

Contrasting

Unclassified

Order By: Relevance

“…= −1 on the other hand gives noncompact algebra su q (1, 1). Subsequently, a single mode realization was found through q-Holstein-Primakov (q-HP) transformation [7,8,9]…”

Section: Q-boson and Q-spinmentioning

confidence: 99%

“…The concept of q-boson was formally introduced as q-parameter deformation of a standard boson, or through two-mode realization of quantum algebra [4,5,6]. Subsequently, the finding of more application oriented single mode q-bosonic realization of quantum algebra through q-deformation of Holstein-Primakov transformation [7,8,9] and linking it to QIS [10] was a significant step. However, it seems that this initial but important step has not been pursued with enough zest to explore the possibility of appearance of q-boson in other QIS and its applications in exactly solvable physical models.…”

Section: Introductionmentioning

confidence: 99%

“…However, it seems that this initial but important step has not been pursued with enough zest to explore the possibility of appearance of q-boson in other QIS and its applications in exactly solvable physical models. It is true that there were attempts to construct interesting q-bosonic and q-spin models in various fields and to study their physical effects [7,8,11,12,13,14,15]. However most of such models could not be related to the underlying YB algebra of a QIS permitting exact treatment by the Bethe ansatz (BA) method.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

q-Boson in Quantum Integrable Systems

Kundu¹

2007

SIGMA

View full text Add to dashboard Cite

Abstract. q-bosonic realization of the underlying Yang-Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode q-bosonic model leading to a coupled two-component derivative NLS model, wide range of q-deformed matter-radiation models, q-anyon model etc. Result on a new exactly solvable interacting anyon gas, linked to q-anyons on the lattice is reported.

show abstract

“…= −1 on the other hand gives noncompact algebra su q (1, 1). Subsequently, a single mode realization was found through q-Holstein-Primakov (q-HP) transformation [7,8,9]…”

Section: Q-boson and Q-spinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

q-Boson in Quantum Integrable Systems

Kundu¹

2007

SIGMA

View full text Add to dashboard Cite

show abstract

“…λν a f ⊗ σ − and λν a † f ⊗ σ + ) of the 'Jaynes-Cummings model with intensity-dependent coupling' studied, for instance, in ref. [22]. Another natural choice of the functions g, f is provided by a more accurate approximation of the interaction term H (t) of the ion trap Hamiltonian, approximation which is adopted by some authors (see, for instance, refs.…”

Section: The Ion Trap Hamiltonian (Revisited)mentioning

confidence: 99%

A new perturbative expansion of the time evolution operator associated with a quantum system

Aniello¹

2005

J. Opt. B: Quantum Semiclass. Opt.

View full text Add to dashboard Cite

A novel expansion of the evolution operator associated with a -in general, time-dependent -perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.

show abstract

“…Several dynamical models where U q (su(1, 1)) appears as a symmetry or a dynamical algebra are known [10]- [14], and it is likely that U q (su(1, 1)) will play a significant role in the models with non-compact spaces. The representation theories of U q (su(1, 1)) were given in [15]- [17] for generic q, i.e., q not a root of unity.…”

Section: Introductionmentioning

confidence: 99%

More on U q(su(1,1)) with q a root of unity

Suzuki

1994

Journal of Mathematical Physics

View full text Add to dashboard Cite

Highest weight representations of U q (su(1, 1)) with q = exp πi/N are investigated. The structures of the irreducible hieghesat weight modules are discussed in detail. The Clebsch-Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2, R) ⊗ U q (su(2)) is also presented in terms of holomorphic sections which also have U q (su(2)) index. Furthermore we realise Z N -graded supersymmetry in terms of the representation. An explicit realization of Osp(1|2) via the heighest weight representation of U q (su(1, 1)) with q 2 = −1 is given.

show abstract

Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model

Cited by 357 publications

References 21 publications

q-Boson in Quantum Integrable Systems

q-Boson in Quantum Integrable Systems

A new perturbative expansion of the time evolution operator associated with a quantum system

More on U q(su(1,1)) with q a root of unity

Contact Info

Product

Resources

About