Nonlinear coherent states

Generalized Coherent States Associated with the Cλ-Extended Oscillator

“…Similarly, the number operator N is represented by 22) where N (0) µ is defined in (5.8). On the contrary, operators giving rise to transitions between different subspaces F µ are represented by nondiagonal operator-valued matrices.…”

“…, λ − 1), generalizing the Calogero-Vasiliev [31] or modified [32] oscillator, to which it reduces for λ = 2. Its coherent states are therefore special cases of the nonlinear CS considered in [18,20,21,22,23,24,25,26].…”

“…The latter is defined in terms of creation, annihilation, and number operators, a † = f (N b )b † , a = bf (N b ), N = N b , satisfying the commutation relations [17,18,19,20] N, a † = a † , [N, a] = −a, a, a † = G(N), (1.2) where f is some Hermitian operator-valued function of the number operator and G(N) = (N + 1)f 2 (N + 1) − Nf 2 (N). Nonlinear CS defined as eigenstates of a [18,20,21,22,23], of a 2 [24], or of an arbitrary power a λ (λ > 2) [25] have, for instance, been considered in connection with nonclassical properties. For a particular class of nonlinearities, the first ones were shown to be realized physically as the stationary states of the centre-of-mass motion of a trapped ion [22].…”

“…Nonlinear CS defined as eigenstates of a [18,20,21,22,23], of a 2 [24], or of an arbitrary power a λ (λ > 2) [25] have, for instance, been considered in connection with nonclassical properties. For a particular class of nonlinearities, the first ones were shown to be realized physically as the stationary states of the centre-of-mass motion of a trapped ion [22]. It should be noted that the algebra (1.2) may also be seen as a deformed su(1,1) algebra.…”

Generalized qubits of the vibrational motion of a trapped ion

“…The method is developed in the non-rotating wave approximation regime, therefore we consider regimes where the dynamics has not been studied. Because the solutions are valid for a more extended range of parameters we call them generalized qubits.PACS numbers: 32.80.Qk, 42.50.Vk Nonclassical states of the center-of-mass motion of a trapped ion have played an important role because of the potential practical applications such as precision spectroscopy [1] [6,7], number states, specific superpositions of them, and in particular, robust to noise (spontaneous emmision) qubits have been proposed [8]. In theoretical and experimental studies of a laser interacting with a single trapped ion it has been usually considered the case in which it may be modeled as a Jaynes-Cummings interaction [5,9,10], then exhibiting the peculiar features of this model like collapses and revivals [11], and the generation of nonclassical states common to such a model or (multi-photon) generalizations of it [12][13][14].…”