Uncertainty relations for a q-deformed coherent spin state

В. В. Еремин, Алексей Александрович Мельдианов

Alessandro Vaglica, G. Vetri

Jian-zu Zhang

Laure Gouba

We consider the time-dependent bi-coherent states that are essentially the Gazeau-Klauder coherent states for the two dimensional noncommutative harmonic oscillator. Starting from some q-deformations of the oscillator algebra for which the entire deformed Fock space can be constructed explicitly, we define the q-deformed bi-coherent states. We verify the generalized Heisenberg’s uncertainty relations projected onto these states. For the initial value in time, the states are shown to satisfy a generalized version of Heisenberg’s uncertainty relations. For the initial value in time and for the parameter of noncommutativity θ = 0, the inequalities are saturated for the simultaneous measurement of the position-momentum observables. When the time evolves, the uncertainty products are different from their values at the initial time and do not always respect the generalized uncertainty relations.

Chadia Qotni

In this paper, we study a spin-1 system’s coherent states in the context of the f-deformed suf(2) algebra. This algebraic framework is used to generate intelligent coherent spin states, and the accompanying uncertainty relations are studied to analyze their quantum features. Nonlinear effects related to absorption saturation and dispersion phenomena are shown by calculating the coherent states of the entire spin system up to third order approximation. The resulting asymptotic formulas show that the excitation frequency and spin state transition processes have a significant influence on the nonlinear behavior. Additionally, we demonstrate that the suggested states have squeezing characteristics typical of intelligent states and meet minimum uncertainty relations. Additionally included are the impact of relaxation effects, material-dependent factors, and higher-order corrections on the nonlinear dynamics. These findings could lead to new advances in quantum information processing, nonlinear quantum systems, and quantum optics.

P. Osland, Jian-zu Zhang A B

Within a self-consistent framework of q-deformed Heisenberg algebra and its equivalent framework of q-deformed boson commutation relations, which relate to the under-cutting phenomenon of Heisenberg's minimal uncertainty relation, special q-deformed squeezed states are constructed. Besides the similar local maximum squeezing as the one in the undeformed case, new strong squeezing appears when the amplitude of the related coherent state increases to large values. A critical phenomenon appears at a large value of the amplitude: the variance of one component of the quadrature of the light field approaches zero, but the variance of the corresponding conjugate quantity remains finite, which is a surprising deviation from Heisenberg's uncertainty relation. The qualitative character exposed by this q-squeezed state may provide some evidence about q-deformed effects in current experiments.