Narrow Results

The optical charge pair coherent states for a two-mode electromagnetic field corresponding to $q_1$- and $q_2$-deformed oscillator algebras that are both of the Arik–Coon or Biedenharn–Macfarlane type are constructed. Next, their associated even and odd cat states are formulated in terms of the charge, deformation parameters $q_1$ and $q_2$, and coherent field, in a linear combination form of two-mode number states of the deformed oscillators. The two-mode higher-order anti-bunching, squeezing, and entanglement traits of the even and odd charge cat states corresponding to the oscillators with the same deformation parameters are considered in terms of the charge and the coherent field as well as different values for deformation parameter itself. We compare the difference of these non-classical behaviors not only between the odd and even states of each two-mode oscillator but also between two-mode Arik–Coon and Biedenharn–Macfarlane oscillators. For example, we answer whether the entanglement of the two-mode cat states increases or decreases with the increase of the charge.

We propose a new model for studying the dark constituents of the universe by regarding the dark energy as a $q$-deformed scalar field interacting with the dark matter, in the framework of standard general relativity. Here we assume that the number of particles in each mode of the $q$-deformed scalar field varies in time by the particle creation and annihilation. We first describe the $q$-deformed scalar field dark energy quantum-field theoretically, then construct the action and the dynamical structure of these interacting dark sectors, in order to study the dynamics of the model. We perform the phase space analysis of the model to confirm and interpret our proposal by searching the stable attractor solutions implying the late-time accelerating phase of the universe. We then obtain the result that when interaction and equation-of-state parameter of the dark matter evolve from the present day values into a particular value, the dark energy turns out to be a $q$-deformed scalar field.

We show that quantum logic gates, viz. the single qubit Hadamard and Phase Shift gates, can also be realized using q-deformed angular momentum states constructed via the Jordan–Schwinger mechanism with two q-deformed oscillators.

It is shown that the two qubit CNOT (controlled NOT) gate can also be realized using q-deformed angular momentum states constructed via the Jordan–Schwinger mechanism. Thus, all the three gates necessary for universality i.e. Hadamard, Phase Shift and the two qubit CNOT gate are realizable with q-deformed oscillators.