Mean-field pictures based on the standard time-dependent variational approach have widely been used in studying nonlinear many-boson systems such as the Bose?Hubbard model. Mean-field schemes relevant to Gutzwiller-like trial states |F, number-preserving states |? and Glauber-like trial states |Z are compared to evidence of specific properties of such schemes. After deriving the Hamiltonian picture relevant to |Z from that based on |F, the latter is shown exhibiting a Poisson algebra equipped with a Weyl?Heisenberg subalgebra which preludes to the |Z-based picture. Then states |Z are shown to be a superposition of -boson states |?, and the similarities/differences between the |Z-based and |?-based pictures are discussed. Finally, after proving that the simple, symmetric state |? indeed corresponds to a SU(M) coherent state, a dual version of states |Z and |? in terms of momentum-mode operators is discussed together with some applications.

Some remarks on the coherent-state variational approach to nonlinear boson models

Photon-added coherent states for exactly solvable Hamiltonians

The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving states $|\xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $\cal N$-boson states $|\xi>$ and the similarities/differences of the $|Z>$-based and $|\xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|\xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and $|\xi>$ in terms of momentum-mode operators is discussed together with some applications.

The evolution of pairwise quantum correlations of Bell cat states under amplitude damping is examined using the concept of quantum discord which goes beyond entanglement. A closed expression of the quantum discord is explicitly derived. We used the Koashi?Winter relation, a relation which facilitates the optimization process of the conditional entropy. We also discuss the temporal evolution of bipartite quantum correlations under a dephasing channel and compare the behaviors of quantum discord and entanglement whose properties are characterized through the concurrence.

https://iopscience.iop.org/article/10.1088/1751-8113/45/32/325302/pdf

Quantum discord of Bell cat states under amplitude damping

We present in this letter a realistic construction of the coherent states for the Morse potential using the Klauder–Perelomov approach. We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.

/pdf/statistical-properties-of-klauder-perelomov-coherent-states-43aqjt283w.pdf

Statistical properties of klauder perelomov coherent states for the morse potential

The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.

The Moyal bracket in the coherent states framework

Generalized intelligent states of the su(N) algebra

The Moyal Bracket in the Coherent States framework

We introduce a special class of truncated Weyl–Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.

https://iopscience.iop.org/article/10.1088/1751-8113/44/32/325301/pdf

M. Daoud

Papers

The Moyal bracket in the coherent states framework

Generalized intelligent states of the su(N) algebra

The Moyal Bracket in the Coherent States framework

Bipartite and Tripartite Entanglement of Truncated Harmonic Oscillator Coherent States via Beam Splitters

Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states