The Bell Based Super Coherent States. Uncertainty Relations, Golden Ratio and Fermion-Boson Entanglement

• URL: http://arxiv.org/abs/2405.08594v1
• Date: Tue, 14 May 2024 13:36:50 GMT
• Title: The Bell Based Super Coherent States. Uncertainty Relations, Golden Ratio and Fermion-Boson Entanglement
• Authors: Oktay K Pashaev, Aygul Kocak,
• Abstract summary: A set of maximally fermion-boson entangled Bell super-coherent states is introduced. A superposition of these states with separable bosonic coherent states is represented by points on the super-Bloch sphere. Entanglement of bosonic and fermionic degrees of freedom in these states is studied by using displacement bosonic operator.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The set of maximally fermion-boson entangled Bell super-coherent states is introduced. A superposition of these states with separable bosonic coherent states, represented by points on the super-Bloch sphere, we call the Bell based super-coherent states. Entanglement of bosonic and fermionic degrees of freedom in these states is studied by using displacement bosonic operator. It acts on the super-qubit reference state, representing superposition of the zero and the one super-number states, forming computational basis super-states. We show that the states are completely characterized by displaced Fock states, as a superposition with non-classical, the photon added coherent states, and the entanglement is independent of coherent state parameter $\alpha$ and of the time evolution. In contrast to never orthogonal Glauber coherent states, our entangled super-coherent states can be orthogonal. The uncertainty relation in the states is monotonically growing function of the concurrence and for entangled states we get non-classical quadrature squeezing and representation of uncertainty by ratio of two Fibonacci numbers. The sequence of concurrences, and corresponding uncertainties $\hbar F_n/F_{n+1}$, in the limit $n \rightarrow \infty $, convergent to the Golden ratio uncertainty $\hbar/\varphi$, where $\varphi = \frac{1 + \sqrt{5}}{2}$ is found.

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