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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2405.08594 |
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| _version_ | 1866914796107988992 |
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| author | Pashaev, Oktay K Kocak, Aygul |
| author_facet | Pashaev, Oktay K Kocak, Aygul |
| contents | 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 $α$ 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 $\hbar/φ$, where $φ= \frac{1 + \sqrt{5}}{2}$ is found. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Bell Based Super Coherent States. Uncertainty Relations, Golden Ratio and Fermion-Boson Entanglement Pashaev, Oktay K Kocak, Aygul Quantum Physics High Energy Physics - Theory 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 $α$ 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 $\hbar/φ$, where $φ= \frac{1 + \sqrt{5}}{2}$ is found. |
| title | The Bell Based Super Coherent States. Uncertainty Relations, Golden Ratio and Fermion-Boson Entanglement |
| topic | Quantum Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.08594 |