Abstract
The states generated by the two-spin generalization of the two-axis countertwisting Hamiltonian are examined. We analyze the behavior at both short and long timescales, by calculating various quantities such as squeezing, spin expectation values, probability distributions, entanglement, Wigner functions, and Bell correlations. In the limit of large spin ensembles and short interaction times, the state can be described by a two-mode squeezed vacuum state; for qubits, Bell state entanglement is produced. We find that the Hamiltonian approximately produces two types of spin-EPR states, and the time evolution produces aperiodic oscillations between them. In a similar way to the basis invariance of Bell states and two-mode squeezed vacuum states, the Fock state correlations of spin-EPR states are basis invariant. We find that it is possible to violate a Bell inequality with such states, although the violation diminishes with increasing ensemble size. Effective methods to detect entanglement are also proposed, and formulas for the optimal times to enhance various properties are calculated.
Highlights
The concept of quantum squeezing has been central to the development of quantum metrology and its applications in quantum information science [1,2,3,4]
We have examined the 2A2S squeezed state from multiple points of view: squeezing, spin expectation values, probability distributions, entanglement, Wigner functions, and Bell correlations
Starting from two Bose-Einstein condensates (BECs) which are polarized in the positive Sz direction, the 2A2S Hamiltonian produces the spin EPR state |EPR−, the analog of the two-mode squeezed state for spins
Summary
The concept of quantum squeezing has been central to the development of quantum metrology and its applications in quantum information science [1,2,3,4]. The most widely known results for two spins are for atomic ensembles pioneered by the group of Polzik and co-workers [21,22,23] In these works, while the physical system is an atomic ensemble, the regime that is examined is where spin variables can be approximated by bosonic modes, according to the Holstein-Primakoff transformation. While the physical system is an atomic ensemble, the regime that is examined is where spin variables can be approximated by bosonic modes, according to the Holstein-Primakoff transformation In these works the entangled state that is produced can be described within this approximation as a two-mode squeezed state. In addition to elucidating the nature of the dynamics and the state, we interestingly find that the state can violate a Bell inequality without parity measurements
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