Multi-qubit entanglement and the critical entangling field

We consider an initial multi-qubit coherent state and study its evolution by the two-axis counter twisting Hamiltonian and investigate its entanglement properties via concurrence in the presence and absence of an external magnetic field. It is observed that in the absence of the external field, the system is not entangled in some time intervals. If the field is increased up to the critical value, the nonexistence periods vanish and barring some separate instances of time, the system becomes continuously entangled. We also define the optimal field at which the time average value of the concurrence assumes the highest possible value [1]. We observe that the fluctuations decrease if the external field is increased, but a tradeoff is involved; the value of the average concurrence is reduced. We plot concurrence versus the external field for several spins and field values.

[1] M. Jafarpour and A. Akhound, Entanglement and squeezing of multi-qubit systems using a two-axis countertwisting Hamiltonian with an external field, Phys. Lett. A 372, (2008).
[2] X. Wang and K. Molmer, Pairwise entanglement in symmetric multi-qubit systems, Eur. Phys. J. D 18 (2002).