Optimal and critical squeezing fields for a multi-qubit spin system

We consider a multi-qubit spin system initially in a coherent state, whose internal interactions are described by a one-axis twisting Hamiltonian [1, 2]. We study its squeezing dynamics and calculate its squeezing parameter in the presence and absence of an external magnetic field. A critical magnetic field is introduced for this system; if the external field is increased up to, the system becomes continuously squeezed. We also introduce an optimal field, at which the average depth of the squeezing parameter is maximized. We may increase the external field to the values higher than to decrease the squeezing fluctuations, but a trade-off is involved; the squeezing depth is decreased as a result.

[1] M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138-5143 (1993).
[2] A. Akhound and M. Jafarpour, Spin squeezing Hamiltonian and optimal spin squeezing parameters, IL NuovoCimento B 122 (6), 885-896, Doi 10.1393/ncb/i2007-10398-2 (2007).