Entanglement and spin squeezing properties for three bosons in two modes

We discuss the canonical form for a pure state of three identical bosons in two modes, and classify its entanglement correlation into two types, the analogous GHZ and the W types as well known in a system of three distinguishable qubits. We have performed a detailed study of two important entanglement measures for such a system, the concurrence $\mathcal{C}$ and the triple entanglement measure $τ$. We have also calculated explicitly the spin squeezing parameter $ξ$ and the result shows that the W state is the most ``anti-squeezing'' state, for which the spin squeezing parameter cannot be regarded as an entanglement measure.