Spin squeezing in a spin-orbit coupled Bose-Einstein condensate

We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as $^{87}$Rb and $^{23}$Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed.