## Upper panel: single-particle dispersion varepsilon _{pm }(p_x) as a function of *p*_{x}/*k*_{r}; lower panel: DoS as a function of varepsilon -varepsilon _{
m min} for Ω = 2*E*_{r}, 4*E*_{r} and 6*E*_{r}, respectively

_{x}

_{r}

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Figures are generally photos, graphs and static images that would be represented in traditional pdf publications.

**Figure 2.** Upper panel: single-particle dispersion \varepsilon _{\pm }(p_x) as a function of *p _{x}*/

*k*; lower panel: DoS as a function of \varepsilon -\varepsilon _{\rm min} for Ω = 2

_{r}*E*, 4

_{r}*E*and 6

_{r}*E*, respectively. \varepsilon _{\rm pmin} denotes the minimum value of single-particle energy. The dashed lines are DoS for the case without the Raman coupling.

_{r}**Abstract**

In this paper we investigate the properties of Bose gases with Raman-induced spin–orbit (SO) coupling. It is found that the SO coupling can greatly modify the single-particle density of state, and thus leads to the non-monotonic behaviour of the condensate depletion, the Lee–Huang–Yang correction of ground-state energy and the transition temperature of a non-interacting Bose–Einstein condensate (BEC). The presence of the SO coupling also breaks the Galilean invariance, and this gives two different critical velocities, corresponding to the movement of the condensate and the impurity respectively. Finally, we show that with the SO coupling, the interactions modify the BEC transition temperature even at the Hartree–Fock level, in contrast to the ordinary Bose gas without the SO coupling. All results presented here can be directly verified in the current cold atom experiments using the Raman laser-induced gauge field.