GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s52> GLYPH<s45>GLYPH<s54> GLYPH<s45>GLYPH<s51> GLYPH<s48> GLYPH<s51> GLYPH<s54> GLYPH<s48>GLYPH<s46> GLYPH<s50> GLYPH<s48>GLYPH<s46> GLYPH<s53> GLYPH<s48>GLYPH<s46> GLYPH<s51> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s47>GLYPH<s32> GLYPH<s107> GLYPH<s66> GLYPH<s84> GLYPH<s49>GLYPH<s32>GLYPH<s47>GLYPH<s32> GLYPH<s110> GLYPH<s49>GLYPH<s47>GLYPH<s51> GLYPH<s97> GLYPH<s115> GLYPH<s97> GLYPH<s115> GLYPH<s32> GLYPH<s47> GLYPH<s32> GLYPH<s100> GLYPH<s66> GLYPH<s32> GLYPH<s61> GLYPH<s32> GLYPH<s49> FIG. 4: Chemical potential µ of the coherent mixture versus 1 /n 1 / $^{3}$a$_{s}$ with a$_{s}$/λ$_{dB}$ =0.2, 0.3, 0.5 and 1.0 respectively, where λ$_{dB}$ = √ 2 π ¯ h $^{2}$/mk$_{B}$ T . From the saddle point condition Eq. (17), the ratio ψ ∗ $_{0}$/ψ$_{0}$ is either 1 or -1, and the quasi-particle excitation energy can be rewritten as E$_{k}$ = √ ( ϵ$_{k}$ + 2 gn$_{0}$ )( ϵ$_{k}$ − 2Δ ψ ∗ $_{0}$/ψ$_{0}$ ) . For fixed total density, the chemical potential and order parameters can be solved from Eq. (17, 18, 19). The solution shows a reentrant behavior near the transition to the molecular- BEC phase, as shown in Fig. 4. The reentrance range in temperature is broadened close to the resonance. This reentrance behavior is likely to be an unphysical result in the mean-field approximation near the transition, similar to that in the Popov approximation of a Bose gas near the atomic BEC temperature [22]. Away from this reentrance, as shown in Fig. 4, the chemical potential µ is a monotonically decreasing function of density n for fixed T and a$_{s}$ , ∂µ/∂n < 0, meaning that compressibility is negative. Therefore the coherent mixture is subject to mechanical collapse. 11 If the excitation energy E$_{k}$ is real, two conditions, gn$_{0}$ > 0 and ψ ∗ $_{0}$/ψ$_{0}$ = − 1, must be true, which cannot be satisfied when the scattering length a$_{s}$ is negative, indicating that the mixture cannot exist with a$_{s}$ < 0. When ψ$_{0}$ = 0, there is a transition from the coherent mixture phase to the molecular-BEC phase. At zero temperature, the transition point between the two phases locates at 1 / ( n 1 / $^{3}$a$_{s}$ ) ≃ 3 . 94.