GLYPH<s45>GLYPH<s56> GLYPH<s45>GLYPH<s52> GLYPH<s48> GLYPH<s52> GLYPH<s56> GLYPH<s48> GLYPH<s53> GLYPH<s49>GLYPH<s48> GLYPH<s49>GLYPH<s53> GLYPH<s48> GLYPH<s49> GLYPH<s50> GLYPH<s51> GLYPH<s52> GLYPH<s48> GLYPH<s51> GLYPH<s54> GLYPH<s57> GLYPH<s32> GLYPH<s32> GLYPH<s69> GLYPH<s98> GLYPH<s32> GLYPH<s47> GLYPH<s32> GLYPH<s107> GLYPH<s66> GLYPH<s84> GLYPH<s97> GLYPH<s49>GLYPH<s32>GLYPH<s47>GLYPH<s32> GLYPH<s110> GLYPH<s49>GLYPH<s47>GLYPH<s51> GLYPH<s97> GLYPH<s115> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s77>GLYPH<s70> GLYPH<s32> GLYPH<s84> GLYPH<s32> GLYPH<s61> GLYPH<s32> GLYPH<s84> GLYPH<s112> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s77>GLYPH<s70> GLYPH<s32> GLYPH<s84> GLYPH<s32> GLYPH<s61> GLYPH<s32> GLYPH<s32> GLYPH<s48> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s32> GLYPH<s118>GLYPH<s97>GLYPH<s99>GLYPH<s117>GLYPH<s117>GLYPH<s109>GLYPH<s32> GLYPH<s53> GLYPH<s48> GLYPH<s50> GLYPH<s51> GLYPH<s51>GLYPH<s46>GLYPH<s57>GLYPH<s52> GLYPH<s32> GLYPH<s32> GLYPH<s69> GLYPH<s98> GLYPH<s32> GLYPH<s47> GLYPH<s32> GLYPH<s107> GLYPH<s66> GLYPH<s84> GLYPH<s97> GLYPH<s84> GLYPH<s32> GLYPH<s47>GLYPH<s32> GLYPH<s84> GLYPH<s97> GLYPH<s49> GLYPH<s32> GLYPH<s47> GLYPH<s32> GLYPH<s110> GLYPH<s49> GLYPH<s47> GLYPH<s51> GLYPH<s97> GLYPH<s115> GLYPH<s32> GLYPH<s61>GLYPH<s32> GLYPH<s32> GLYPH<s53>GLYPH<s46>GLYPH<s53> GLYPH<s52>GLYPH<s46>GLYPH<s53> FIG. 1: Binding energy of Feshbach molecules in molecular-BEC state. The solid and dashed lines are binding energies at T = T$_{p}$ and T = 0K. The dotted line is the binding energy in vacuum, E$_{b}$$_{0}$ = ¯ h $^{2}$/ ( ma 2 $_{s}$). The inset shows the temperature dependence of the binding energy for different n 1 / $^{3}$a$_{s}$ . where I is the identity matrix. The molecular excitation is gapless in the long-wavelength limit, k = 0 and ω = 0, following Eq. (4). At small k and ω , to the leading order of k , the molecular excitation frequency is linearly dispersed. The detail of molecular excitations will be studied in our future work. The binding energy E$_{b}$ of a Feshbach molecule in the molecular-BEC state is defined as the energy difference between two atomic and one molecular excitations at k = 0. Since the molecular excitation energy is gapless in the molecular-BEC state, the binding energy of Feshbach molecules is twice the energy gap of atomic excitations, E$_{b}$ = 2 E$_{0}$ . Due to many-body effect, the binding energy E$_{b}$ is different from its vacuum value E$_{b}$$_{0}$ = ¯ h $^{2}$/ ( ma 2 $_{s}$). At the superfluid transition temperature T$_{p}$ , the binding energy is given by E$_{b}$ ( T$_{p}$ ) = − 2 µ $^{′}$. In the limit of weakly-attractive interaction, n 1 / $^{3}$a$_{s}$ → 0 $^{−}$, we obtain C. Binding energy E$_{b}$ ( T$_{p}$ ) = 16 πζ − 2 / $^{3}$(3 / 2) n 2 3 | a$_{s}$ | $^{2}$k$_{B}$ T$_{a}$, where ζ ( x ) is the Riemann-zeta function and T$_{a}$ is the ideal BEC temperature, T$_{a}$ = (2 π ¯ h $^{2}$/mk$_{B}$ )[ n/ζ (3 / 2)] 2 / $^{3}$; in the limit of weakly repulsion, n 1 / $^{3}$a$_{s}$ → 0 $^{+}$, the binding en- 5