Figure 1

(a) The breathing mode frequency for a Bose-Einstein condensate immersed in a Fermi sea as a function of interaction parameter $a_c/a_{bf}$. The experimental data from Ref. [54] are denoted by stars. The theoretical data from Ref. [54] are indicated by black solid (full phase separation model) and black dashed (adiabatic Fermi sea model) lines. The rest of the points comes from combined classical fields and pseudowave function model from this work. The blue color indicates zero-temperature calculation, while the orange and red colors pertain to finite temperature calculations. The black color signifies the oscillation frequency of the thermal cloud associated with the red markers. The calculations are performed within the lowest-order constrained variational approach. For nonzero temperature calculation that involves temperature taken from the experiment [54] (red markers), the initial condensed fraction of bosons is 40% (initial temperature $T_0/T_c=0.84$) and the ratio of condensed bosons to fermions is $N_b^0/N_f=0.16$. The orange markers denote lower temperature, with the same $N_b^0/N_f=0.16$, but with the condensed fraction being 53% ($T_0/T_c=0.77$). The theory from Ref. [54] clearly overestimates the experimental curve and does not reproduce nonmonotonicity for a strong interaction. So does the zero temperature calculation, however, to lesser extent. The full nonzero temperature calculation grasps the experimental data both qualitatively and quantitatively. For a strong interaction, up-shift of thermal cloud’s frequency is observed. (b) The breathing mode frequency as a function of number of condensed bosons to number of fermions ratio, $N_b^0/N_f$. The interaction strength is kept constant, at $a_c/a_{bf}=0.45$. Analogously, the blue markers pertain to the zero-temperature model and the red ones to the nonzero one. Again, the former overestimates the experimental data, however, to the lesser extent than FPS and APS models. Accounting for a finite temperature allows us to reproduce the experimental results.