## 3 Results
### Experimental Setup  
A complete description of the experimental setup and experimental sequence for producing a Bose-Einstein condensate of \({}^{23}\)Na atoms is described in [40]. Here, we present a short description of the system giving the experimental parameters relevant for the simulations performed later in this Section.  
Briefly, sodium and potassium atoms coming from independent two-dimensional magneto-optical traps (2D-MOTs) [48; 49] are combined in a common vacuum chamber where they will be trapped and further cooled in a three-dimensional MOT (3D-MOT). Due to the strong interspecies losses present in the Na-K mixture [40; 50], the operation of an intial two-color MOT is not the best alternative in our experiment. Instead, we chose to favor the minority species (potassium) during the MOT phase, starting the MOT sequence with the loading of a single species MOT of \({}^{39}\)K until it reaches the saturation value (\(\sim\)20 s). Next, we operate the two-color MOT by switching on the lights responsible for trapping and cooling sodium atoms. We control the initial atom number ratio \(N_{\text{Na}}^{0}/N_{\text{K}}^{0}\) by changing the time duration of the loading of the sodium atoms in the two-color MOT operation.  
Once the two species are loaded, we perform subsequent cooling procedures followed by a fine pumping stage which transfer both species to the \(F=1\) ground-state before turning on an optically plugged Quadrupole trap [51]. At the beginning of the magnetic trap the atomic clouds have \(N_{\text{Na}}\)\(\sim\)\(1\times 10^{9}\) atoms and \(N_{\text{K}}\)\(\sim\)\(1\times 10^{6}\) atoms both at \(T=220\)\(\upmu\)K trapped in the \(|F=1,m_{F}=-1>\) hyperfine ground-state.  
Evaporative cooling [52] of sodium is performed with microwave radiation at \(\sim\)1.7 GHz while potassium atoms are sympathetic cooled [53; 54] decreasing its temperature without significant atom loss. At \(T\)\(\sim\)6-7 \(\upmu\)K, the atomic clouds are transferred to a pure optical dipole trap (ODT) [55] where the interspecies interaction can be tuned with the use of Feshbach resonances [27] by applying a uniform magnetic field. We have atomic clouds with \(N_{\text{Na}}=5\times 10^{6}\) and \(N_{\text{K}}=8\times 10^{5}\) at the beginning of the ODT for maximum atoms number of \({}^{39}\)K. In single-species operation for sodium under the same conditions, we obtain an almost pure BEC (with BEC fraction \(>80\%\)) with \(N=1\times 10^{6}\) atoms at \(T\)\(\sim\)80\(\upmu\)K after applying an optical evaporation which reduces the initial ODT potential height by a factor of five in 4.2 s. The final ODT configuration exhibits a planar geometry with equal frequencies in the \(xy\)-plane perpendicular to the gravity direction. The final frequencies are \(\omega_{\text{x,y}}=2\pi\times 107(137)\) Hz and \(\omega_{\text{z}}=2\pi\times 148(193)\) Hz for Na(K), respectively. This is the actual situation of our experimental system and, following the initial atom number difference in the ODT, we estimate to be able to obtain a two-species BEC once implemented the Feshbach field. Following these experimental numbers we performed the simulations described in Section 2.2 which results are presented in the following.