= 500$. \[Fig:DynSF\]](Fig4){width="3.4in"}

![image](Fig5){width="7in"}

As we saw in Fig. \[Fig:PhaseD\], the regime of small intracomponent interactions shifts the immiscibility phase transition higher than the thermodynamic-limit prediction, i.e. $g_{12}^{\rm c}>g_{12}^{\rm c,TD}=g$. This opens up a region of forced miscibility, $g<g_{12}<g_{12}^{\rm c}$, within which quantum spin fluctuations are greatly enhanced thanks to an effective attractive interaction [^3]. Bragg spectroscopy provides an especially useful tool for observing quantum fluctuations since it provides access to the $T=0$ component of the structure factor, even at finite $T$. Thus, in this section, we numerically calculate the $T=0$ spin and density structure factors to show how the enhanced quantum fluctuations can be studied in experimentally accessible settings.

### Dynamic structure factor

For reference, we first consider a BEC in the Thomas-Fermi regime, $g\gg1$, where the immiscibility transition occurs near the thermodynamic-limit prediction, $g_{12}^{\rm c}\approx g$, and the effective interactions experienced by the spin excitations are always repulsive. When the two components are uncoupled, $g_{12}=0$, Figs. \[Fig:DynSF\] (a-b) show that the spin (left) and density (right), dynamic structure factors are identical, as expected. On the other hand, a remarkable phenomenon emerges at the phase transition, where $g_{12}=g$. While here the density structure factor \[Fig. \[Fig:DynSF\] (d)\] is much 