that even though quantum fluctuations are large, the condensate depletion need not be, unless of course the system is very close to the immiscibility transition. This can be understood by the following. When interactions are effectively repulsive for a given excitation, the $v_\alpha^\kappa$ \[see Eq. (\[Eq:SF\])\] is approximately equal to $u_\alpha^\kappa$, but with opposite sign. The ensuing cancellation within Eq. (\[Eq:SF\]) results in a suppressed structure factor, implying anti-bunching with respect to the noninteracting limit. For attractive interactions, on the other hand, both $v_i$ and $u_i$ have the same sign, resulting in enhanced fluctuations (bunching). This sign reversal of $v_i$ is reminiscent of the weakly-interacting dipolar roton [@Santos2003], for which the effective interaction is momentum dependent, switching from repulsive to attractive near the roton wavelength [@Bisset2013C; @Blakie2013].

![(a) Density $S_\mathcal{D}$, spin $S_\mathcal{S}$, and one-component static structure factor $S_1$ for $g_{12}/g = 1.51$. The horizontal dashed lines indicate the structure factor peaks. (b) Spin and one-component static structure factor peaks as a function of $g_{12}/g$. The vertical dashed line indicates the interaction strength considered in (a). Note that $g_{12}^{\rm c}/g=1.55$ and $g=8$. \[Fig:SFpeak\]](Fig6){width="3.4in"}

### Single-component Bragg spectroscopy

While spin Bragg spectroscopy should provide the most-direct signal of quantum spin fluctuations, this 