fluctuations have energies that soften on approach to the transition and, as can be seen in Figs. \[Fig:SFandE\](b1) and \[Fig:SFandE\](c1), these typically have energies of the same order as the radial confinement energy $\hbar\omega_\rho$. Again choosing $\omega_\rho=2\pi\times 1$ Hz means that without Bragg spectroscopy, for quantum fluctuations to dominate, experiments would otherwise need to be in the very-low-temperature regime, $T< 0.1$ nK. Concerning the validity of the quasi-2D approximation for the candidate regime above, we note that for $g=8$ the chemical potential relative to that of the noninteracting ground state is $\mu/\hbar\omega_z = 0.149$, where $\mu_1=\mu_2\equiv\mu$, thus satisfying the requirement that $\mu/\hbar\omega_z \ll 1$.

Conclusions {#Sec:Conclusions}
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In quantum fluids, quantum fluctuations are typically not important unless the dimensionality is low, the density is high or the particle number is very low. We have proposed an alternative scheme for enhanced quantum fluctuations that does not require any of these conditions to be satisfied, but instead relies on engineering an effective attractive interaction for the spin excitations of a two-component BEC. A strength of this approach is that the BEC is not vulnerable to dynamic instability, as would be the case for true attractive interactions.

In addition to numerical calculations, we 