Method System Quantity measured Response function Bragg Spectroscopy Gases Momentum transferred Im χ$_{nn}$ ( q , ω ) Neutron Spectroscopy $^{4}$He Number of scattered neutrons S ( q , ω ) Brillouin Spectroscopy ( ω ≪ T ) $^{4}$He Number of scattered photons S ( q , ω ) ∼ T $_{ω}$Im χ$_{nn}$ ( q , ω ) Density pulse Gases Pulse amplitude 1 $_{ω}$Im χ$_{nn}$ ( q , ω ) TABLE I: Summary of experimental probes. From left to right: the experimental method, the system(s) to which the method can be applied, the quantity being measured, and the density response function involved. In the two-fluid region of strongly interacting Fermi gases and $^{4}$He, second sound is weakly coupled to density fluctuations but has a small frequency ω at high temper- atures (below T$_{c}$ ). This means that, as a result of the extra factor of 1 /ω multiplying the density response function, Brillouin spectroscopy and density pulses are more sensitive to second sound than Bragg and neutron scattering. where ω$_{z}$ is the frequency of the harmonic trap along the axis of light propagation ( q = ˆ z q ), the momentum transferred is where V is the strength of the potential induced by the lasers and τ is the pulse duration. As noted recently by Arahata and Nikuni [10], the density response function can also be measured by exciting a density pulse in a uniform gas. Within linear response theory, the density fluctuation δn ( r , t ) induced by the application of an external perturbing potential δV ( r , t ) is where δV ( q , ω ) is the Fourier transform of the perturbing potential. Similar to the sound propagation experiments in [21, 22], consider a localized potential applied for a short du- ration τ < t < 0, and turned off at t = 0. Assuming for simplicity that the perturbing 6 Δ P$_{z}$ = 2 qτ ( V 2 ) 2 Im χ$_{nn}$ ( q, ω ) , (4) δn ( r , t ) = ∫ d q (2 π ) 3 ∫ dω 2 π χ$_{nn}$ ( q , ω ) δV ( q , ω ) e i q $^{·}$r− $^{iωt}$, (5)