= Solution
Two complementary signatures are suppressed low-speed dissipation and <quantized circulation>. Condensation alone establishes macroscopic occupation, not all of these flow properties. In a uniform weakly interacting condensate, the <Landau criterion> gives
$$
v_L=\inf_{p>0}\frac{E(p)}p=c_s=\sqrt{\mu/m}
$$
for the <Bogoliubov spectrum>. Creating an excitation in a flow changes <energy> by $E(\mathbf p)-\mathbf v\cdot\mathbf p$; a negative value allows <energy> transfer. Boundaries and vortex nucleation can make an actual measured threshold lower than this ideal bulk sound speed.
In the <moving-obstacle test of atomic superfluidity>, a blue-detuned focused <laser> repelled atoms in a sodium condensate and was scanned at different speeds. After a fixed exposure, time-of-flight <absorption imaging> measured the reduction of <condensate fraction> as a heating indicator. Low-speed heating was small, with a pronounced onset near $1.6\,\mathrm{mm/s}$, below the peak-density sound speed near $6.2\,\mathrm{mm/s}$. A stationary-beam control showed no heating; above-transition clouds constrained heating through the noncondensed fraction. Changing scan <frequency> and amplitude at common obstacle <velocity> helped separate a flow threshold from a particular trap resonance. Density inhomogeneity, obstacle geometry and vortex nucleation limit identification of the observed onset with a unique homogeneous Landau <velocity>.<Evidence for a Critical Velocity in a Bose-Einstein Condensed Gas by C. Raman and others>[pp. 2502–2504, Figs. 1–3, stationary-beam and above-transition controls]{ref}
\Image[/past-exam-of-the-atomic-and-optical-physics-course-of-the-university-of-cambridge/2015/paper-1-superfluid-experiments.png]
{title=Original moving-obstacle and rotating-anisotropy schematics for two superfluidity tests}
A second experiment stirred <rubidium-87> in a magnetic trap by rotating a small transverse anisotropy generated with a far-detuned attractive <laser>. After stirring, the cloud expanded for $27\,\mathrm{ms}$ and <absorption imaging> along the rotation axis revealed vortex cores. Below a threshold no cores appeared; faster rotation produced one or several. Ramping the stirrer down before release reduced additional excitation, and waiting after removing it tested vortex survival. Beam-centre stability and residual trap anisotropy are important controls; an isolated density dip without the rotation and persistence evidence would be less conclusive. This <stirred-condensate vortex experiment> is a response to rotation, distinct from merely imaging the appearance of a condensate.<Vortex Formation in a Stirred Bose-Einstein Condensate by K. W. Madison and others>[preprint pp. 1–3, rotating dipole anisotropy, time-of-flight imaging and single-vortex lifetime]{ref}
The <superfluid velocity> is $\mathbf v_s=(\hbar/m)\nabla\theta$. A closed loop avoiding a core must return a single-valued <order parameter>, so
$$
\boxed{\oint\mathbf v_s\cdot d\mathbf l=\frac\hbar m\,2\pi\ell=\ell\frac hm,\qquad\ell\in\mathbb Z.}
$$
A singly quantized vortex therefore has $2\pi$ <phase> winding and circulation $h/m$, with depleted density in a core of order the <healing length>. This quantized rotational response differs from ordinary rigid-body flow. The experiment supports that interpretation through controlled stirring and vortex formation; imaging cores alone does not independently measure every <phase> winding or an absolute zero dissipative rate.
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