“Second Sound” Made Visible

Executive summary

In 2024–2025, physicists directly imaged “second sound” — heat moving as a wave rather than diffusing — inside an ultracold superfluid of lithium-6 atoms. Using a new, radio-frequency–based thermography method with sub-nanokelvin sensitivity, the team watched a hotspot sloshing back and forth through the gas, cleanly crossing from ordinary diffusive heat flow to a bona-fide entropy wave predicted by Landau’s two-fluid theory. Beyond being a technical tour de force, the result provides a precision testbed for superfluid hydrodynamics and offers fresh handles on problems ranging from high-$T_c$ superconductors to the superfluid interiors of neutron stars. (MIT News, Science, quantumgas.mit.edu)

What is “second sound”

First sound is the everyday sound you know: a pressure/density wave. In a superfluid, Landau’s two-fluid model says the liquid behaves as two interpenetrating components: a normal part (viscous, carries entropy) and a superfluid part (inviscid, carries no entropy). Small oscillations in this coupled fluid admit two propagating modes. The second, in which entropy and temperature oscillate while total density barely moves, is called second sound — literally a wave of heat. (web.pa.msu.edu, Wikipedia)

At long wavelengths (neglecting dissipation), Landau’s hydrodynamics gives the characteristic second-sound speed $c_2$ as

$$c_2^{2}\;=\;\frac{\rho_s}{\rho_n}\,\frac{s^{2}\,T}{c_p}\,,$$

where $\rho_s$ and $\rho_n$ are the superfluid and normal-fluid mass densities, $s$ is entropy per unit mass, $T$ the temperature, and $c_p$ the isobaric specific heat. Two morals drop out immediately: (i) no superfluid fraction, no second sound ($\rho_s\to 0 \Rightarrow c_2\to 0$); and (ii) the mode is a thermodynamic wave, governed by entropy and heat capacities rather than compressibility. (Wikipedia, TechRxiv)

Historically, second sound was discovered in helium-II in the 1940s and mapped with resonators and pulsed techniques over a wide temperature range, becoming a textbook hallmark of superfluidity. Variants have since been reported in other platforms (including phonon-hydrodynamic solids like graphite at >200 K), but until now, direct imaging of the heat wave in a quantum gas had remained out of reach. (Physical Review, Nature)

What did the new experiments actually do

Platform and challenge

The MIT team used a strongly interacting (unitary) Fermi gas of $^{6}$Li cooled to quantum degeneracy. That platform is ideal for precision superfluid hydrodynamics — but there is a catch: at nanokelvin temperatures the sample emits essentially no infrared light, so conventional thermal cameras are useless. (MIT News)

Key idea: radio-frequency thermography

They turned the atoms themselves into a thermometer. The gas’ radio-frequency spectrum shifts in a temperature-dependent way; by scanning RF and imaging which atoms flip internal state, they infer a spatial temperature map with sub-nK resolution — effectively a quantum-gas thermal camera. This established “thermography of a strongly interacting Fermi gas” as a general technique. (Science, quantumgas.mit.edu)

Experiment in a sentence

Create a controlled hotspot in the trapped cloud → record time-resolved temperature maps → watch the hotspot either diffuse (normal fluid) or propagate as a standing/traveling heat wave (second sound) depending on $T$. The data show a sharp switch from diffusion to wave-like motion at the superfluid transition, along with the dispersion and damping of the second-sound mode. (Science)

What we did learn

1. Direct visualization of second sound
   The movies reveal temperature maxima moving while density looks nearly still, precisely the entropy-wave signature long anticipated by Landau. This explicitly distinguishes second sound from weak “echoes” in density that earlier indirect probes had to rely on. (MIT News)

2. The superfluid transition, seen thermally
   As temperature crosses $T_c$, the heat transport changes character: diffusive above $T_c$, oscillatory below. That dynamical contrast provides a clean, operational definition of the phase transition in a many-body quantum gas. (quantumgas.mit.edu)

3. Hydrodynamic parameters and transport
   By measuring the heat and density response, the experiment constrains the full suite of two-fluid hydrodynamic coefficients — enabling extraction (or tight bounds) on the superfluid fraction, thermal conductivity, specific heats, and the second-sound speed $c_2$ in the unitary Fermi gas. That is a rare window into strong-coupling thermodynamics. (Science)

4. A broadly applicable thermometer
   RF thermography is platform-agnostic within ultracold gases and could be ported to Bose gases, spin-imbalanced Fermi mixtures, or systems with engineered disorder — turning temperature itself into a microscope observable. (Science)

Why this is a big deal (beyond beautiful movies)

• Validating and extending two-fluid hydrodynamics. Second sound has been a pillar of superfluid theory for eight decades; doing precision, space-time–resolved tests in a tunable, strongly interacting Fermi fluid lets us benchmark Landau’s framework in regimes helium cannot reach. (web.pa.msu.edu)

• Bridging to superconductors. In charged superfluids (superconductors), entropy waves couple to electromagnetic fields, but the underlying entropy transport remains central. Seeing where heat behaves ballistically versus diffusively clarifies the hydrodynamic window relevant to high-$T_c$ materials. (MIT News)

• Astrophysical relevance. Neutron-star crusts and interiors are believed to host superfluid neutrons; their thermal relaxation, glitches, and oscillation spectra depend sensitively on entropy transport. Laboratory control of entropy waves gives theorists hard numbers and models to plug into stellar simulations. (Live Science)

• A method, not just a measurement. The RF-thermography approach — temperature as a directly imageable field — is a powerful idea that should generalize to studies of vortex turbulence, quantum shock waves, and spin-caloritronic effects in ultracold matter. (Science)

Clearing up common misconceptions

• “First time second sound was seen?”
  No: second sound was discovered in helium-II in the 1940s and explored extensively with resonant and pulse techniques. The novelty here is direct, real-space imaging in an ultracold atomic superfluid Fermi gas, resolving the heat wave itself. (Physical Review, Science)

• “Is it unique to superfluids?”
  The superfluid case is canonical, but hydrodynamic heat waves can also occur in solids where phonon-phonon scattering enters the hydrodynamic regime; graphite is a modern example. The physics differs in detail, yet the unifying theme is collective, wave-like entropy transport. (Nature)

A short technical appendix (for the mathematically inclined)

Start from two-fluid hydrodynamics: mass continuity $\partial_t\rho + \nabla\!\cdot(\rho_s\mathbf v_s+\rho_n\mathbf v_n)=0$, entropy continuity $\partial_t(\rho s)+\nabla\!\cdot(\rho s\,\mathbf v_n)=0$ (entropy rides the normal component), and linearized Euler-type equations for $\mathbf v_s,\mathbf v_n$. Linearize about equilibrium, eliminate pressure using thermodynamics, and seek plane waves $\propto e^{i(\mathbf k\cdot\mathbf r-\omega t)}$. One obtains two eigenmodes with speeds $c_1$ (ordinary sound) and $c_2$ (above), plus dissipative corrections from viscosity and thermal conductivity that set the quality factor and diffusivity near $T_c$. Measuring $\omega(k)$ and the damping rate $\Gamma(k)$ from the movies is precisely how the MIT team read off the hydrodynamic parameters of their gas. (web.pa.msu.edu)

Where this goes next

1. Dispersion and nonlinearity. Map $c_2(k)$ and the crossover to nonlinear regimes (shock formation for entropy waves), testing generalized two-fluid theories. (arXiv)

2. Vortex-coupled calorimetry. Watch how the entropy wave scatters off quantized vortices to probe quantum turbulence. (CERN Document Server)

3. Designer materials. Adapt RF thermography to optical lattices and disordered potentials to study heat flow across quantum phase transitions in situ. (Science)

Sources

• Science (2024): Thermography of the superfluid transition in a strongly interacting atomic Fermi gas — establishes RF thermography and visualizes the diffusion→second-sound switch. (Science)

• MIT News (2024): Plain-language overview with figures and quotes from the team. (MIT News)

• MIT Quantum Gases Group page: Method details and note on sub-nK spatial thermometry. (quantumgas.mit.edu)

• Historical context: Early helium-II measurements of second sound and reviews of the two-fluid model. (Physical Review, web.pa.msu.edu)

• Broader landscape: Second sound in graphite (phonon hydrodynamics above 200 K), illustrating the wider relevance of entropy waves. (Nature)