Observation of the Fermionic Joule-Thomson Effect

We report the first observation of the quantum Joule-Thomson (JT) effect in ideal and unitary Fermi gases. We study the temperature dynamics of these systems while they undergo an energy-per-particle conserving rarefaction. For scale-invariant systems, whose equations of state satisfy the relation $U\propto PV$, this rarefaction conserves the specific enthalpy, which makes it thermodynamically equivalent to a JT throttling process. We observe JT heating in an ideal Fermi gas, a direct consequence of Pauli blocking. In a unitary Fermi gas, we observe that the JT heating is marginal in the temperature range $0.2\lesssim T/T_{\mathrm{F}}\lesssim 0.8$ as the repulsive quantum-statistical effect is lessened by the attractive interparticle interactions.

Figure 1

Joule-Thomson rarefaction of a homogeneous Fermi gas. (a) Classic throttling process. A thermally isolated gas is forced from a high pressure chamber (left) to a low pressure one (right). (b) JT process through a rarefaction at fixed energy per particle $u$ and volume $V$; $N_{\mathrm{i}}$ is the initial particle number. The images to the left of the cartoons are in situ optical density (OD) images of homogeneous Fermi gases of ${}^6\mathrm{Li}$ atoms, before (left, purple) and after (right, green) rarefaction. (c) Cuts along the white dotted lines on the OD images. The solid lines are fits to extract the box volume. The length and radius of this cylindrical box are $L=58(1)\mathrm{\mu }\mathrm{m}$ and $R=77(2)\mathrm{\mu }\mathrm{m}$, and remain essentially unchanged during rarefaction (see vertical dashed gray lines as guides to the eye, located at the same positions between the left and right panels). The density cuts are colored according to panel (b).

Figure 2

Joule-Thomson effect of the ideal Fermi gas. (a) Sketch of an energy-independent atom loss due to collisions with high-energy background particles (red empty circle). (b) Decay of a noninteracting Fermi gas (black circles) and weakly interacting Fermi gases (colored diamonds) at different initial $T/T_{\mathrm{F}}$ (see legend). The solid lines are exponential fits. The same marker color is used in (c) and (d). (c) Azimuthally averaged radial momentum distribution of Fermi gases extracted from column integrated OD after a time-of-flight expansion of duration $t_{\mathrm{TOF}}$. The distributions are normalized such that $\int \tilde{n}(k_r/k_{\mathrm{F}})(2\pi k_r/k_{\mathrm{F}})\mathrm{d}(k_r/k_{\mathrm{F}})=1$; here $k_r=m\sqrt{y^2+z^2}/(\hslash t_{\mathrm{TOF}})$ and $k_{\mathrm{F}}$ is the Fermi wave number. The distributions correspond to the initial points in (b). The solid lines are fits to Fermi-Dirac distributions to extract temperatures. The black dashed line shows the momentum distribution at $T=0$. (d) Temperature evolution of weakly interacting Fermi gases during a JT rarefaction. The solid lines are theoretical predictions fixing $(T/T_{\mathrm{F}}{)}_{\mathrm{i}}$ to the experimentally measured values, with the (barely visible) bands representing the uncertainty on $(T/T_{\mathrm{F}}{)}_{\mathrm{i}}$. The dashed lines take into account the effect of technical heating in the box (see text and [14]). The dotted lines show the evolution of $T/T_{\mathrm{F}}$ at constant $T$. (e) Sketch of Fermi hole heating at $T\ll T_{\mathrm{F}}$. The blue (respectively brown) point represents a particle whose removal causes no temperature change (respectively causes heating). (f) Quantum-statistical interaction potential $U_{\text{q}}$ of ideal quantum gases in the high-$T$ limit.

Figure 3

Joule-Thomson effect of the unitary Fermi gas. (a) Breit-Rabi diagram of the ground state manifold of ${}^6\mathrm{Li}$ (sketch not to scale). Solid (open) symbols represent the initial (final) states of the microwave transfer. (b) Microwave-driven decay of a unitary Fermi gas. Pink and blue diamonds are the populations in states $|1⟩$ and $|3⟩$ respectively. The black empty diamond shows the reference decay without microwave field. (c) Radio-frequency (rf) thermometry. The cartoon shows the internal states used in the rf spectroscopy: the gas, initially in a balanced mixture of $|1⟩–|3⟩$, is driven on the transition $|1⟩\to |2⟩$; the states that are imaged are marked with the lightning symbols. Green and magenta diamonds are the spectra at $t_{\mathrm{\mu }\mathrm{w}}=0\mathrm{s}$ and $t_{\mathrm{\mu }\mathrm{w}}=0.5\mathrm{s}$, and black diamonds correspond to the spectrum after 0.7 s no-microwave hold. Dot-dashed vertical lines mark the peak response. (d) Degeneracy of a unitary Fermi gas during isenthalpic rarefaction. The peak frequency response $E_{\mathrm{p}}$ and $T/T_{\mathrm{F}}$ are shown along the rarefaction $N/N_{\mathrm{i}}$, respectively in the upper and lower panel. The green and magenta diamonds correspond to the spectra in (c). The blue solid line is the prediction based on the EOS [27], fixing $(T/T_{\mathrm{F}}{)}_{\mathrm{i}}$ to the experimental values. The blue band is the uncertainty arising from the uncertainty on $(T/T_{\mathrm{F}}{)}_{\mathrm{i}}$. The dotted line shows the evolution of $T/T_{\mathrm{F}}$ at constant $T$. The purple (respectively yellow) dot-dashed line is the theoretical temperature evolution of an ideal Fermi (respectively Bose) gas during JT process; $T_{\mathrm{F}}$ is defined with the density of the corresponding (Bose or Fermi) gas.