Quantum Joule-Thomson Effect in a Saturated Homogeneous Bose Gas

We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasihomogeneous atomic gas, prepared in an optical-box trap. We characterize the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein’s textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient ${\mu }_{\mathrm{JT}}>10^9\mathrm{K}/\mathrm{bar}$, about 10 orders of magnitude larger than observed in classical gases.

Figure 1

Quasihomogeneous Bose gas in an optical-box trap. We show a schematic of our cylindrically shaped trap, formed by intersecting one tubelike and two sheetlike green laser beams, and an in situ absorption image of the atomic cloud.

Figure 2

Critical point for condensation. A power-law fit, $N_c\propto T^{{\alpha }_c}$, gives ${\alpha }_c\approx {\alpha }_f=1.65$ (see the text). Bottom inset: Within errors, ${\alpha }_c={\alpha }_f$ (solid line) is satisfied for $1.6\lesssim {\alpha }_f\lesssim 1.7$. Top inset: Comparison with theory of a perfectly homogeneous gas, with fixed ${\alpha }_c={\alpha }_f=3/2$.

Figure 3

Saturation of the thermal component in a partially condensed gas. In the box trap the gas follows the ideal-gas prediction $N^{\prime }=N_c$, whereas in the harmonic trap the thermal component is strongly nonsaturated. The dashed red line shows the theoretical prediction for the harmonic trap. (For the harmonic-trap data, $T\approx 110\mathrm{nK}$ and $N_c\approx 65\times 10^3$.)

Figure 4

Quantum Joule-Thomson effect. (a) Isoenthalpic rarefaction. In a conventional JT process $V$ is increased, whereas in our experiments $N$ is reduced, but for an ideal gas both processes conserve specific enthalpy and are thermodynamically equivalent. (b) Microscopic origin of JT cooling in a saturated quantum gas. Removal of a thermal atom requires a zero-energy particle to come out of the BEC in order to maintain $N^{\prime }=N_c$, while energy conservation requires redistribution of atoms between energy levels. Cooling is seen in the change of the relative populations of the excited states. In this cartoon we neglect the fact that $N_c$ also slowly decreases. (c) Measurements with a partially condensed and a thermal cloud. The solid and dashed blue lines are predictions of Eq. (2) with $\alpha =1.65$ and $\alpha =3/2$, respectively. The dotted red line is a numerical calculation (see the text).