Entropy Exchange in a Mixture of Ultracold Atoms

We investigate experimentally the entropy transfer between two distinguishable atomic quantum gases at ultralow temperatures. Exploiting a species-selective trapping potential, we are able to control the entropy of one target gas in presence of a second auxiliary gas. With this method, we drive the target gas into the degenerate regime in conditions of controlled temperature by transferring entropy to the auxiliary gas. We envision that our method could be useful both to achieve the low entropies required to realize new quantum phases and to measure the temperature of atoms in deep optical lattices. We verified the thermalization of the two species in a 1D lattice.

Figure 1

Schematic of our experimental procedure. Left: the harmonic magnetic potential is common to both gases, auxiliary (red, larger) and target (blue, smaller). Right: the species-selective dipole beam compresses the target sample and drives it into the degenerate regime. Trapping potentials for the auxiliary Rb (dashed line) and the target K gas (solid line) are sketched on the background panels together with the K density distributions.

Figure 2

BEC fraction of the K sample as a function of the K harmonic frequency after the compression. Data (circles) are compared to the theoretical predictions based on the numerical (solid line) and analytical approximate (dashed line) solutions of Eq. (3). On the right axis, the approximated value $S/(N{k}_B)=4[\zeta (4)/\zeta (3)](1-f_c)$ is shown. The inset displays absorption images of the K sample before (a) and after (b) the compression.

Figure 3

Trajectories in the entropy-temperature diagram of the K sample (see text). For the experimental data, the entropy is determined with the formulas in text. The dashed lines show the ideal entropy for a sample of $1.1\times {10}^5$ K atoms at the harmonic frequencies of the magnetic trap (${\omega }_{\mathrm{K}}=2\pi \times 128\mathrm{Hz}$) and of the SSDP maximally compressed trap (${\omega }_{\mathrm{K}}=2\pi \times 216\mathrm{Hz}$). The shaded boxes highlight the isothermal SSDP compressions.

Figure 4

Cycles of compressions and decompressions, the K condensate fraction changes in a reversible manner as we modulate the K harmonic frequency over time from 128 to 216 Hz (the solid line guides the eye). The inset shows the relative intensity of the SSDP beam.