Spin Gradient Demagnetization Cooling of Ultracold Atoms

We demonstrate a new cooling method in which a time-varying magnetic field gradient is applied to an ultracold spin mixture. This enables preparation of isolated spin distributions at positive and negative effective spin temperatures of $\pm 50\mathrm{pK}$. The spin system can also be used to cool other degrees of freedom, and we have used this coupling to cool an apparently equilibrated Mott insulator of rubidium atoms to 350 pK. These are the lowest temperatures ever measured in any system. The entropy of the spin mixture is in the regime where magnetic ordering is expected.

Figure 1

Two different cooling protocols realizing the cases of isolated and equilibrated spin systems. (a) Experimental “phase diagram” of lattice depth vs applied gradient. Dashed lines show two different paths which connect the high-gradient superfluid state and the low-gradient Mott insulating state. (b) and (c) show the lattice depth (solid line) and gradient strength (dashed line) vs time for the two cases (equilibrated spins and isolated spins, respectively) in (a). The shape of the lattice ramp-up is designed to ensure maximum equilibration.

Figure 2

Preparation of low positive and negative spin temperatures. Measured spin temperature vs final gradient, for the case of isolated spins. Error bars are statistical.

Figure 3

Entropy transfer from other degrees of freedom to the spin system. Circles represent measured width of the mixed region vs final magnetic field gradient, for the “equilibrated spins” protocol (see Fig. 1). Error bars are statistical. The dashed line represents the expected behavior assuming no cooling. The dash-dotted line shows the minimum resolvable width. The solid curve is the theoretical prediction, assuming an initial temperature of 6.3 nK and including the effects of optical resolution (see Ref. 25 for details). Insets show spin images at the indicated points, the corresponding vertically integrated spin profiles (squares), and the fit to the expected form of a tanh function times the overall density distribution (solid line; see Ref. 20 for details). Axis units and gray scales in the two insets are arbitrary but identical.

Figure 4

Spin gradient demagnetization cooling. Circles represent measured temperature vs final magnetic field gradient, for the equilibrated spins protocol (see Fig. 1). Error bars are statistical. These measurements are the same as those shown in Fig. 3. The dashed line follows the isothermal trajectory, and the dash-dotted line shows the resolution limit. The solid line is the theoretical prediction, assuming an initial temperature of 6.3 nK and including the effects of optical resolution. The dotted line is the theoretical prediction without the effects of optical resolution.