Spin Gradient Thermometry for Ultracold Atoms in Optical Lattices

We demonstrate spin gradient thermometry, a new general method of measuring the temperature of ultracold atoms in optical lattices. We realize a mixture of spins separated by a magnetic field gradient. Measurement of the width of the transition layer between the two spin domains serves as a new method of thermometry which is observed to work over a broad range of lattice depths and temperatures, including in the Mott insulator regime. We demonstrate the thermometry using ultracold rubidium atoms, and suggest that interesting spin physics can be realized in this system. The lowest measured temperature is 1 nK, indicating that the system has reached the quantum regime, where insulating shells are separated by superfluid layers.

Figure 1

Images used for spin gradient thermometry. Data on the left were taken at a lower optical trap power than data on the right. Panels (a) and (b) are images of the spin distribution. Panels (c) and (d) show the mean spin versus $x$ position. The fit to (c) gives a temperature of 52 nK; the fit to (d) gives a temperature of 296 nK. The inset of (a) shows the axes referred to in the text. The bar in (b) is a size scale.

Figure 2

Independence of the measured temperature on the applied field gradient. The inverse of the width of the spin profile is plotted as a function of magnetic field gradient for two data sets at two different temperatures. For constant temperature, a linear curve is expected. The width is defined as the distance from the center to the position where the mean spin is $1/2$. The solid (dashed) line assumes a temperature of 123 nK (7 nK) and perfect imaging. The measured width of the colder data set saturates at high gradient because of finite imaging resolution. The dotted line assumes a temperature of 7 nK and an imaging resolution of $4\mu \mathrm{m}$.

Figure 3

Validation of spin gradient thermometry. Comparison of two measured temperatures versus final power in one of the optical trapping beams. Squares represent the results of in-trap cloud width thermometry, and circles represent the results of spin gradient thermometry (see text for details). Error bars represent estimated uncertainties. The dashed line is a linear fit to the spin gradient thermometry data. The closeness of this fit suggests that the temperature reached is proportional to the trap depth.