Physicists in the US have developed a new kind of thermometer that can measure down to as low as one billionth of a degree above absolute zero and has the potential to reach just a few trillionths of a degree. The ability to measure such chilly temperatures could allow scientists to use ultracold gases to simulate condensed-matter systems that are otherwise very hard to study – such as high-temperature superconductors.

In several labs around the world, ultracold gases can be cooled to temperatures of just a few nanokelvin (10-9 K) and the current record low just under a nanoKelvin. However, physicists would like to cool atoms even further to around a picoKelvin (10-12 K). Such atoms could be used to mimic how electrons interact in high-temperature superconductors, for example, by holding the atoms in a lattice of potential wells created by the interference of multiple laser beams. Then, the interactions between atoms and the depth and spacing of the wells could be varied by adjusting the lasers or an applied magnetic field.

In such a laser lattice, however, the interaction energy between atoms would be the equivalent to a thermal energy that is much lower than room temperature. In order to see the effects of the interactions, the atoms must be cooled to very low temperatures – but before that can happen, physicists need an effective way of measuring such low temperatures.

Caught in the 'dimples'

A common way of measuring the temperature of an ultracold gas is to determine the size of the trapped atom cloud. At low temperatures, an image of the trap will show all of the atoms concentrated in a central region. At higher temperatures, however, the atoms spread out, resulting in a visibly larger cloud of atoms.

David Pritchard of the Massachusetts Institute of Technology (MIT) in the US compares the atoms to a collection of ball bearings in a shallow bowl with small dimples to represent the lattice. "If they didn’t have any thermal energy the ball bearings would collect in the dimples at the bottom of bowl," he says. "But once they acquire energy and start to shake, some would have the energy to climb into dimples higher up the sides of the bowl."

While this approach works well at relatively high temperatures, when the atoms are quite independent of one another, it does not work at lower temperatures when interactions between atoms prevents further shrinkage of the cloud.

Spin separation

Now, Pritchard, David Weld, Wolfgang Ketterle and colleagues at MIT have devised an alternative method that works better at lower temperatures. The team begin with a laser lattice loaded with a collection of rubidium-87 atoms in two different spin states – up and down. The atoms are then exposed to a magnetic field gradient, which separates the atoms by sending ups and downs to opposite ends of the trap

At extremely low temperatures, the up and down atoms would be separated by a sharp dividing line – and a plot of the mean spin of the atoms along the magnetic field gradient shows a steep transition. However, as the temperature is increased the atoms have more thermal energy and therefore increasingly mix with one another, resisting to some extent the magnetic gradient. This mixing results in a more gradual shift in spin across the trap.

According to Pritchard, in their experiment the conventional technique permits temperature measurements down to about 100 nK, whereas this new approach can get down to about 1nK. He says this is significant because the interaction energy of two rubidium atoms in a lattice site is equivalent to about 40 nK. At a temperature of 100 nK, most of the atoms would therefore have enough thermal energy to tunnel across the lattice and share a site with another atom, whereas at 1 nK they would not. Being able to cool the sample down to 1 nK therefore ensures that each site is occupied by one atom, as intended.

Down to 50 pK

Pritchard says that the new thermometer may be able to measure down to about 50 pK, unless it is limited by a different kind of tunnelling effect. However, reaching such temperatures requires a weaker magnetic gradient to increase the distance between spin-up and spin-down atoms to where it can be resolved. But this can’t be done without reducing stray magnetic fields, vibrations, and unevenness in the laser lattice. "To get down to ever lower temperatures we have to very carefully re-engineer all of these potential interferences," he says. "We don’t yet know how to reach such low temperatures. But we know how to measure them once we get there."

The work is reported in Physical Review Letters.