An entry level review can be read here. All the details can be found in these publications:
- Drake, T. E., Sagi, Y., Paudel, R., & Jin, D. S. Direct Observation of the Fermi Surface in an Ultracold Atomic Gas. PRA 86, 031601(R) (2012).
- Sagi, Y., Drake, T. E., Paudel, R., & Jin, D. S. Measurement of the Homogeneous Contact of a Unitary Gas. Phys. Rev. Lett. 109, 220402 (2012).
The density inhomogeneity problem of a trapped gas
One problem that arises in almost all cold-atoms experiments done to date is the density inhomogeneity of the gas. The cloud is held in a confining potential (i.e. optical dipole trap), and since this potential is never uniform, the density of the trap gas is non-uniform as well. The implication of density inhomogeneity is that measured observables are averaged, and sharp features are inevitably washed out. Different many-body theories usually differ in such sharp features around phase transitions (i.e. the superfluid phase transition), which makes the density inhomogeneity a major obstacle in obtaining decisive results that can benchmark theories.
A canonical example of a sharp feature which is washed out by the density variation of a trapped gas is the sharp step in the momentum distribution of non-interacting Fermions, commonly referred to as the Fermi surface. This sharp feature is a direct manifestation of Fermi-Dirac statistics, in which only a single fermion can occupy a particular quantum state at a given time. The Fermi-Dirac statistics was tested in countless indirect measurements, however, the Fermi surface was never observed in a direct measurement of the momentum distribution of a non-interacting Fermions. The main reason why it was never observed in a Fermi gas experiment is demonstrated in the following figure. While the momentum distribution of a homogeneous non-interacting Fermi gas at T/TF=0.1 is expected to show a clear Fermi surface (blue line), harmonic confinement washes out this feature and gives rise to a much smoother function (red line).
Overcoming the density inhomogeneity problem
We have developed a new probing technique to overcome the density variation problem. The new technique is based on the local density approximation: locally, a trapped gas behaves as uniform gas in the same local conditions. One can use this idea and probe a gas with a more uniform density simply by probing a smaller fraction of the atoms within the trapped gas. To probe only a small region of the cloud, we use two intersecting hollow-core light beams whose frequencies are tuned to optically pump atoms to a state which is invisible to our detection beam (see illustration below). This means that in areas where the beam is stronger, the atoms are more likely to become “dark” and not appear in the measurement. Since the intensity of the two beams converges to zero in their centers, we can change the fraction of the probed atoms by changing the beams’ power.
The first use of this technique was to observe the emergence of a sharp Fermi surface as the fraction of probed atoms decreases (see figure below). Furthermore, the average density and temperature of the probed atoms can be determined from the location and sharpness of the Fermi surface. This is truly a “textbook” observation!
