Degenerate Fermi gas

On July 12, 2005, we observed a cloud of 40K atoms at 0.9TF. Later data and analysis revealed an unambiguous signature of quantum degeneracy, the first time this regime has been reached using an atom chip. The links below present our preliminary data about this observation. Please see the page about our BEC (Bose-Einstein condensation) observation for a description of the experimental apparatus, which has not changed substantially since then.

  1. Loading sequence
  2. Sympathetic cooling
  3. Cooling below TF
  4. Non-Gaussian statistics
  5. Conclusions and future directions
  6. Team and acknowledgements

1. Loading sequence.

Six laser beams intersect at the center of a magnetic quadrupole field to form a magneto-optical trap (MOT) of alkali atoms. Fermionic Potassium 40 (40K) alone is trapped for 25s with trap and repump light near 767nm; then both 40K and bosonic Rubidium 87 (87Rb) are colledcted for 3s. After brief optical compression and cooling steps, 87Rb and 40K atoms are loaded into a pure magnetic trap and transferred to the microfabricated magnetic trap 5cm above the original MOT location. A Ioffe-Pritchard trap is formed with a 'Z'-shaped, 60µm-wide wire with 2A of current, in the presence of a 21G bias field. 2e7 87Rb and 2e5 40K atoms are loaded into this trap.

2. Sympathetic cooling on a chip

Evaporative cooling of the Rb atoms is forced by a transverse oscillating field generated by an adjacent wire on the chip. In 6s, the frequency of the RF field is reduced (as shown at right), and the Rb atoms are cooled from 300µK to less than 1µK. 40K atoms are sympathetically cooled to the same final temperature by thermalizing with the Rb cloud. Note that the evaporative ramp used in this two-species process is over twice as slow as the ramp used for to Rb alone to quantum degeneracy. A faster ramp results in significant loss of K, since thermalization is at first slow between the two species, and the RF field can remove K directly if it is sufficiently hot.

3. Cooling below TF

In time-of-flight imaging, we can see (below, first three images) that as the temperature is reduced, fermions are herded into the “quantum corral” -- ie, within the ring at a ballistic energy of EF -- however Pauli pressure keeps the outer edge of the cloud from going to any lower energy. By comparison, bosons (rightmost image) are easily herded into a EF-sized corral (if you ignore the fact that they are Bosons and calculate what would be the Fermi energy for that number of fermions)

4. Non-Gaussian statistics

At our lowest temperatures, we can distinguish the non-Gaussian shape of the cloud. At right is radially averaged data (blue) from the sum of several images, taken on August 4, 2005. Two theoretical models are fit to the data: a Gaussian (green line),which assumes Boltzmann statistics, and a Polylog (red line), which assumes Fermi statistics.

As shown by the normalized residuals, the Fermi distribution is a better fit: the data is flatter at its center and sharper at its edges than the Gaussian cloud shape. The Chi squared of the polylog is over four times lower than that of a Gaussian.

From the polylog fit we find a temperature of 230nK, or about 0.2TF, where TF is 1.1µK, N is 6e4, and the oscillation frequencies in the trap are 2π x 826Hz (radial) and 2π x 49Hz (longitudinal). The images are taken after 9ms of free-flight expansion time.

5. Conclusions and future work

We have successfully demonstrated that microfabricated magnetic traps can be used to trap and cool fermions to quantum degeneracy. We are still in the process of refining our understanding of the data, as there are callibrations and systematic effects to address, such as a discrepency between temperature measured along the radial and longitudinal axes. We are also in the process of measuring the thermalization rate between rubidium and potassium during the evaporation, as the cross-section is predicted to drop dramatically at higher temperatures. Future work will use this Fermi gas as a starting point to explore the implications of Fermi degeneracy in a system of neutral atoms.

6. Team and acknowledgments

The team of people responsible for this achievement include:

Graduate students: Marcius Extavour, Lindsay LeBlanc
Undergraduate students: Dave McKay, Ian Leroux
Postdoctoral fellows: Dr. Seth Aubin, Dr. Stefan Myrskog
Technologist: Alan Stummer
Faculty member: Prof. Joseph Thywissen

We are also indebted to collaboration and technical assistance of Phillippe Bouyer, Robert Nyman, and Jerome Esteve. Finally, we thank the useful conversations with Alain Aspect, Brian DeMarco, Debbie Jin, John Bohn, and Christoph Salomon.