Fermionic Studies in 6Lithium
Lithium has two stable isotopes: 6lithium, a fermion; and 7lithium, a boson. In 1995, our lab observed Bose-Einstein Condensation (BEC) in lithium 7. Now that degenerate bosons have been observed, it naturally follows that we would like to observe and study fermions in the degenerate regime...
The general procedure is to load a magento-optical trap (MOT) with lithium atoms at about 1 mK, doppler-cool the cloud to ~200 mK, and energize the Ioffe-Prichard trap to magnetically confine the atoms.
From this point forward, the differing characteristics of bosons and fermions become important. In 7Li (boson), BEC can be achieved by using microwaves to selectively spin-flip hot atoms out of the magnetic trap. The remaining atoms then collide and re-thermalize, thereby reducing the overall temperature of the atom cloud. This method, known as evaporative cooling, achieves temperatures in the 100 nK range.
For 6Li (fermion), however, this method fails because fermions, unlike bosons, obey the Pauli-exclusion principle, which states that no two fermions can exist in identical states. This simple restriction prevents ultra-cold fermion atoms from colliding with one another and thereby eliminates an integral part of evaporative cooling.
The trick is to load the trap with both 6Li and 7Li and then evaporatively cool the 7Li. 6Li is not forbidden to collide with 7Li and is therefore cooled through thermal contact with the bosons. This form of cooling is known as sympathetic cooling and has been used at JILA to create dual BECs.
We have developed a new apparatus to trap, cool and study degenerate fermions. It consists of a UHV (~10-12 torr) chamber, a set of electro-magnetic coils, and two lithium sources. A dual Zeeman slower is used to load both 6Li and 7Li. The coils can either be energized in a anti-Hemholtz configuration for an MOT or in a Ioffe-Pritchard configuration for magnetic confinement of the atoms.
We have produced a quantum degenerate Fermi gas of 6Li atoms using sympathetic cooling with 7Li atoms, and, in doing so, we have effectively produced the first quantum degenerate boson/fermion gas mixture.
The achievement of simultaneous Bose/Fermi degeneracy enables a direct and striking comparison between bosons and fermions at low temperatures. The figure below shows pairs of images corresponding to clouds of trapped 6Li and 7Li atoms at three successively lower temperatures. Although the atoms are spatially interpenetrating, the two isotopes can be imaged independently using two separate laser beams at their slightly different absorption frequencies.
The upper set of images corresponds to a temperature T = 800 nK. At this temperature, the 7Li atoms are at about 1.5 Tc, the transition temperature for BEC, while for the 6Li atoms, the ratio of T to the Fermi temperature TF is equal to 1.0. At this temperature, the gas behaves more classically than quantum mechanically, and little difference between the bosons and fermions can be discerned.
However, in the middle set, with T/TF = 0.56, the 6Li distribution is seen to be slightly broader than that of the 7Li, and in the bottom set, corresponding to T/TF = 0.25, the relative broadening of the 6Li cloud is unmistakable. The effect of quantum statistics on the sizes and shapes of the clouds can readily be seen in the axial profiles of the images for the temperatures T/TF = 1.0 and 0.25 (Figure below, A and B, respectively). Indeed, the deviations in the sizes and shapes of these clouds highlight their dissimilar quantum statistical natures.
The square of the radius of the 6Li clouds is plotted against T/TF in Figure 3, where it becomes apparent that at relatively high temperatures, the radius decreases as T1/2 as expected for a classical gas (represented by the dashed line). At a temperature near 0.5 TF, however, the radius deviates from the classical prediction, and at the lowest temperatures, it plateaus to a value near the Fermi radius. At T = 0, every trap state is singly occupied up to the Fermi energy, giving rise to a nonzero mean energy and a resulting Fermi pressure. Fermi pressure is responsible for the minimum radius and is a dramatic manifestation of Fermi-Dirac statistics. In white dwarf and neutron stars, which are essentially "dead" due to the depletion of their nuclear fuel, it is the Fermi pressure that stabilizes the stars against gravitational collapse. The stabilization of the size of the atom cloud with decreasing temperature is another manifestation of the same physics. A group at the Ecole Normal in Paris has recently performed a similar experiment and has made similar observations.
Conversion of Ultra-Cold Fermionic 6Li Atoms to Bosonic Molecules
We have utilized an adiabatic sweep through a Feshbach resonance to convert a spin mixture of fermionic 6Li atoms into bosonic diatomic molecules with up to 50% efficiency. Feshbach resonances occur when the energy of a dissociated atom pair is equal to that of a molecular bound-state energy level. Due to differing magnetic moments between the atomic and molecular states, the system may be tuned into resonance through the use of an external bias magnetic field. In our case, the molecular energy is lower than that of the atoms at low magnetic field. As the field is swept down, the initially free atom pairs traverse an avoided crossing between the molecular and atomic energy levels, thereby becoming molecules (see the figure below).
More details can be found in "Conversion of an Atomic Fermi Gas to a Long-Lived Molecular Bose Gas".