Lithium-Lab (BEC I)


Background: The Sodium-Lithium Double-Species Experiment

This experiment aims at the study of Bose-Fermi mixtures and degenerate, strongly interacting Fermi gases (see also PhD theses of Subhadeep Gupta (pdf) and Zoran Hadzibabic (pdf)). The machine is the same that produced the first sodium Bose-Einstein condensates (BECs) in 1995. In 2001, the machine was upgraded to a double-species machine by adding fermionic lithium-6 atoms (PhD thesis and review paper by Claudiu Stan) and a new laser system for laser-cooling of lithium (undergraduate thesis: Martin Zwierlein (pdf)). Using sodium as the "refrigerant", spin-polarized fermionic lithium is cooled to degenerate temperatures in a magnetic trap. One can now choose to either leave sodium in the trap and study this Bose-Fermi mixture, or one can focus on fermions by evaporating all the sodium away. Typically, all further experiments take place in an optical dipole trap, which can hold atoms regardless of their spin-orientation. By applying high magnetic fields, it is then possible to access regimes of strong interactions in Bose-Fermi mixtures or spin mixtures of fermions close to so-called Feshbach resonances.

Feshbach Resonances and the BEC-BCS crossover

Feshbach model

Feshbach resonances are a unique tool for atomic physics. By the simple change of a magnetic field the interactions between atoms can be controlled over an enormous range. This tunability arises from the coupling of free unbound atoms to a molecular state in which the atoms are tightly bound. The closer this molecular level lies with respect to the energy of two free atoms, the stronger the interaction between them. In the example on the left, the two free atoms are both "spin up", whereas the molecular state is a "singlet", in which the atoms have opposite spin, adding up to zero total magnetic moment. Thus, a magnetic field shifts the energies of two free atoms relative to the molecular state and thereby controls the interatomic interaction strength.

From BEC to BCS
The interaction between two atoms can be described by the scattering length, shown on the right versus magnetic field close to a Feshbach resonance. On the side where the scattering length is positive, the molecular energy level is lower in energy than the energy of two unbound atoms. The molecular state is thus "real" and stable, and atoms tend to form molecules. If those atoms are fermions, the resulting molecule is a boson. A gas of these molecules can thus undergo Bose-Einstein condensation (BEC). This side of the resonance is therefore called "BEC-side". On the side of the resonance where the scattering length is negative, isolated molecules are unstable. Nevertheless, when surrounded by the medium of others, two fermions can still form a loosely bound pair, whose size can become comparable to or even larger than the average distance between particles. A Bose-Einstein condensate of these fragile pairs is called a "BCS-state", after Bardeen, Cooper and Schrieffer. This is what occurs in superconductors, in which current flows without resistance thanks to a condensate of electron pairs ("Cooper pairs").

The universal regime
Directly on resonance, the molecular energy is equal to that of two free atoms. The scattering length diverges and does not play any role anymore in the description of the gas. Physics is said to be "universal" in this regime, where the only length scale of importance is the average distance between particles. It uniquely determines the energy content of the gas, its pressure and all other properties. Here, the size of fermion pairs must necessarily be comparable to the interparticle distance. Condensation of these pairs will occur and the gas will be a superfluid at low enough temperatures.

An ideal model system
We see that with the simple change of a magnetic field close to a Feshbach resonance, a Fermi gas of atoms can be brought into very different regimes of pairing. From a Bose-Einstein condensate of tightly bound molecules on the BEC-side, through the universal regime on resonance and to a BCS superfluid of long-range pairs. Fermi gases thus provide the ideal testbed to study strongly interacting systems which occur in vastly different areas of physics, from superfluid Helium-3 to High-T_C superconductors, from the quark-gluon plasma of the early Universe to neutron stars.