Ultracold Fermions in Optical Lattices
Motivation
- The experimental setup
In this series of experiments we study the many-body physics of fermionic atoms in an optical lattice. One important motivation -besides this being an intriguing many-body system by itself - is the close resemblance between this system and correlated electron systems in condensed matter:
A full theoretical description of electrons in a solid is nearly impossible, as one would need to take the effects of electrons in different bands, lattice vibrations, lattice defects and impurities as well as the long-range Coulomb interaction between all electrons and all ions into account. Therefore, an important theme in solid state physics is the search for simple models that include only the physics necessary to describe a given effect.
One of the most important model systems is the so-called Fermi-Hubbard model, which takes only tunnelling of an electron from one ion to the next and a local effective interaction between the electrons into account.
Despite its apparent simplicity, this model is widely used in solid-state research to describe the effects of electron-electron interactions and the resulting strongly correlated states.
The most important strongly correlated states is the so-called Mott insulator, that appears in a half-filled band when the mutual repulsion between the electrons effectively localizes the electrons and thereby drives a transition from a metallic to an insulating state.
Furthermore different superfluid states as well as several charge or spin ordered states can be found in the Fermi-Hubbard model, which is also considered by many as the fundamental model to describe High-T_c superconductors.
Fermionic atoms in an optical lattice provide a clean and defect-free implementation of the Hubbard model and display the additional advantage that all relevant parameters, including the potential depth, the particle density and the interaction strength can be independently controlled.
As the exact solutions of the Fermi-Hubbard model are in general not known, such an experimental implementation is even more needed in order to verify the predictions of the approximate theories.
Our experiments so far include
- the transition from metallic to Mott-Insulating and ultimately band insulating states at repulsive interactions
- the effects of finite entropy in the attractive Hubbard model
- and the dynamics of an initial band-insulating cloud in a homogeneous Hubbard model
Fermions vs. Bosons
- Bosons: Bose-Einstein condensate (left) Fermions: Fermi Sea (right)
While Bosons condense into a so-called Bose-Einstein condensate at low temperatures, in which all Bosons occupy the same single-particle state, Fermions need to obey the Pauli principle, which forbids the occupation of any single-particle state by more than one identical fermion.
Consequently they form a so-called Fermi-Sea at low temperatures, in which every single-particle state upto the so-called Fermi-energy is occupied by one fermion.
In our Experiment we use a mixture of laser-cooled bosonic Rubidium 87Rb and fermionic Potassium 40K, which are cooled to simultaneous quantum degeneracy by evaporative cooling in an optically plugged quadrupole trap followed by an optical dipole trap.