Colorado Physicists Generate SU(N) Fermions That Literally Imitate Boson Behavior

 

Recall  when we briefly investigated quantum statistics (Nov. 20, 2014 post)  we saw that   bosons have integral spin values and so  an orbital may be populated by any number of bosons so the Pauli Exclusion principle doesn’t apply. (The Pauli Exclusion Principle prohibits two particles having identical quantum numbers from occupying the same energy level  in a multi-electron atom.)

Thus  the number of electrons (Fermi particles) which can occur between energies e and e + de .  in a quantum system is limited because they possess half integral spin so must conform to the Pauli exclusion principle.   Recall the bosons obey the Bose-Einstein distribution function, e.g.

[ n(e )]  =  1/ [exp ( e -  m)/ t  -   1]

While the fermions obey the Fermi-Dirac distribution, e.g.

[ n(e )]  =  1/ [exp ( e -  m)/ t  +    1]

But imagine what new physics would emerge if fermions could act more like bosons.  I.e. no limits to the occupancy of the same level.  As it turns out, Alkaline-earth fermionic atoms can do just that. Because their nuclear spin states are decoupled from their electronic states, atoms with different nuclear spin states have identical energy levels and wavefunctions in an optical trap. But the atoms aren’t identical, so fermionic atoms, each with a different spin, can cluster together in the same energy level and interact.  (See extreme right image in graphic)

These are called SU(N) fermions.  

For the Alkaline-Earth fermions the inter-atom interactions are independent of the nuclear spin state.  Thus, for N atoms with different spins the 2-body interactions will have an N-fold symmetry.  The interacton then is identical between any atom and each of the other N- 1 atoms sharing its energy level.   For SU(N) fermions the so-called SU(N) symmetry enhances those interactions and boosts otherwise weak effects into more pronounced ones.    

This is why physicists are interested in SU(N) symmetric systems as a model or template by which to explore the physics behind a range of condensed matter systems.  Enter now he University of Colorado Boulder’s Jun Ye and his colleagues have created a gas with a record-high number of fermions in each energy level. Their ultra-cold strontium-87 gas with 10 distinct nuclear spin states shows clear signs of inter-atom interactions in its thermodynamics.

To prepare their gas, the researchers used two stages of laser cooling down to 2 μK and then introduced a single dimple trap for the atoms to pool into. To finish the cooling process, they left the gas to evaporate for as short as 0.6 s, down from about 10 s for two-spin gases. The more fermions that are colliding in each energy level, the faster they cool.

The researchers prepared Sr (strontium) atoms with all 10 possible nuclear spin states—that is, 10 atoms per energy level—and 5 × 104 atoms per spin state by the end of evaporation. Although the fermion interactions are weak, they measurably change the system’s density fluctuations, compressibility, and time-of-flight dynamics, in agreement with theoretical models.   

Incredibly, research into SU(N) Fermi gases started only in the past decade.  Not too surprising given that previous studies were limited by fact the temperature  regimes accessible for the gases were too low.   Hence, the resulting interactions didn't significantly alter the system's thermodynamic behavior, i.e. compared to non-iteracting Fermi gases that lack SU(N) symmetric interactions.

Now that researchers have an efficient preparation method and a basic understanding of the properties of interacting Fermi gases, says Ye, the gases will be “premium fuel for a quantum simulator.” Different combinations of kinetic energy, interaction energy, and nuclear spins can be used to systematically explore the phase diagram of, for example, the Fermi–Hubbard model (see the article by Gabriel Kotliar and Dieter Vollhardt, Physics Today, March 2004,