Ménage à trois, plus un:
Few-Body Physics in Ultracold Lithium
A surprising result occurs in few-body physics where three interacting particles can form a three-body bound state (trimer) in circumstances where any two of the three would not normally bind together. These so-called Efimov trimers appear when the strength of the pair-wise interaction between particles becomes sufficiently large such that the addition of a third particle tips the balance to create a stable trimer. This bound state is like the Borromean rings (shown at right), where removing any one ring causes the other two to unbind.
It also turns out that if the interaction strength is increased by 22.7, then another three-body bound state--larger in size but more weakly bound--is formed, and when increased by that same amount again produces another bound state, and so on, creating an infinite series of trimer states with increasing interaction strength. The details of the interparticle potential are not important in determining the properties of these bound states; all that is important is the strength of the interaction. This means that the size and binding energies of Efimov trimers follow a universal scaling regardless of the type of particles that make them up: so they are the same for lithium atoms, cesium atoms, neutrons, protons, and even electrons, follow this universal scaling .
We tune the strength of the interparticle interaction via a collisional resonance known as a Feshbach resonance, where a tunable magnetic field brings a two-body bound state (dimer) into resonance with two interacting free atoms . The plot below shows the energies of the weakly bound dimer (blue) and several of the Efimov trimers (red) as a function of the interaction strength a. The trimer states are separated in a by factors of 22.7, and by factors of 22.72 = 515 in their binding energies. The location of the collisional resonance is where 1/a = 0, i.e., the interaction strength becomes infinite.
The Efimov trimer state offer additional processes by which atoms can interact. When the trimer binding energy is coincident with the energy of the free atoms (nearly zero energy in the plot) there will be an enhancement in the inelastic collisions that cause loss of atoms from a trapped sample.These clocations are called Efimov resonances.
Enhanced loss also occurs when the bound state energy of a trimer is coincident with the energy of a dimer plus a free atom. At this atom-dimer resonance we also expect an increase in the atom loss rate .
A quantum interference effect causes a reduction in loss near this atom-dimer resonance.
| In order to study Efimov physics, we create a trapped ultracold gas of bosonic lithium atoms using methods previously described. When three atoms interact they can recombine into a weakly-bound dimer plus a third atom. This is an inelastic collision, where the binding energy of the dimer is transfered to the kinetic energy of the reaction products, resulting in both the dimer and the third atom being ejected from of the trap. The rate at which atoms leave the trap is dependent on the strength of the interactions between the particles. |
In the plot on the right we show decay curves of the number of atoms in our trap as a function of time at different interaction strengths a. We fit these curves to extract the loss rate coefficient.
The extracted loss rate coefficient data shows many features that punctuate an overall a4 scaling. On the right hand side of panel A (where a < 0) there are two Efimov resonances a–1 and a–2, separated by a scaling factor or 21.1, which is in nearly perfect agreement with universal theory! On the left hand side (where a > 0), we see two recombination minima due to quantum interference at a+1 and a+2 (separated by 22.5), along with an atom-dimer resonance associated with the second Efimov trimer at a*2 (panel B). The green lines are the energies of the Efimov trimers and the solid black lines are fits to a universal theory. We also see new features (panels C and D) which may be associated with four-body physics.
The universality seen between three bodies is expected to extend to conditions when a fourth is added. We extract the four-body loss rate coefficient simultaneously with the three-body one when fitting the decay curves. The figure below shows our results, along with an extended Efimov energy diagram including the four-body tetramer energy levels .
The locations of the observed features reflect on the universal nature of Efimov physics. Deviations from the predicted locations lend insight into how the short-range physics (that's the physics that was neglected in the universal theory) influences the interactions between particles. By comparing our results with predictions theorists can formulate a more complete theory of few-body physics, and better describe the quantum many-body physics present in the world around us.
For more details see the references below and our paper:
Universality in Three- and Four-Body Bound States of Ultracold Atoms,
S. E. Pollack, D. Dries, and R. G. Hulet, Science 326, 1683 (2009).
Originally published in Science Express (Science.1182840) on 19 November 2009.
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