Efimov states in ultracold gases
1University of Oulu, Faculty of Science, Department of Physics, Geoscience and Chemistry, Physics
|Online Access:||PDF Full Text (PDF, 0.6 MB)|
|Persistent link:|| http://urn.fi/URN:NBN:fi:oulu-201403111157
|Publish Date:|| 2014-03-11
|Thesis type:||Master's thesis
This work will introduce the Efimov effect and the resonant and scaling limits and derive the formula for the binding energies of the Efimov states. We use the hyperspherical coordinates for the stationary wave function of three particles and solve the low-energy Faddeev equation with the hyperspherical expansion and use the expansion for solving the channel eigenvalues. The channel eigenvalues are defined by a constant, which is the solution of the resulting transcendental equation. We also solve the scaling-violation parameter and finally compile all the results to derive the Efimov states. In the unitary limit we find infinitely many Efimov states, with an accumulation point at zero energy and an asymptotic discrete scaling symmetry with the discrete scaling factor of about 22.7. In this work, we will also delve into effective field theories, which can be used to numerically analyze and solve Efimov states in different cases. We will first go through the two-body problem which is used as a simpler example on how to solve the three-body problem and to solve the two-body coupling constant, which will also appear in the three-body problem. By using the diatom field trick introduced by Bedaque, Hammer and van Kolck, we derive the Skorniakov-Ter-Martirosian equation for the three-body problem. Finally this work will take a quick look at the first experimental evidences for Efimov states that were found since 2006. In the experiment, proper Efimov resonances in measurements of three-body recombination have been observed.
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