Zero-Range Three-Body Physics in Ultracold Bosonic Gases

Abstract

Due to their universality, effective field theories developed in the study of nuclear physics have found a direct application in the research of many-body physics in quantum degenerate gases such as Bose-Einstein condensates. This thesis will reproduce from one such theory, the zero-range model, the discrete scaling symmetries emergent for the physical observables of three-body physics in bosonic gases within the ultracold temperature regime. The conditions of the ultracold regime allow for the treatment of bosonic gas atoms as quantum-mechanical point particles interacting exclusively through scattering in the s-wave channel. The Feynman rules of the zero-range model are derived and implemented to formulate the three-body scattering amplitude and the three-body bound state equation using the inclusion of an auxiliary diatomic field operator. The zero-range model has been shown to be renormalisable within the three-body sector utilizing a renormalisation group limit cycle through numerical tests of an ultraviolet cutoff momentum dependent three-body scaling term G(Λ) parametrised by a three-body parameter Λ∗. The universal properties of the Efimov effect have been confirmed for the three-body physics of a single species of bosonic gas, as well as for mixtures of species distinguished by different masses. Furthermore, results for the three-body scattering amplitude demonstrate the impact of different parameters Λ∗ and two-body scattering lengths on the three-body scattering length of the quantum degenerate gas. In conclusion, the zero-range model enables the description of few-body physics of bosonic quantum degenerate gases with respect to a finite set of parameters: the masses of gas species, the spin-statistic of gas species, the two-body scattering length and the three-body parameter, and the temperature of the gas.