Three-body Universality Controlled by a Feshbach Resonance
Abstract: The quantum Efimov effect manifests itself in the limit of resonant two-body interactions, where the scattering length diverges. In this scenario, an infinite number of shallow bound trimer states are formed with binding energies that obey a discrete geometric scaling law. The effect is universal in the sense that it can, in principle, appear in any system of bosons with resonant interactions. These states have been studied experimentally in dilute gases of ultracold atoms, where the magnetic-field-dependent coupling to a different molecular state, i.e., where a Feshbach resonance, can be used to tune the scattering length to the resonant regime. A limited number of Efimov states can also be formed for scattering lengths of finite magnitude. As experimental observations of these states accumulated, an unexpected regularity was found in the value of the scattering length where the first Efimov state emerges from the three-body continuum. This regularity is commonly referred to as van der Waals universality. It is believed to exclusively appear when broad Feshbach resonances are used to tune the scattering length. Theoretical predictions suggest a different kind of regularity for narrow Feshbach resonances, but the few experimental observations that exist are inconclusive in regard to these predictions.This thesis summarises the methodology I have used for developing a multichannel model that includes a magnetically tunable Feshbach resonance used for varying the scattering length. With this model, I am able to study effects related to the resonance width, which the commonly used single-channel models are unable to capture. By solving the Schrödinger equation in the adiabatic hyperspherical approximation, I obtain three-body hyperradial potentials, which I subsequently use to obtain the discrete Efimov energy spectrum. The origin of the van der Waals universality is believed to be caused by a universally positioned repulsive wall in the three-body effective hyperradial potential responsible for the Efimov effect. I observe a slight shift in the position of this wall as the system approaches the narrow resonance limit. More notably, the attractive well becomes exceedingly shallow. In the Efimov energy spectra, I find a clear dependence on the width of the resonance and the position of the first appearing Efimov state. The results agree qualitatively with the predictions of others but for the narrow resonance, there is a large quantitative difference. The observed scaling between consecutive Efimov states agrees well with Efimov's prediction.
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