Quantum Dot Dynamics in a Bose-Einstein Condensate

Abstract

This thesis investigates the dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensate (BEC) via particle exchange and interactions. This is motivated by the possibility of using such a system as a non-destructive probe of the BEC. A review of the physics of a BEC and relevant impurity models is presented. The collisional blockade regime of the AQD is considered, and the AQD is modelled as a spin-12 pseudospin. Having expressed the BEC in terms of number and phase, the semi-classical ground state of the system is determined. The fluctuations in number and phase around this ground state are assumed to be small. Using Fermi’s golden rule, the decay rates of the system are calculated. The system dynamics are found to be highly dependent on dimensionality and the coupling between AQD and BEC. Having derived the action for this system, it is found that the small phase fluctuation assumption fails in two dimensions and for certain limits in three dimensions. We attempt to circumvent this difficulty using a canonical transformation. The resulting system is related to a biased spin-boson model. Expressing the pseudospin in terms of Schwinger bosons, the self energy for this system is determined. Green’s functions for the system are derived by solving Dyson’s equation, and a decay rate is extracted. Determining the spin-spin temporal correlation functions by solving the Bethe-Salpeter equation is found to be intractable due to the Schwinger boson number constraint. The possibility of avoiding this problem using the Holstein-Primakoff representation in a large-S generalisation of the AQD states is explored. We find that the pseudospin precession can be controlled by tuning the coupling parameters and the interactions in the BEC. In particular, we found two unexpected regimes where the pseudospin precession can be slowed down to arbitrarily small frequencies.