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We study the critical point for the emergence of coherence in a harmonicallytrapped two-dimensional Bose gas with tuneable interactions. Over a wide rangeof interaction strengths we find excellent agreement with the classical-fieldpredictions for the critical point of the Berezinskii-Kosterlitz-Thouless (BKT)superfluid transition. This allows us to quantitatively show, without any freeparameters, that the interaction-driven BKT transition smoothly converges ontothe purely quantum-statistical Bose-Einstein condensation (BEC) transition inthe limit of vanishing interactions.

Connecting Berezinskii-Kosterlitz-Thouless and BEC phase transitions by tuning interactions in a trapped gas