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Abstract

In this work we experimentally study the rich interplay of a linear coupling and non-linear interactions between the two components of an elongated Bose-Einstein condensate of 87Rb. In the limit of strong linear coupling we generate dressed states and explore the effective interactions between them. We find that the miscibility of dressed states is opposite to that of the atomic states. If the characteristic energies of interactions and linear coupling are equal they give rise to a miscible-immiscible quantum phase transition. We study the linear response of the system to sudden quenches in the vicinity of the critical point by analyzing spin correlations in the system. A power law scaling of the characteristic length scales is observed on both sides of the phase transition and the scaling exponents agree with the mean field prediction. Temporal scaling is found on the miscible side in agreement with a prediction based on Bogoliubov theory. In addition, experimental results for finite-time quenches through the critical point are presented. The good control over amplitude and phase of the linear coupling field offers new possibilities for the study of both equilibrium and dynamical properties of phase transitions.