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A quantum phase transition from the miscible to the immiscible phase of aquasi-1D binary Bose-Einstein condensate is driven by ramping down the couplingamplitude of its two hyperfine states. It results in a random pattern ofspatial domains where the symmetry is broken separated by defects. Indistinction to previous studies [J. Sabbatini et al., Phys. Rev. Lett. 107,230402 (2011), New J. Phys. 14 095030], we include non-zero detuning betweenthe light field and the energy difference of the states which provides a biastowards one of the states. Using the truncated Wigner method, we test thebiased version of the quantum Kibble-Zurek mechanism [M. Rams et al., Phys.Rev. Lett. 123, 130603 (2019)] and observe a crossover to the adiabatic regimewhen the quench is sufficiently fast to dominate the effect of the bias. Weverify a universal power law for the population imbalance in the non-adiabaticregime both at the critical point and by the end of the ramp. Shrinking andannihilation of domains of the unfavourable phase after the ramp -- that is,already in the broken symmetry phase -- enlarges the defect-free sections bythe end of the ramp. The consequences of this phase ordering effect can becaptured by a phenomenological power law.

Biased dynamics of the miscible-immiscible quantum phase transition in a binary Bose-Einstein condensate