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The out-of-equilibrium quantum dynamics of an interacting Bose gas trapped ina 1D asymmetric double-well potential is studied by solving the many-bodySchr\"odinger equation numerically accurately. We examine how the loss ofsymmetry of the confining trap affects the macroscopic quantum tunnelingdynamics of the system between the two wells. In an asymmetric DW, the twowells are not equivalent anymore -the left well is deeper than the right one.Accordingly, we analyze the dynamics by initially preparing the condensate inboth the left and the right well. We examined the frequencies and amplitudes ofthe oscillations of the survival probabilities, the time scale for thedevelopment of fragmentation and its degree, and the growth and oscillatorybehavior of the many-body position and momentum variances. There is an overallsuppression of the oscillations of the survival probabilities in an asymmetricdouble well. However, depending on whether the condensate is initially preparedin the left or right well, the repulsive inter-atomic interactions affect thesurvival probabilities differently. The degree of fragmentation depends both onthe asymmetry of the trap and the initial well in which the condensate isprepared in a non-trivial manner. Overall, the many-body position and momentumvariances bear the prominent signatures of the density oscillations of thesystem in the asymmetric double well as well as a breathing-mode oscillation.Finally, a universality of fragmentation for systems made of different numbersof particles but the same interaction parameter is also found. The phenomenonis robust despite the asymmetry of the junction and admits amacroscopically-large fragmented condensate characterized by a divergingmany-body position variance.

Many-body quantum dynamics of an asymmetric bosonic Josephson junction