Spin-1 Bose gases quenched to spin degeneracy exhibit fragmentation: the appearance of a condensate in more than one single-particle state. Due to its highly entangled nature, this collective state is beyond the scope of a Gaussian variational approximation of the many-body wave function. Here, we improve the performance of the Gaussian variational Ansatz by considering dissipation into a fictitious environment, effectively suppressing entanglement within individual quantum trajectories at the expense of introducing a classical mixture of states. We find that this quantum trajectory approach captures the dynamical formation of a fragmented condensate, and analyze how much dissipation should be added to the experiment in order to keep a single realization in a non-fragmented state.
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