Multiconfigurational time-dependent Hartree method for bosons with internal degrees of freedom:Theory and composite fragmentation of multicomponent Bose-Einstein condensates
Résumé
In this paper, the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method is derived forthe case ofNidentical bosons with internal degrees of freedom. The theory for bosons with internal degrees offreedom constitutes a generalization of the MCTDHB method that substantially enriches the many-body physicsthat can be described. We demonstrate that the numerically exact solution of the time-dependent many-bodySchr ̈odinger equation for interacting bosonic particles with internal degrees of freedom is now feasible. We reporton the MCTDHB equations of motion for bosons with internal degrees of freedom and their implementationfor a general many-body Hamiltonian with one-body and two-body terms, both of which may depend on theinternal states of the considered particles and time. To demonstrate the capabilities of the theory and its softwareimplementation integrated in theMCTDH-Xsoftware, we apply MCTDHB to the emergence of fragmentation ofparabolically trapped bosons with two internal states: we study the ground state ofN=100 bosons as a functionof the separation between the state-dependent minima of the two parabolic potentials. To quantify the coherenceof the system, we compute its normalized first-order correlation function. We find that the coherence within eachinternal state of the atoms is maintained, while it is lost between the different internal states. This is a hallmark of akind of fragmentation absent in bosons without internal structure. We term the emergent phenomenon “compositefragmentation.”
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