Multiconfigurational timedependent Hartree method for bosons with internal degrees of freedom: Theory and composite fragmentation of multicomponent BoseEinstein condensates
Abstract
In this paper, the multiconfigurational timedependent Hartree for bosons (MCTDHB) method is derived for the case of N identical bosons with internal degrees of freedom. The theory for bosons with internal degrees of freedom constitutes a generalization of the MCTDHB method that substantially enriches the manybody physics that can be described. We demonstrate that the numerically exact solution of the timedependent manybody Schrödinger equation for interacting bosonic particles with internal degrees of freedom is now feasible. We report on the MCTDHB equations of motion for bosons with internal degrees of freedom and their implementation for a general manybody Hamiltonian with onebody and twobody terms, both of which may depend on the internal states of the considered particles and time. To demonstrate the capabilities of the theory and its software implementation integrated in the mctdhx software, we apply MCTDHB to the emergence of fragmentation of parabolically trapped bosons with two internal states: we study the ground state of N =100 bosons as a function of the separation between the statedependent minima of the two parabolic potentials. To quantify the coherence of the system, we compute its normalized firstorder correlation function. We find that the coherence within each internal state of the atoms is maintained, while it is lost between the different internal states. This is a hallmark of a kind of fragmentation absent in bosons without internal structure. We term the emergent phenomenon "composite fragmentation."
 Publication:

Physical Review A
 Pub Date:
 June 2016
 DOI:
 10.1103/PhysRevA.93.063601
 arXiv:
 arXiv:1602.05791
 Bibcode:
 2016PhRvA..93f3601L
 Keywords:

 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 24 pages, 5 figures. Software available at http://ultracold.org