Optical lattices have become a widely used tool to study and simulate several models of condensed matter physics. In  quantum information they have shown to deliver a promising resource for quantum computers and quantum simulators. Especially the Mott-Insulator phase of bosons described by the Bose-Hubbard model creates the basis of a scalable quantum computer.

 

In order to realise this phase in the experiment a  Bose-Einstein  condensate  is  created  and loaded  into a  harmonic  trap. Then an optical  lattice  is  ramped  up adiabatically across the Superfluid-Mott-Insulator phase transition until the  desired  state  is  reached.  This  process however  is  slow  in the order of  hundreds of  milliseconds and still leads to defects. Applying optimal control to  this  problem  can  do  both, reduce the ramp time  and  additionally reduce the defects in the Mott-Insulator state. For this purpose  we  investigate  the  time  dependent ramp of a superfluid state to the Mott-Insulator phase in one  dimension  via  DMRG  and optimise this ramp for several parameters.

 

Two-dimensional  Mott-Insulators can be optimised using  experimental  output instead of the DMRG simulation. This output gets processed in a closed-loop setup by updating the guess ramp  every  time  one  loop  cycle  has  finished.

Because of the close relation of this work to applications in lattice experiments we work closely with experimentalists realising optical lattices with bosons in 1D and 2D.