Optimal control of quantum phase transition in the bilinear biquadratic model



One of our research topics concerns the optimal control of quantum phase transition (QPT). Studies of the manipulation of QPT, more generally many body dynamics, are very promising from different point of view and useful for quantum metrology and quantum computation. Some quantum phases show topological properties. Such states have very good robustness properties which are crucial properties to make stable and robust computation. The bilinear biquadratic model exhibits a phase with topological properties: the Haldane phase. The model corresponds to a linear chain of spin S=1 with linear and quadratic  Heisenberg  nearest neighbor interactions. Depending on the weight between the linear and quadratic part, the system exhibits different behavior (see phase diagram).


Our goal is to drive the system into the Haldane phase. The topological nature of the final state obtained is done by the measure of the string order parameter. We use optimal control theory to find the evolution of control  parameter. The driving of QPT through optimal control is fundamental in order to decrease the time duration of  the transition. Indeed experiments are never perfect and suffer from decoherence. This imperfection prevents the use of adiabatic driving which requires a long duration to be effective. This long duration makes the adiabatic strategy very sensitive to decoherence.