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(October 3)Next-to-Nearest Neighbour Couplings And Entanglement Generation in Spin Chains and Optical Arrays
Sep 28, 2016

Title:

Next-to-Nearest  Neighbour Couplings And Entanglement Generation in Spin Chains and Optical  Arrays

Lecturer:

Prof. Luc Vinet

Time:

10:00, October 3,  2016

Venue:

609, New Science & Technology Building, North Campus

Lecturer  Profile

Professor  Luc Vinet is one of Canada leading mathematical and theoretical physicists who  has made outstanding contributions in numerous areas. The unifying feature of  his research is the innovative use of group theoretical and algebraic methods,  the emphasis on exact solutions of physical problems and the originality of his  approach. He has made important contributions that have had great impact on  both physics and mathematics. He explored various algebraic structures  appropriate to describe symmetries in different physical problems. These go  well beyond standard Lie groups and algebras. They include polynomial, quantum,  super- and para super-algebras. He is very well known for his influential work  on quantum many body problems and for his application of this work to a proof  of the long outstanding Macdonald conjecture on properties of multivariate  orthogonal polynomials. His contributions to the symmetry theory of difference  and q-difference equations are truly pioneering. In 2011, he has discovered new  families of orthogonal polynomials, associated to reflections. These have  already found many applications. In the context of quantum information theory,  he has shown how spin chains can be used to design perfect quantum wires.

Lecture  Abstract

It  is known that perfect state transfer (PST) can be achieved in XX spin chains  with properly engineered nearest-neighbour (NN) couplings. The simplest model  with this feature is based on the Krawtchouk polynomials. In view of the  mathematical equivalence between the equations governing the dynamics of single  excitations in XX spin chains and those describing photon propagation in arrays  of evanescently coupled waveguides, PST can be experimentally realized in  photonic lattices. In this context restricting to NN interactions is obviously  an approximation. The phenomenon of fractional revival (FR) or wave packet  splitting that has smaller but identical packets reproduce periodically, can  also be seen in certain XX spin chains. This is not so however in the NN  Krawtchouk model. Like PST, FR brings useful new tools in quantum information  and can generate for instance quantum entanglement. I shall present an analytic  extension of the NN Krawtchouk model that includes next-tonearest neighbour  couplings. Under certain conditions, it will be shown to admit PST as well as  FR in distinction to the NN situation. Its application to coherent transport in  photonic lattices will be discussed.

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