Abstract:
Quantum walks are the quantum mechanical analogues of classical random walks, in which the walker simultaneously moves to all neighbouring sites of a graph at each step. These can lead to the fastest known quantum algorithms, much like random walks often optimize classical algorithms. I will discuss how one can modify quantum walks in order to perform a generalized Fourier transform. This idea will be extended to show how one could experimentally obtain the energy distribution of weakly interacting ultracold bosons in optical lattices, simply by allowing the gas to evolve in time within a suitably prepared lattice. The results are robust against imperfections in the implementation and particle interactions. In this way, it should be possible to directly cool bosons in optical lattices, using standard experimental techniques.

Nicolai Nygaard

Institut for Fysik og Astronomi

Aarhus Universitet

Ny Munkegade 120, Bygn. 1520 (kontor 634)

8000 Århus C

Denmark

Telephone: +45 89 42 36 80

Fax: +45 86 12 07 40

Email: nygaard@phys.au.dk

Web: www.phys.au.dk/~nygaard