Abstract:
The study of strongly correlated electrons systems is often difficult
due to the complexity of interacting quantum systems. Even for
moderate size systems, the complexity is too large to be solvable by
numerical calculations with classical computers. Feynman[1], and later
Lloyd[2], proposed to solve this problem by building controllable and
clean quantum systems simulating the Hamiltonian one wants to solve,
and study the physics of this Hamiltonian through experiments on these
controlled quantum systems.
Laterally-defined quantum dots display very interesting features for a
quantum simulator. They naturally map the Hubbard Hamiltonian, their
tunability is excellent, and their use in dilution fridge allows
access to low temperature phases of the Hubbard model, where magnetic
ordering effects start to appear.
In this talk, I will present two different projects aiming to use
laterally defined dots for quantum simulations. I will show that a
plaquette of four dots allows studying a rather surprising effect
called Nagaoka’s ferromagnetism and I will present ideas to realize
large arrays of quantum dots for the study of Mott Insulating systems,
and, maybe, the observation of the onset of large scale magnetic
ordering in the Hubbard model.
[1] Feynman, Simulating Physics with Computers. International Journal
of Theoretical Physics 21: 467, (1982)
[2] Lloyd, Universal quantum simulators. Science 273, 5278, (1996)