A 2x2 quantum dot analogue simulator

The interaction between electrons in arrays of electrostatically defined quantum dots is naturally described by a Fermi-Hubbard Hamiltonian. Moreover, the high-degree of tunability of these systems make them a perfect platform to simulate different regimes of the Hubbard model. We present an array of 2x2 gate-defined quantum dots in a AlGaAs/GaAs heterostructure.
This 2-dimensional quantum simulator presents symmetries not accessible in the more common linear arrays, which enable experimentally novel simulations such as the demonstration of Nagaoka ferromagnetism, and observation of resonating valence bond states, which have been predicted for high-temperature superconductors. The device has been fabricated using a multi-layer gate technique, allowing good tunability of the tunnel coupling between the dots. Ongoing measurements on this device show control of the simultaneous occupation of all four dots to the single-electron regime, as well as individual control of the tunnel-couplings, which we have been able to tune in the range of 20-40 μeV for each nearest-neighbour coupling. Additionally, nearby RF charge sensors allow us to perform fast (~1 μs) single-shot readout of the spin state of electrons in the dots, through spin to charge conversion and Pauli spin blockade.