Sudden and slow quenches into the antiferromagnetic phase of ultracold fermions
We propose a method to reach the antiferromagnetic state of two-dimensional Fermi gases trapped in optical lattices: Independent subsystems are prepared in suitable initial states and then connected by a sudden or slow quench of the tunneling between the subsystems. Examples of suitable low-entropy subsystems are double wells or plaquettes, which can be experimentally realised in Mott insulating shells using optical super-lattices. We estimate the effective temperature T* of the system after the quench by calculating the distribution of excitations created using the spin wave approximation in a Heisenberg model. We investigate the effect of an initial staggered magnetic field and find that for an optimal polarisation of the initial state the effective temperature can be significantly reduced from T*$\approx$1.7 Tc at zero polarisation to T*<0.65Tc, where Tc is the crossover temperature to the antiferromagnetic state. The temperature can be further reduced using a finite quench time. We also show that T* decreases logarithmically with the linear size of the subsystem.