Adiabatic preparation of many-body states in optical lattices

We analyze a technique for the preparation of low-entropy many-body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions.

Figure 1

Time evolution of the Neel magnetization when the staggered magnetic field is turned off. The full curves show the evolution for various imperfections in the initial preparation (counting from above $P=0$, 0.05, 0.1, 0.15, 0.2). For comparison the dots show the magnetization of the ground state of the instantaneous Hamiltonian. (a) Adiabatic turn off with $\alpha =J$ and $h_0=20J$. (b) Without staggered magnetic field $h_0=0$. The dashed curve in (a) shows the evolution starting from a state with the spin aligned oppositely $\langle {\mathrm{S̃}}_z\rangle =-1/2$ for $P=0$.

Figure 2

Neel magnetization $\langle {\mathrm{S̃}}^z\rangle$ at the end of the adiabatic evolution. (a) As a function of the initial magnetic field $h_0$ and extinction rate $\alpha$ for a perfect initial state $P=0$, and (b) as a function of extinction rate $\alpha$ and imperfection in the initial state $P$ with a fixed initial field $h_0=10J$.