  We consider performing adiabatic rapid passage (ARP) using frequency-swept
driving pulses to excite a collection of interacting two-level systems. Such a
model arises in a wide range of many-body quantum systems, such as cavity QED
or quantum dots, where a nonlinear component couples to light. We analyze the
one-dimensional case using the Jordan-Wigner transformation, as well as the
mean field limit where the system is described by a Lipkin-Meshkov-Glick
Hamiltonian. These limits provide complementary insights into the behavior of
many-body systems under ARP, suggesting our results are generally applicable.
We demonstrate that ARP can be used for state preparation in the presence of
interactions, and identify the dependence of the required pulse shapes on the
interaction strength. In general interactions increase the pulse bandwidth
required for successful state transfer, introducing new restrictions on the
pulse forms required.
