  Quantum simulators based on atoms or molecules often have long-range
interactions due to dipolar or Coulomb interactions. We present a method based
on Floquet engineering to turn a long-range interaction into a short-range one.
By modulating a magnetic-field gradient with one or a few frequencies, one
reshapes the interaction profile, such that the system behaves as if it only
had nearest-neighbor interactions. Our approach works in both one and two
dimensions and for both spin-1/2 and spin-1 systems. It does not require
individual addressing, and is applicable to all experimental systems with
long-range interactions: trapped ions, polar molecules, Rydberg atoms,
nitrogen-vacancy centers, and cavity QED. Our approach allows one achieve a
short-range interaction without relying on Hubbard superexchange.
