Exchange interaction
Virtual tunneling creates a controllable spin–spin coupling.
$$H_{\rm ex}=J\mathbf S_1\cdot\mathbf S_2$$
Physical intuition
Virtual tunneling creates a controllable spin–spin coupling.
Deep dive: physical mechanism
In a Hubbard-like model, exchange scales approximately as tunnel coupling squared over charging energy.
What is measured experimentally?
Exchange oscillations and conditional gates characterize J.
Assumptions, noise and limitations
Charge noise can strongly modulate J.
Research and simulation exercise
Compare exact two-site Hubbard energies with the exchange approximation.
Connect the ideas
Explore the chapter overview, learning path, and references.