Coherent spin-spin coupling mediated by virtual microwave photons

Understand

We report the coherent coupling of two electron spins at a distance via virtual microwave photons.

• Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around $g_s/2\pi = 40 \ \text{MHz}$.
• As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around $2J/2\pi = 20 \ \text{MHz}$.
• In addition, photon-number states are resolved from the shift $2\chi_s/2\pi = -13 \ \text{MHz}$ that they induce on the spin frequency.