 Dispersive atom-cavity coupling

Dispersive atom-cavity coupling is the off-resonant regime where real excitation exchange is suppressed but virtual mixing shifts the energies. For a two-level system describing an chemical atom coupled to one mode, the scale $\chi \simeq g^2/\Delta$ appears when $|\Delta |$ is large compared with the relevant occupation-enhanced coupling $g\sqrt{n+1}$.

An effective term proportional to $\hslash \chi a^{†}a{\sigma }_z$ then makes the atomic phase depend on photon number and the cavity frequency depend on atomic state. Measuring that phase can infer field occupation without resonantly absorbing a photon in the ideal approximation. Finite detuning, losses and probe backaction still matter; dispersive does not mean completely uncoupled or universally disturbance-free. A model must state detuning sign and the retained perturbative order.