A generic
electromagnetic field can always be expressed in terms of a
mode expansion where individual components form a
complete set of modes. Such modes can be constructed with different methods and they can, e.g., be energy eigenstate, generic spatial modes, or temporal modes. Once these light
mode are chosen, their effect on the quantized electromagnetic field can be described by
Boson creation and annihilation operators \hat{B}^\dagger and \hat{B} for
photons, respectively. The quantum fluctuations of the light field can be uniquely defined by the photon
correlations \Delta\langle\left [ B^ {\dagger}\right]^J\, B^K\rangle that contain the pure (J+K)-particle correlations as defined with the
cluster-expansion approach. Using the same
second-quantization formalism for the matter being studied, typical electronic excitations in matter can be described by
Fermion operators for electronic excitations and holes, i.e.~electronic vacancies left behind to the many-body
ground state. The corresponding electron–hole excitations can be described by operators \hat{X}^\dagger and \hat{X} that create and annihilate an electron–hole pair, respectively. In several relevant cases, the light–matter interaction can be described using the dipole interaction \hat{H}_{\mathrm{lm}}=-\sum\mathcal{F}\,\hat{B}\hat{X}^{\dagger}+\mathrm{h.c.}\,, where the summation is implicitly taken over all possibilities to create an electron–hole pair (the \hat{X}^\dagger part) via a photon absorption (the \hat{B} part); the Hamiltonian also contains the
Hermitian conjugate (abbreviated as h.c.) of the terms that are explicitly written. The
coupling strength between light and matter is defined by \mathcal{F}. When the electron–hole pairs are excited resonantly with a single-mode light \hat{B}, the photon correlations are directly injected into the many-body correlations. More specifically, the fundamental form of the light–matter interaction inevitably leads to a correlation-transfer relation \Delta\langle\left[\hat{X}^{\dagger}\right]^J\hat{X}^K\rangle=\eta^{\frac{J+K}{2}} \Delta\langle\left [ B^ { \dagger }\right]^JB^K\rangle\,, between photons and electron–hole excitations. Strictly speaking, this relation is valid before the onset of scattering induced by the
Coulomb and
phonon interactions in the solid. Therefore, it is desirable to use laser pulses that are faster than the dominant scattering processes. This regime is relatively easy to realize in present-day laser spectroscopy because lasers can already output
femtosecond, or even
attosecond, pulses with a high precision in controllability. ==Realization==