A Shpolskii (or Shpol'skii) matrix is a low-temperature host-guest system consisting of guest or impurity chromophore embedded in a crystaline matrix. The fluorescence emission spectra and absorption spectra of Shpolskii matrices exhibit narrow lines instead of the inhomogeneously broadened features normally associated with spectra of chromophores in liquids or solids. The phenomena was first described by Éduard Vladimirovich Shpol'skiĭ in the 1950s and 1960's in the journals Transactions of the U.S.S.R. Academy of Sciences and Soviet Physics Uspekhi.
Shpolskii matrices are formed when each chromophore neatly replaces one or more molecules in the host crystaline lattice. A good match between the chromophore and the host lattice leads to a uniform environment for all the chromophores and hence greatly reduces the inhomogeneous broadening of the electronic transitions. In addition to the weak inhomogeneous broadening of the transitions, the quasi-lines observed at very low tempeatures are phonon-less transitions. Since phonons originate in the lattice, an additional requirement is weak chromophore-lattice coupling. Weak coupling increases the probability of phonon-less transitions and hence favors the narrow zero phonon lines. The weak coupling is usually expressed in terms of the Debye-Waller factor, where a maximum value of one indicates no coupling between the chromophore and the lattice phonons. The narrow lines characteristic of the Shpolskii matrix are only observed at cryogenic temperatures because at higher temperatures many phonons are active in the lattice and all of the amplitude of the transition shifts to the broad phonon sideband. The original observation was made at liquid nitrogen temperature (77 kelvins), but using temperatures close to that of liquid helium (4.2 K) yields much sharper spectral lines and is the usual practice.
Shpolskii matrices result from fortuitous compatibility between the chromophore and the host matrix and most of the known systems consist of dilute solutions of mono- or polycyclic aromatic hydrocarbons in low molecular weight linear alkanes. The solution is often flash frozen with cold helium gas. Linear alkanes interact weakly with the chromophores and crystallize when frozen. The length of the alkanes is often chosen to approximately match the dimensions of the chromophore, and are usually in the size range between n-pentane and n-dodecane.