Cooperative phases and phase transitions of Bose condensed light in dye filled cavities

Abstract

Recent realization of Bose-Einstein condensation of light in 2D provides a new platform for studying novel phases and phase transitions. The combination of low effective mass of the confined light and the presence of the dye molecules with randomly oriented directions of the dipolar transition engages a competition between disorder and the tendency to forming algebraic off-diagonal order. The phase diagram of possible phases is constructed at the mean field level. One of the phases is the condensate of photon pairs induced solely by the orientational disorder. Such a geometrical mechanism of pairing has no analogy in other systems.

Cooperative phase transitions in a system of photons and dye molecules

“…Each dye molecule described as TLS is characterized by its center of mass position (x i , y i , z i ), where the index i runs over all N such molecules, and by the orientation given by the unit vector n i along d. As emphasized in Ref. [1], it is important that this transition (S 0 → S 1 characterized by real matrix element d) is non-degenerate which leads to lowering the symmetry from O(4) to O(2)×Z 2 , and, thus, allows the condensation to occur in 2D geometry in the algebraic sense. At time scales longer than few ns the vector field n i becomes classical order parameter.…”

“…As noted in Refs. [1], virtual electronic transitions within each molecule introduce anisotropy lowering the symmetry of the photonic order parameter from O(4) to O(2)×Z 2 (see also in Ref. [11]).…”

“…As a result, under certain conditions the transition can become discontinuous into a linearly polarized photonic condensate -in contrast to the short time situations analyzed in Ref. [1]. Initially, the system is considered in the limit when spatial distribution of the dye is uniform and fixed as an external parameter, while the orientation of the molecules is allowed to relax in the local field of the photonic condensate.…”

“…One consequence of this is the possibility of the formation of so called geometrically paired photonic condensate [1]. This phase is possible as a transient phenomenon on the time scale characterized by three orders of magnitude -from few ps to few ns when the dye molecules can be treated as a source of static disorder.…”

“…This phase is possible as a transient phenomenon on the time scale characterized by three orders of magnitude -from few ps to few ns when the dye molecules can be treated as a source of static disorder. [Such a phase can be made an equilibrium one by imposing additional optical fields [1]). At longer time scales the rotational and translational molecular degrees of freedom come into play.…”