Exciton-polariton kinematic interactions in organic microcavities Hashem Zoubi and G. C. La Rocca Scuola Normale Superiore and INFM, Piazza dei Cavalieri 7, 56126 Pisa, Italy Received 13 May 2005; published 7 September 2005 We analyze the exciton-exciton and polariton-polariton kinematic interactions in crystalline organic micro- cavities. The kinematic interactions are derived using the Agranovich-Toshich transformation, which trans- forms the Frenkel excitons from paulions into bosons. From the calculated exciton-scattering cross section in an organic crystalline monolayer, we find that the scattering due to the exciton-exciton kinematic interaction can be described as the scattering between hard disks. We show that, as in the case of two-dimensional ultracold trapped boson atom gas, excitons in a confined monolayer may behave as a dilute degenerate boson gas at low temperature. In an organic cavity, with an organic crystalline monolayer as a resonant material, we derive the polariton-polariton kinematic interaction, which stems from the polariton excitonic part. We calcu- late the polariton-scattering cross section due to the polariton-polariton kinematic interaction, and recognize the scattering effective potential. We show that, due to the smallness of the polariton effective mass, polaritons in organic cavities may behave as a dilute degenerate boson gas up to room temperature. The comparison between the polariton-polariton kinematic interaction in organic cavities and the polariton-polariton nonlinear interac- tion in inorganic semiconductor cavities shows that both interactions are of the same order. DOI: 10.1103/PhysRevB.72.125306 PACS numbers: 71.35.y, 71.35.Aa, 71.36.c I. INTRODUCTION The Frenkel exciton, which is an electronic excitation in a molecular crystal, can be viewed as a coupled electron-hole pair localized on the same crystal molecule, and has a neutral charge and an integer spin. 1 In molecular crystals, each mol- ecule retains its identity, whereas the wave-function overlaps are neglected, and the molecules are bounded by the van der Waals forces. The Frenkel exciton can transfer among the crystal molecules due to the electrostatic interactions, whereas only a single excitation is allowed in each crystal molecule. Such an excitation is represented by a wave that propagates in the crystal. The Frenkel excitons in organic molecular crystals behave as paulion particles, that is, the exciton operators obey the Fermi anticommutation relations in the same crystal site and obey the Bose commutation re- lations between different sites. The paulion particles have no defined quantum statistics Fermi-Dirac or Bose-Einstein sta- tistics. Hence, it is often convenient to transform from a paulion description to a boson or fermion one. At low con- centration, the excitons behave approximately as bosons. Therefore, in this limit, usually the excitons are considered as boson particles, whereas the paulion operators are re- placed by boson ones. This replacement permits a state with more than one excitation being localized on the same crystal molecule, which is considered as an unphysical state. To avoid the appearance of these unphysical states, an exact transformation from the Pauli operators to the Bose operators is required. Such a transformation was derived by Agranov- ich and Toshich, 2 and is called the Agranovich-Toshich trans- formation ATT. In the ATT, each Pauli operator is repre- sented by a power series of Bose operators. In weakly excited organic crystals, it is a good approximation to keep only the lowest-order terms of the series. In applying the ATT, the system of free paulions is replaced by interacting bosons, and the transformation gives rise to additional inter- action terms between the bosons, called kinematic interac- tions KIs. In this paper, we neglect the exciton-exciton dy- namical interactions, i.e., those due to the Coulomb interactions, as the kinematic ones are dominant in molecular crystals. At low temperature, the KI leads only to scattering between excitons, and the formation of bound exciton states due to the KI is immaterial. 2 The KI has the form of a contact potential, which is of the order of the crystal molecule tran- sition energy. In the center-of-mass frame, the kinematic scattering is equivalent to the scattering of an exciton from an impurity in the crystal. Agranovich et al. 2 investigated the KI effects on excitons in a bulk organic crystal, and using the scattering cross section of an exciton from an impurity in a bulk molecular crystal that was derived by Dubovskii et al., 3 they showed that excitons behave as a dilute degenerate bo- son gas of hard spheres at low temperature. Organic microcavities have attracted great interest for their ability to control the light-matter coupling. 4 In the strong-coupling regime, where the photon-exciton interac- tion is larger than the exciton and photon damping rates, the cavity photons and the excitons are coherently coupled to produce the system eigenmodes that are the cavity exciton- polaritons. The polariton, dispersion relation splits into two branches that are separated by the Rabi splitting frequency, which is proportional to the transition dipole moment. The advantage in using organic microcavities is due to the large oscillator strength of the organic materials. The strong cou- pling between the Frenkel excitons in organic materials and the cavity photons results in a Rabi splitting that is easily an order of magnitude larger than that of inorganic microcavities, 5 whereas in typical quantum-well microcavi- ties, the coupling between the Wannier-Mott excitons and the cavity photons yields Rabi splitting values of the order of 10 meV. 6 In particular, a strong-coupling regime has been observed in an organic microcavity containing J aggregates of cyanine dye, 7 which have an absorption line-width of about 40 meV, where the Rabi splitting is between 80 meV and 300 meV, at room temperature. Such organic microcavi- PHYSICAL REVIEW B 72, 125306 2005 1098-0121/2005/7212/12530613/$23.00 ©2005 The American Physical Society 125306-1