Direct measurement of polariton–polariton interaction strength

Abstract

Exciton-polaritons in a microcavity are composite two-dimensional bosonic quasiparticles, arising from the strong coupling between confined light modes in a resonant planar optical cavity and excitonic transitions, typically using excitons in semiconductor quantum wells (QWs) placed at the antinodes of the same cavity. Quantum phenomena such as Bose-Einstein condensation (BEC) [1, 2], superfluidity [3], quantized vortices [4][5][6][7][8], and macroscopic quantum states [9, 10] have been realized at temperatures from tens of Kelvin up to room temperatures [11][12][13], and polaritonic devices such as spin switches [14] and optical transistors [15] have also been reported. Many of these effects of exciton-polaritons depend crucially on the polariton-polariton interaction strength. Despite the importance of this parameter, it has been difficult to make an accurate experimental measurement, mostly because of the difficulty of determining the absolute densities of polaritons and bare excitons. Here we report the direct measurement of the polariton-polariton interaction strength in a very high-Q microcavity structure. By allowing polaritons to propagate over 40 µm to the center of a lasergenerated annular trap, we are able to separate the polariton-polariton interactions from polariton-exciton interactions. The interaction strength is deduced from the energy renormalization of the polariton dispersion as the polariton density is increased, using the polariton condensation as a benchmark for the density. We find that the interaction strength is about two orders of magnitude larger than previous theoretical estimates, putting polaritons squarely into the strongly-interacting regime. When there is a condensate, we see a sharp transition to a different dependence of the renormalization on the density, which is evidence of many-body effects.Much of the physics of polaritons is dominated by the fact that they have extremely light effective mass. When an exciton is mixed with a cavity photon to become an excitonpolariton, it has an effective mass about four orders of magnitude less than a vacuum electron, and about three orders of magnitude less than a typical semiconductor quantum well exciton. (The Supplementary Information gives a basic introduction to the properties of exciton-polaritons.) Therefore one can view the polaritons as excitons which are given much longer diffusion length, with propagation distance of polaritons up to millimeters [16,17]; this may have implications for solar cells, which depend crucially on the diffusive 2 migration of excitons [18]. Alternatively, exciton-polaritons can be viewed as photons with nonlinear interactions many orders of magnitude higher than in typical optical materials, due to their excitonic components [19]. The light effective mass of the polaritons (typically 10 −8 that of a hydrogen atom) allows for quantum phenomena to be realized at much higher temperatures than in cold atomic gases.Interactions among polaritons. The interaction of exciton-polaritons is presumed to come...

Two-dimensional infrared spectroscopy of vibrational polaritons of molecules in an optical cavity

“…show three distinct peaks along Ω 2 axis with energies resonant to Ω f 1 g = 2Ω e 1 g − V 11 , Ω f 2 g = 2Ω e 1 g and Ω f 3 g = 2Ω e 2 g − V 33 respectively. Along Ω 3 axis, |S i (Ω 3 , Ω 2 , 0)| (Fig.…”

“…6)(a): The coupled Amide-I+II vibrations of NMA is effectively a three level system with two singly excited states and three doubly excited states in absence of cavity coupling. The two singly excited states are resonant with Ω e 1 g and Ωe 2 g. The three doubly excited states are resonant with frequencies Ω f 1 g = 2Ω e 1 g −∆ 11 , Ω f 2 g = Ω e 1 g +Ω e 2 g and Ω f 3 g = 2Ω e 2 g −∆ 22 (Sec. SII of supplementary material 34 , Table I).…”

“…Electronic polaritons in molecules have been extensively studied both experimentally and theoretically [3][4][5] . Vibrational polaritons in the infrared has been recently demonstrated in molecular aggregates [6][7][8][9] and in semiconductor nano-structures [10][11][12] . The radiation matter coupling is related to cavity frequency ω c by, g i = √ N µ i · e c ( ω c /2 0 V ), where, N is the number of molecules.…”

Microscopic theory of equilibrium polariton condensates

“…3, we find that for a fixed detuning there is a minimum value of the chemical potential at which an equilibrium polariton condensate can be established, and that the chemical potential increases linearly with polariton density in the low density limit in agreement with experiment. 4,17 We identify the smallest value of the chemical potential at which mutual equilibrium between photons and matter excitations can be established as the lower-polariton energy, LP . The value of LP predicted by the microscopic mean-field equations can be compared with the value predicted by the analytic expression Eq.…”

“…2, we first solve µ = ex + U n ex − Ω n ph n ex (17) to obtain n ex as a function of n ph and µ and then use…”