Microscopic theory of quantization of radiation in molecular dielectrics: Normal-mode representation of operators for local and averaged (macroscopic) fields
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Quantization of radiation has been performed from first principles in a realistic molecular medium, represented by an arbitrary number of energy levels (electronic, vibrational, rotational, etc.) for each constituent molecule. Adopting a polariton model, the field operators have been expanded in terms of normal Bose operators for polariton creation and annihilation. The expansion coefficients have been derived explicitly for the normal modes characterized by wavelengths exceeding considerably the characteristic distance of separation between the molecules. Accordingly, the formalism applies to the long-wavelength region of the spectrum for which description in terms of the macroscopic refractive index is relevant; furthermore, consideration is restricted to the nonabsorbing areas of the spectrum. The theory has been formulated in a manner that made possible a parallel and comparative consideration of operators for both the averaged (macroscopic) and local fields. Consequently, the mode expansions derived cover both the local displacement-field operator and also the averaged (macroscopic) operators for the electric, displacement, magnetic, and polarization fields, and the vectorial potential. The expansions, involving summation over an arbitrary number of branches of polariton dispersion, manifestly embody the refractive influences as well. To this end, the local-field effects intrinsically emerge within the present formalism that treats systematically the photon umklapp processes. Relations have been established between the expansion components of the local and averaged field operators. The relationships support some previous attempts to link the amplitudes of local and macroscopic field operators phenomenologically, and are also consistent with the familiar results of classical electrodynamics. Equal-time commutation relations have been demonstrated to be preserved, expressing the operators for the averaged fields in terms of the normal Bose operators. On the other hand, the commutation relations between the macroscopic fields are of the same form as those for their microscopic counterparts, subject to the coarse-graining procedure. Finally, the present study dealing with the macroscopic and local operators provides a tool for combined investigation of both propagation of the quantized fields in molecular dielectrics and also interaction of the fields with the embedded molecules or atoms. \textcopyright{} 1996 The American Physical Society.Keywords:
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A method for an exact theoretical treatment of nonlinear (anharmonic) effects in crystals in the second quantization representation is presented. The method represents essentially a generalization of Bogolyubov's method of approximate second quantization. In addition, the Fermi representation of elementary excitation creation and annihilation operators is given.
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Lead halide perovskites exhibit good performance in room-temperature exciton–polariton lasers and efficient flow of polariton condensates. Shaping and directing polariton condensates by confining the potential is essential for polariton-based optoelectronic devices, which have seldom been explored based on perovskite materials. Here, we investigate the trapping of polaritons in micron-sized CsPbBr3 flakes embedded in a microcavity by varying the negative detuning energy (from −36 to −172 meV) at room temperature. The confinement by the crystal edge results in quantized polariton states both below and above the condensed threshold. As the cavity is more negatively detuned (Δ ≤ −118 meV), the condensed polaritons undergo a transition from the ground state to metastable states with a finite group velocity (∼50 μm/ps at Δ = −118 meV). The metastable polariton condensates can be optically and stably driven between different polariton states by simply changing the pump fluence. The manipulations of the polariton states reveal the effective control of polariton relaxation in quantized polariton states by the underlying exciton–polariton and polariton–polariton scattering. Our findings pave the way for novel polaritonic light sources and integrated polariton devices through the trap engineering of perovskite microcavities.
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Abstract We analyzed the features of CARS from polaritons caused by the ability of polaritons to propagate over macroscopic distances in a crystal. The polariton propagation is taken into account by retaining both a driven and a free polariton wave in complete solution of the wave equation for polaritons. It is shown that the polariton propagation can broaden CARS spectra. This broadening originates from the fact that polaritons can escape from the excitation region and the value of the broadening depends on the ratio L θ / L p of the dimension L θ of the excitation region along the coherently excited polariton direction and the mean path of coherent polaritons L p . We also find that when the phase‐matching Δ k a = 0 for the overall anti‐Stokes generation process is not fulfilled, an additional peak in the spectrum of CARS may appear even when the polariton damping is appreciable. These predictions are corroborated by our experimental investigations of CARS from polaritons in a BeO crystal. Copyright © 2002 John Wiley & Sons, Ltd.
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The second-order coherence formation in the condensate of polaritons in a semiconductor microcavity is studied. The finite lifetime of polaritons allows to neglect the polariton-polariton interaction at low occupations of the polariton condensate, and the initial stage of condensate formation can be analyzed analytically. Then I discuss the decisive role of polariton-polariton repulsion and other nonlinearities in the suppression of the amplitude fluctuation of the order parameter and the second-order coherence build-up. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Nonlinear processes involving polaritons in organic crystalline microcavities are theoretically studied by taking the kinematic polariton-polariton interactions as a source of nonlinearity. The polariton mean-field equations of motion are derived and used to explain the polariton parametric amplifications, which are predicted here for angle-resolved resonant pump-probe experiments in organic microcavities. We show that around zero exciton-photon detuning and for long-wavelength polaritons in a laterally confined microcavity, the polariton kinematic interactions result in a blueshift in the amplified probe field, while for large negative detuning the amplified probe field is redshifted. The parametric amplifications are studied for different processes which include the upper and lower polariton branches.
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We demonstrate a novel way to realize room-temperature polariton parametric scattering in a one-dimensional ZnO microcavity. The polariton parametric scattering is driven by a polariton condensate, with a balanced polariton pair generated at the adjacent polariton mode. This parametric scattering is experimentally investigated by the angle-resolved photoluminescence spectroscopy technique under different pump powers and it is well described by the rate equation of interacting bosons. The direct relation between the intensity of the scattered polariton signal and that of the polariton reservoir is acquired under nonresonant excitation, exhibiting the explicit nonlinear characteristic of this room-temperature polariton parametric process.
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Bosonic condensates of exciton polaritons (light-matter quasiparticles in a semiconductor) provide a solid-state platform for studies of non-equilibrium quantum systems with a spontaneous macroscopic coherence. These driven, dissipative condensates typically coexist and interact with an incoherent reservoir, which undermines measurements of key parameters of the condensate. Here, we overcome this limitation by creating a high-density exciton-polariton condensate in an optically-induced "box" trap. In this so-called Thomas-Fermi regime, the condensate is fully separated from the reservoir and its behaviour is dominated by interparticle interactions. We use this regime to directly measure the polariton-polariton interaction strength, and reduce the existing uncertainty in its value from four orders of magnitude to within three times the theoretical prediction. The Thomas-Fermi regime has previously been demonstrated only in ultracold atomic gases in thermal equilibrium. In a non-equilibrium exciton-polariton system, this regime offers a novel opportunity to study interaction-driven effects unmasked by an incoherent reservoir.
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