Bipolariton Model Research Articles

Nonlinear transmission and reflection of ultrashort laser pulses by a thin semiconductorfilm under two-photon generation of biexcitons

The transmission and reflection of an ultrashort laser pulse by a thin semiconductor filmunder the conditions of resonance excitation of biexcitons by two photons are theoreticallyinvestigated. The numerical solutions of the macroscopic equations are found for variousvalues of the film thickness, the detuning from the two-photon resonance, the laser pulseduration, and the intensity. These equations have been obtained in the framework of thegeneralized bipolariton model. In this model a biexciton is formed from virtual excitons offour kinds and only some of them interact with the light. It is shown that the thin filmsubstantially transforms the incident pulse. For specific conditions, high and narrowtransmission and reflection peaks can appear, or even trains of such peaks. In some casestheir height can considerably exceed the amplitude of the incident pulse. Theresults are compared with similar results obtained on the basis of other models.

Real-time analysis of the optical response of cavity bipolaritons: Four-wave mixing and dynamics of formation

We theoretically investigate the four-wave mixing (FWM) of a biexciton in a microcavity in the framework of cavity bipolariton. Cavity bipolaritons are stably formed in the strong-coupling regime with an exciton-cavity coupling comparable to the biexciton binding energy. The FWM signal obtained from our bipolariton model, where the biexciton and unbound two-exciton states form a complete system, agrees well with the experimental data [Baars et al., Phys. Rev. B 63, 165311 (2001)]. A strong FWM signal is obtained when a cavity bipolariton is formed by a superposition state of a biexciton and unbound two-cavity-polariton states. We also analyze the dynamics of the formation of biexciton and cavity polaritons by numerically solving the optical master equation in time domain. Efficient excitation of cavity bipolariton requires a specific pulse duration and/or pulse delay so that two-cavity polaritons are formed before the biexciton is excited.

Evidence for two-photon generation of propagating bipolaritons in CuCl

Unlike the conventional theory of giant oscillator strength, the recently proposed bipolariton model describes two-photon excitation of an excitonic molecule in terms of resonant polariton-polariton Coulomb scattering. Using angle-resolved spectroscopy, we directly measure the angular dependence of the molecule luminescence under resonant two-photon excitation. We find that the observed photoluminescence is highly directional and well correlated with the propagation direction of the incident laser. This observation unambiguously supports the core idea of this model that replaces the idea of a biexciton by that of a mutually bound propagating polariton molecule.

Radiative corrections to the excitonic molecule state in GaAs microcavities

The optical properties of excitonic molecules (XXs) in GaAs-based quantum well microcavities (MCs) are studied, both theoretically and experimentally. We show that the radiative corrections to the XX state, the Lamb shift $\Delta^{\rm MC}_{\rm XX}$ and radiative width $\Gamma^{\rm MC}_{\rm XX}$, are large, about $10-30 %$ of the molecule binding energy $\epsilon_{\rm XX}$, and definitely cannot be neglected. The optics of excitonic molecules is dominated by the in-plane resonant dissociation of the molecules into outgoing 1$\lambda$-mode and 0$\lambda$-mode cavity polaritons. The later decay channel, ``excitonic molecule $\to$ 0$\lambda$-mode polariton + 0$\lambda$-mode polariton'', deals with the short-wavelength MC polaritons invisible in standard optical experiments, i.e., refers to ``hidden'' optics of microcavities. By using transient four-wave mixing and pump-probe spectroscopies, we infer that the radiative width, associated with excitonic molecules of the binding energy $\epsilon_{\rm XX} \simeq 0.9-1.1$ meV, is $\Gamma^{\rm MC}_{\rm XX} \simeq 0.2-0.3$ meV in the microcavities and $\Gamma^{\rm QW}_{\rm XX} \simeq 0.1$ meV in a reference GaAs single quantum well (QW). We show that for our high-quality quasi-two-dimensional nanostructures the $T_2 = 2 T_1$ limit, relevant to the XX states, holds at temperatures below 10 K, and that the bipolariton model of excitonic molecules explains quantitatively and self-consistently the measured XX radiative widths. We also find and characterize two critical points in the dependence of the radiative corrections against the microcavity detuning, and propose to use the critical points for high-precision measurements of the molecule bindingenergy and microcavity Rabi splitting.

Coherent dynamics of bipolaritons in bulk CdS

The coherent dynamics of an optically driven exciton--photon--bipolariton system is studied in bulk CdS. Applying backward-scattering four-wave mixing (FWM) spectroscopy, we analyze the two-photon polarization associated with excitonic molecules and determine the dephasing time ${T}_{2}\ensuremath{\simeq}4.8 \mathrm{ps}.$ We demonstrate that the molecule-mediated FWM signal persists at positive time delays even in the ${\ensuremath{\chi}}^{(3)}$ limit, due to the spatial pinning of coherent polaritons induced by the second pulse. By generalizing the bipolariton model to uniaxial semiconductors, we calculate ${\ensuremath{\tau}}_{\mathrm{rad}}^{\mathrm{XX}}\ensuremath{\simeq}2.8 \mathrm{ps},$ justify the ${T}_{2}{=2T}_{1}$ limit, and prove the bipolariton representation for excitonic molecules in CdS.

Bipolariton coupling in biexciton optical decay: Degenerate and nondegenerate polariton emissions in CuCl

Radiative decay of biexcitons wave-vector $(\mathbf{K})$ selectively generated in a low-$K$ region $(0<~|\mathbf{K}|\ensuremath{\lesssim}{2k}_{0})$ is studied in CuCl, where ${2k}_{0}$ is the biexciton wave number of degenerate two-photon excitation, and the bipolariton nature of low-$K$ biexcitons is experimentally demonstrated. All the radiative relaxation channels of low-$K$ biexcitons are clarified, which dissociate into two lower-branch polaritons and into upper- and lower-branch polaritons yielding nearly degenerate and nondegenerate pair emission lines, respectively. The three-dimensional scattering geometry allows for simultaneous observation of both degenerate and nondegenerate lines. Nearly degenerate two-polariton emissions have larger intensities than nondegenerate emissions. Completely degenerate emissions from $\mathbf{K}=2{\mathbf{k}}_{0}$ biexcitons have the largest intensity, reflecting singularity of the joint density of polariton states. These features are in remarkable contrast with the resonant two-photon absorption process of biexcitons, which shows resonance enhancement not at the degenerate two-photon energy but at the exciton resonance. In spite of the larger transition probability, nearly degenerate emissions have a negligible contribution to the emission band arising from thermally distributed biexcitons. The dispersion curve of the ${Z}_{1,2}{(Z}_{3})$-exciton lower(upper)-branch polariton is determined from the K dependence of the emission energies. The observed emission lines are all unambiguously assigned and the relative intensities of the simultaneously observed lines are compared with a biexciton radiative decay theory based on the bipolariton model. The energy dependence of the transition probability of the observed biexciton radiative decay channels is quantitatively reproduced by the theory, verifying that the biexciton radiative decay rate is determined by the exciton components in final-state polaritons (Hopfield coefficients) through the exciton-exciton Coulomb interaction. The radiative lifetimes of $K\ensuremath{\simeq}0$ biexcitons are found to be shorter than those of $K\ensuremath{\simeq}{2k}_{0}$ biexcitons as expected from the theory. The lifetimes of low-$K$ biexcitons are strongly affected by the coupling with final two-polariton states, leading to a 20% reduction of the lifetimes compared with the case of no polariton effects.

Hopfield coefficients measured by inverse polariton series

We report observation of the inverse polariton series and a detailed experimental study of the exciton components in polaritons (Hopfield coefficients). Spontaneous emission of excitonic molecules into outgoing polaritons associated with the $i(=1,2,3,4,5)\mathrm{th}$ exciton states in bulk CuCl is detected and analyzed by the bipolariton model. Because the intensities of the emission lines, which form the inverse polariton series, are determined by the exciton components in the final-state polaritons, we are able to measure the Hopfield coefficients for the highly composite outgoing polaritons. Quantum interference in the optical decay of excitonic molecules, due to the multiple exciton components in the polariton and biexciton states, is also demonstrated.

Inverse exciton series for observation of bipolariton coupling

We report the first observation of inverse polariton series (LP series) in CuCl, due to the radiative decay of excitonic molecules selectively excited at mode K m from the band 0⩽K m ⩽0.3×10 6 cm −1 . In order to explain the experimental data, the bipolariton model of an excitonic molecule is adapted to describe the LP ns lines ( n=1, 2, 3 and 4) in terms of the scattering scheme “two incoming polaritons → excitonic molecule → two outgoing polaritons, associated with 1s and ns excitonic states”. We show that the efficiency of the multi-branch polariton scattering is determined by the excitonic component of the final-state (outgoing) polaritons.

Inverse exciton series in the optical decay of an excitonic molecule

As a reply to the Comment by I.S. Gorban {\it et al.} (Phys. Rev. B, preceding paper) we summarize our criticism on their claim of the first observation of the $M$ series in $\beta$-ZnP$_2$. We support our analysis by reporting the first observation of inverse {\it polariton} series from the excitonic molecules selectively generated at ${\bf K}_m \simeq {\bf 0}$ in a CuCl single crystal. This observation and its explanation within the bipolariton model complete our proof of the biexcitonic origin of the inverse series.

The bipolariton model and the concept of excitonic-biexcitonic mixed modes in semiconductors

An alternative approach to the so called bipolariton concept has been proposed. We have shown that the bipolariton approximation can indeed be used for calculating the elementary excitation spectrum in the photon-exciton-biexciton system in its biexciton part. The bipolariton concept does not provide the correct spectrum in the excitonic-polariton energy part, where the existence of four-particle electron-hole bound states should be considered. In order to go beyond the bipolariton approximation we developed a Green function formalism for the theory of an interacting electron-photon system in which photons, excitons and biexcitons are treated on an equal level. Our approach is a completely microscopic treatment and is based on the assumption that the excitons and biexcitons are two- and four-particle bound states, formed by electrons and holes. The method of Legendre transforms is used to derive a set of nine independent exact equations for the corresponding vertex and Green functions. Knowledge of the solutions of the above equations provide the excitation energies of the quasiparticles (excitonic-biexcitonic polaritons) formed by coupling of photons with excitons and biexcitons. Those elementary excitations manifest themselves as common poles of the photon propagator, two- and four-particle electron-hole Green functions.

High precision measurement of biexciton dispersion at k ~ 0 in CuCl

Dispersion curve of a biexciton (XX) at k ~ 0 in CuCl is measured using a high-precision polarization rotation spectroscopy. An energy minimum around k = 1 × 10 5 cm −1 is observed in the XX dispersion in some crystals. The fact is consistent with radiative renormalization effects of XX predicted by the bipolariton model. Theoretical examinations of the exciton-exciton potential and more experimental examinations are expected for quantitative comparison of the value of the minimum.

Coherent transient in photoluminescence of excitonic molecules in GaAs quantum wells

Time-resolved photoluminescence (PL) of excitonic molecules in GaAs quantum wells (QW's) reveals an initial transient characterized by a finite rise and an extremely fast nonexponential decay [H. Wang, J. Shah, and T. C. Damen et al., Solid State Commun. 98, 807 (1996)]. The transient is attributed to coherent quantum evolution towards the molecule ground state of two optically correlated excitons, ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}},$ which undergo the Coulombic attraction. In the present paper, we develop a theory of the transient PL and fit the experimental data. The radiative decay of a quasi-two-dimensional (2D) excitonic molecule is analyzed with the giant oscillator strength model adapted to QW's and with the bipolariton model. Within the 2D bipolariton model, the main ``hidden'' channel of the radiative decay of an excitonic molecule is the resonant dissociation into two outgoing interface (surface) polaritons rather than the observable decay into the bulk radiative modes. We conclude that quasi-2D molecules dissociate already within the initial transient of PL, while the following exponential decay of the molecule-mediated PL is due to the escape of secondary interface polaritons into the bulk modes. According to the 2D bipolariton model, the sequence ``two incoming $\mathrm{photons}\ensuremath{\rightarrow}\mathrm{two}$ virtual $\mathrm{excitons}\ensuremath{\rightarrow}2\mathrm{D}$ $\mathrm{molecule}\ensuremath{\rightarrow}\mathrm{two}$ outgoing interface polaritons'' is a completely coherent process. The fit of the time-resolved molecule-mediated PL provides us with numerical estimates of the exciton-photon coupling in GaAs QW's.

Bipolariton in quantum wells

We develop the bipolariton concept for a quasi-2D excitonic molecule (m) in quantum wells (QWLs). The bipolariton wave equation, which includes both the exciton-exciton (x-x) attraction and thex-photon (γ) coupling, is analysed. In the 2D bipolariton model, a quasi-2Dm exists in QWLs mainly as two quasi-boundsurface polaritons and, consequently, decays mainly into two outgoing surface polaritons. In quasi-2D GaAs QWLs the polariton renormalizations give rise to a «Mexican hat» structure in them dispersion at small momenta together with a considerable increase of both them effective binding energy ɛm and the inversem radiative lifetimeГm. A van Hove singularity in the joint density of polariton states is responsible for this effect.

Two-photon generation of excitonic molecules in CuCl: An exactly solvable bipolariton model and high-precision experiments.

The conventional giant oscillator strength model of the two-photon (\ensuremath{\gamma}) generation of an excitonic molecule (m) attributes this process to the x-\ensuremath{\gamma} optical conversion (where x is the exciton) i.e, to the scheme \ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}x+\ensuremath{\gamma}\ensuremath{\rightarrow}m. Recenty [A.L. Ivanov and H. Haug, Phys. Rev. B 48, 1490 (1993)], it was argued that a more adequate description can be done within the bipolariton model which follows the other scenario: \ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}x+x\ensuremath{\rightarrow}m, where the Coulombic resonant coupling of the x components of the two interacting polaritons gives rise to the m formation. In the present work, we develop and analyze for the deuteron potential of an x-x interaction an exactly solvable bipolariton model of the two-\ensuremath{\gamma} m generation. This model treats an m optical creation in terms of the polariton-polariton resonant scattering and includes both the x-y polariton coupling and the x-x attraction beyond a low-order perturbation theory. The bipolariton model and the giant oscillator strength model give different descriptions of the third-order m nonlinear optical susceptibility ${\mathrm{\ensuremath{\chi}}}^{(3)}$ and of the two-\ensuremath{\gamma} m absorption. With the high-precision measurements in CuCl of the m radiative width ${\mathrm{\ensuremath{\Gamma}}}^{\mathit{m}}$, ${\mathrm{\ensuremath{\chi}}}^{(3)}$, and the two-\ensuremath{\gamma} m absorption coefficient ${\mathit{K}}^{(2)}$, we make a systematic comparison between the experiments and the two models, which allows us to unambiguously discriminate both models in favor of the bipolariton one.