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Physical review. B, Condensed matter

Coherent dynamics of bipolaritons in bulk CdS

Ch. Mann, W. Langbein, U. Woggon, A. L. Ivanov

Published Nov 27, 2001• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.64.235206

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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 T2\ensuremath≃4.8ps.{T}_{2}\ensuremath{\simeq}4.8 \mathrm{ps}.T2​\ensuremath≃4.8ps. We demonstrate that the molecule-mediated FWM signal persists at positive time delays even in the \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(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 \ensuremathτradXX\ensuremath≃2.8ps,{\ensuremath{\tau}}_{\mathrm{rad}}^{\mathrm{XX}}\ensuremath{\simeq}2.8 \mathrm{ps},\ensuremathτradXX​\ensuremath≃2.8ps, justify the T2=2T1{T}_{2}{=2T}_{1}T2​=2T1​ limit, and prove the bipolariton representation for excitonic molecules in CdS.
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.
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.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.
Coherent optical spectroscopy in the form of nonlinear transient four-wave mixing (TFWM) and linear resonant Rayleigh scattering (RRS) has been applied to investigate the exciton dynamics of low-dimensional semiconductor heterostructures. The dephasing times of excitons are determined from the decay of the spectrally resolved non- linear signal as a function of the delay between the incident pulses in a two-beam TFWM experiment, and from the real time analysis of single speckles in RRS experiments (pure dephasing). From the density- and temperature- dependence of the dephasing times the exciton-exciton and the exciton-phonon interactions are determined. The degree of coherence of the secondary emission is determined from the speckle analysis.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.
Summary form only given. The coherence decay of optically excited electronic systems provides one of the most powerful tools to investigate interaction processes of excited states. In semiconductors, the optical coherence phenomena are usually investigated by nonlinear techniques such as four wave mixing (FWM), photon echo, or reflectivity experiments. Exciton-phonon, exciton-exciton, or exciton-free carriers scattering processes have been explored in recent years with these techniques. As demonstrated recently, a direct measurement of the optical dephasing time can be obtained through the temporal coherent control of electronic excitations. In these experiments, the emission following the excitation by an ultrashort optical pulse sequence, is detected in a non-specular direction (secondary emission). This provides an alternative approach to FWM techniques, which allows us to analyse the scattering processes either with phonons or due to mutual collisions. Using the coherent control technique monitored through the secondary emission (SE), we report on the coherent dynamics of excitons in bare quantum wells (QW) and compare it to that of exciton-polaritons in microcavity (MC) embedded quantum wells.