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arXiv:1308.2165 · Physical Review Letters

Coherent Coupling of Excitons and Trions in a Photoexcited CdTe/CdMgTe Quantum Well

Galan Moody, Ilya A. Akimov, Hebin Li, Rohan Singh, Dmitri R. Yakovlev, G. Karczewski, M. Wiater, T. Wójtowicz, M. Bayer, Steven T. Cundiff

Published Mar 3, 2014• 72 citations
arXivHTMLPDF

Abstract

We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.

DOI
10.1103/physrevlett.112.097401

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We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.
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Optical control of the spin coherence of quantum well electrons by short laser pulses with circular or linear polarization is studied experimentally and theoretically. For that purpose the coherent electron spin dynamics in a nnn-doped CdTe/(Cd,Mg)Te quantum well structure was measured by time-resolved pump-probe Kerr rotation, using resonant excitation of the negatively charged exciton (trion) state. The amplitude and phase shifts of the electron spin beat signal in an external magnetic field, that are induced by laser control pulses, depend on the pump-control delay and polarization of the control relative to the pump pulse. Additive and nonadditive contributions to pump-induced signal due to the control are isolated experimentally. These contributions can be well described in the framework of a two-level model for the optical excitation of the resident electron to the trion.
I report on the effect of a moderate excess electron population on nonlinearities in modulation-doped CdTe quantum wells. I show that the electron population does not qualitatively affect the nature of correlations between excitons. In this respect, I bring strong evidence of the existence of unbound and bound (stable) two-exciton states in the presence of electrons and charged excitons (trions). In time-resolved pump and probe experiment, they lead to the observation of electromagnetically induced transparency and optical Stark shift of the exciton resonance. Rabi flopping of excitons within a sea of electrons is also clearly evidenced through ac Stark splitting and gain without inversion. The quantum coherence is more robust to electron induced dephasing than what would have been expected. I demonstrate third and higher-order exciton correlations in the presence of electrons, which manifest, for increasing exciton densities, through the blue-shift of counter-polarized exciton resonance, the red-shift of the biexciton resonance and the exciton to biexciton crossover. I also evidence correlated behavior of excitons and trions under excitation which manifests itself by crossed trion-exciton effects. I observe a wealth of phenomena encompassing bleaching, crossed bleaching, induced-absorption and energy shifts of the resonances. Significant differences are found between the nonlinear optical effects induced by an exciton and a trion population. Electron scattering with electron and exciton is shown to strongly broaden the high energy tail of exciton and trion resonance lineshapes. Variations of electron density result in a clear modification of both resonance lineshapes. The dynamics of the formation of trions is also studied. I propose a two-channel mechanism for their formation; they are formed through bi- and tri-molecular processes. This implies that both negatively and positively charged excitons coexist in a quantum well, even in the absence of excess carriers. The model is applied to a time-resolved photoluminescence experiment performed on a very high quality InGaAs quantum well sample, in which the photoluminescence contributions at the energy of the trion, exciton and at the band edge can be clearly separated and traced over a broad range of times and densities. The unresolved discrepancy between the theoretical and experimental radiative decay time of the exciton in a doped semiconductor is explained.
Generation mechanisms of long‐lived spin coherence of two‐dimensional electron gas (2DEG) have been studied theoretically and experimentally, the latter by means of a picosecond pump‐probe Kerr rotation technique. CdTe/(Cd,Mg)Te quantum wells with a diluted two‐dimensional electron gas have been addressed. Strong Coulomb interaction between electrons and holes, which results in large binding energies of neutral and negatively charged excitons (trions), allows selective addressing of exciton and trion states with resonant optical excitation. Different scenarios of coherence generation have been analyzed, namely, direct trion photocreation, formation of trions from photogenerated excitons and electron‐exciton exchange scattering.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver detailed information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φφφ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a 20-nm-thick CdTe/(Cd,Mg)Te quantum well at temperature of 1.5~K. Applying narrow-band optical excitation we selectively excite different exciton complexes including the exciton, the trion, and the donor-bound exciton D0^00X. We find that polarimetry of the photon echo on the trion and D0^00X is substantially different from the exciton: The echoes of the trion and D0^00X are linearly polarized at the angle 2φ2φ2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φφφ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cos⁡φ\cosφcosφ.
Semiconductors systems exhibiting excitonic properties are discussed in terms of their coherent response, which is extracted using two-dimensional coherent spectroscopy. This control method allows for separation of quantum pathways that comprise the optical response, such as interactions between excitons, their dephasing rates, the effects of many-body interactions and the role of structure on the microscopic electronic environment. Additional controls, such as polarization can be used to further distinguish biexcitons and suppress many-body interactions. These result are compared and contrasted with those from a semiconductor microcavity where the excitons form polaritonic modes due to normal-mode splitting. Rephrasing spectra map the detuning dependence of the exciton-polariton branches. Increasing the detuning shifts all features to higher energy and the expected anti-crossing is observed. An isolated biexciton is seen only at negative detuning, separated by a binding energy. For positive detuning, the spectral weight of the off-diagonal features swap, as the lower polariton branch and biexciton come into resonance. This indicates that the off-diagonal features are sensitive to the interactions of the exciton-polaritons and other resonances in the system.