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Simulation of propagation-distorted 2DFT spectra of dense rubidium vapor and pump-probe spectroscopy of carrier dynamics in colloidal indium arsenide quantum dots

Austin P. Spencer

Published Jan 1, 2014• 1 citation
OpenAlex

Abstract

Two-dimensional Fourier-transform (2DFT) spectra of the D2 line of rubidium vapor in argon buffer gas are simulated using a three-dimensional frequency domain solution of Maxwell's equations that treats linear propagation distortions exactly. Simulations for the homogeneous optical Bloch model at optical densities of up to 3 are compared to measured rephasing 2DFT spectra. Experimentally observed propagation distortions are qualitatively reproduced in calculated 2DFT spectra, including peak broadening, peak splitting, and peak twisting. Varying beam overlap through the sample is crudely modeled in simulations, demonstrating that reduced beam overlap causes narrowing of the peak shape in the excitation dimension and an overall reduction in signal size. Propagation distortions, including peak splitting depth and peak twist, are found to vary with waiting time and with the excited state lifetime at a fixed total dephasing time, suggesting a coherent mechanism.\nA new method for reducing repetitive excitation of the sample by scanning beams with respect to a stationary sample cell using a fast steering mirror is described. This apparatus extends the average time between excitations at any point in the sample to >0.3 s and accommodates a wide variety of sample cell formats, including cryostats, air-tight cuvettes, and flow cells.\nColloidal indium arsenide (InAs) quantum dots (QDs) are interrogated by degenerate pump{ probe transient absorption spectroscopy at a photon energy of approximately 1.5 times the band gap using spatially-averaged excitation probabilities lower than in previously reported studies. Signatures of Auger recombination appear with a timescale of 26 +/- 5 ps. Carrier cooling and recombination pathways are explored, revealing new dynamics not observed in studies that probe the band edge.

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A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.

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Two-dimensional Fourier-transform (2DFT) spectra of the D2 line of rubidium vapor in argon buffer gas are simulated using a three-dimensional frequency domain solution of Maxwell's equations that treats linear propagation distortions exactly. Simulations for the homogeneous optical Bloch model at optical densities of up to 3 are compared to measured rephasing 2DFT spectra. Experimentally observed propagation distortions are qualitatively reproduced in calculated 2DFT spectra, including peak broadening, peak splitting, and peak twisting. Varying beam overlap through the sample is crudely modeled in simulations, demonstrating that reduced beam overlap causes narrowing of the peak shape in the excitation dimension and an overall reduction in signal size. Propagation distortions, including peak splitting depth and peak twist, are found to vary with waiting time and with the excited state lifetime at a fixed total dephasing time, suggesting a coherent mechanism.\nA new method for reducing repetitive excitation of the sample by scanning beams with respect to a stationary sample cell using a fast steering mirror is described. This apparatus extends the average time between excitations at any point in the sample to >0.3 s and accommodates a wide variety of sample cell formats, including cryostats, air-tight cuvettes, and flow cells.\nColloidal indium arsenide (InAs) quantum dots (QDs) are interrogated by degenerate pump{ probe transient absorption spectroscopy at a photon energy of approximately 1.5 times the band gap using spatially-averaged excitation probabilities lower than in previously reported studies. Signatures of Auger recombination appear with a timescale of 26 +/- 5 ps. Carrier cooling and recombination pathways are explored, revealing new dynamics not observed in studies that probe the band edge.
A solution to Maxwell's equations in the three-dimensional frequency domain is used to calculate rephasing two-dimensional Fourier transform (2DFT) spectra of the D2 line of atomic rubidium vapor in argon buffer gas. Experimental distortions from the spatial propagation of pulses through the sample are simulated in 2DFT spectra calculated for the homogeneous Bloch line shape model. Spectral features that appear at optical densities of up to 3 are investigated. As optical density increases, absorptive and dispersive distortions start with peak shape broadening, progress to peak splitting, and ultimately result in a previously unexplored coherent transient twisting of the split peaks. In contrast to the low optical density limit, where the 2D peak shape for the Bloch model depends only on the total dephasing time, these distortions of the 2D peak shape at finite optical density vary with the waiting time and the excited state lifetime through coherent transient effects. Experiment-specific conditions are explored, demonstrating the effects of varying beam overlap within the sample and of pseudo-time domain filtering. For beam overlap starting at the sample entrance, decreasing the length of beam overlap reduces the line width along the ωτ axis but also reduces signal intensity. A pseudo-time domain filter, where signal prior to the center of the last excitation pulse is excluded from the FID-referenced 2D signal, reduces propagation distortions along the ωt axis. It is demonstrated that 2DFT rephasing spectra cannot take advantage of an excitation-detection transformation that can eliminate propagation distortions in 2DFT relaxation spectra. Finally, the high optical density experimental 2DFT spectrum of rubidium vapor in argon buffer gas [J. Phys. Chem. A 2013, 117, 6279-6287] is quantitatively compared, in line width, in depth of peak splitting, and in coherent transient peak twisting, to a simulation with optical density higher than that reported.
Optical two-dimensional Fourier-transform (2DFT) spectroscopy is used to study the coherent optical response of potassium vapor in a thin transmission cell. Rephasing and nonrephasing spectra of the D1{D}_{1}D1​ and D2{D}_{2}D2​ transitions are obtained and compared to numerical simulations. Non-perturbative calculations using the optical Bloch equations give very good agreement with the experimental peak strengths and line shapes. Nonradiative Raman-like coherences are isolated using a different 2DFT projection. Comparison between the optical and Raman linewidths shows that dephasing is due to partially correlated energy fluctuations. Density-dependent measurements show distortion of 2DFT spectra due to pulse propagation effects.
The three-dimensional confinement created by the ultrasmall semiconductor structures known as quantum dots greatly modifies the optical properties of the spatially localized carriers. These systems are presently of great interest to the research community, both for the improved understanding of the physics of confined structures, and for the potential applications of these systems to areas such as optoelectronics and quantum computing. Here, the techniques of transient coherent nonlinear optical spectroscopy are applied to the investigation of excitons confined within InAs/GaAs self-assembled quantum dots. These methods provide a powerful tool for the study of dynamic processes in these novel materials. The nonlinear measurements are based on the differential transmission experimental geometry, and utilize ultrafast pulsed lasers in order to temporally resolve the carrier dynamics after excitation. The experiments performed here are resonant with the ground state absorption of the quantum dots, as evidenced by comparison with the photoluminescence measurements which are used to characterize the sample. The incoherent relaxation dynamics of the population of photoexcited excitons are examined, allowing for a determination of both the lifetime of the excitons and the time scale for relaxation between the two polarization eigenstates of the system. The three-dimensional quantum confinement results in the suppression of these relaxation processes, as predicted. The use of coherent spectroscopic techniques allows for the first unambiguous demonstration of an optically-induced nonradiative Raman coherence in these quantum dots. Simultaneous excitation of both polarization states of the exciton results in a coherent superposition state, whose temporal evolution is observed through the homodyne-detection scheme. In these transient experiments, this is manifested as a beating in the nonlinear response, which allows us to directly measure the fine-structure splitting between the polarization states. Utilizing optical pulse shaping techniques, transient spectral hole burning is performed, which allows for the nonlinear response to be spectrally resolved. As expected for the strongly confined quantum dot excitons, the results show that diffusion among the localized states is not a significant effect. Temperature dependent measurements show that at elevated temperatures, extra dephasing processes, potentially related to acoustic phonon scattering, become important. Finally, this technique allows for the first direct observation of the induced absorption from the exciton to biexciton transition in these InAs quantum dots, and a measurement of the associated binding energy. These results lay the foundation for future studies in this material system, and for the possible development of quantum logic devices utilizing quantum dots.
Transient four-wave mixing studies of bulk GaAs under conditions of broad bandwidth excitation of primarily interband transitions have enabled four-particle correlations tied to degenerate (exciton-exciton) and nondegenerate (exciton-carrier) interactions to be studied. Real two-dimensional Fourier-transform spectroscopy (2DFTS) spectra reveal a complex response at the heavy-hole exciton emission energy that varies with the absorption energy, ranging from dispersive on the diagonal through absorptive for low-energy interband transitions to dispersive with the opposite sign for interband transitions high above band gap. Simulations using a multilevel model augmented by many-body effects provide excellent agreement with the 2DFTS experiments and indicate that excitation-induced dephasing (EID) and excitation-induced shift (EIS) affect degenerate and nondegenerate interactions equivalently, with stronger exciton-carrier coupling relative to exciton-exciton coupling by approximately an order of magnitude. These simulations also indicate that EID effects are three times stronger than EIS in contributing to the coherent response of the semiconductor.
Electronic structure and dynamics are captured by optical 2D-Fourier-transform (2DFT) spectroscopy, which tracks the phase of the nonlinear signal during two time delays of a multi-pulse excitation sequence. These Fourier-transformed spectra separate and isolate overlapping and competing contributions to the coherent response. We have developed an ultra-stable platform consisting of nested interferometers with active phase control, allowing for exploration of single- and two-quantum coherences. Phase-resolved spectra are retrieved by all-optical determination of experimental phase ambiguities. GaAs quantum wells show suppression of many-body interactions in cross-linear polarized 2DFT spectra and many-body two-quantum coherences. Potassium vapor also shows unexpected two-quantum coherences.
We identify carrier scattering at densities below that which has previously been observed in semiconductor quantum wells. These effects are evident in the peak shapes of 2D double-quantum spectra, which change as a function of excitation density. At high excitation densities (>109 excitons/cm2), we observe untilted peaks similar to those reported in previous experiments. At low excitation densities (<108 excitons/cm2), we observe narrower tilted peaks. Using a simple simulation, we show that tilted peak shapes are expected in double-quantum spectra when inhomogeneous broadening is much larger than homogeneous broadening, and that fast pure-decoherence of the double-quantum coherence can obscure this peak tilt. These results show that carrier interactions are important at lower densities than previously expected, and that the “natural” double-quantum peak shapes are hidden by carrier interactions at the excitation densities typically used. Furthermore, these results demonstrate that analysis of 2D peak shapes in double-quantum spectroscopy provides an incisive tool for identifying interactions at low excitation density.