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arXiv:1607.04410 · Laser & Photonics Review

Separating pathways in double‐quantum optical spectroscopy reveals excitonic interactions

Jonathan Owen Tollerud, Jeffrey A. Davis

Published Dec 7, 2016• 27 citations
arXivHTMLPDF

Abstract

Abstract Techniques for coherent multidimensional optical spectroscopy have been developed and utilised to understand many different processes, including energy transfer in photosynthesis and many‐body effects in semiconductor nanostructures. Double‐quantum 2D spectroscopy is one variation that has been particularly useful for understanding many‐body effects. In condensed matter systems, however, there are often many competing signal pathways, which can make it difficult to isolate different contributions and retrieve quantitative information. Here, a means of separating overlapping pathways while maintaining the fidelity of the relevant peak/s is demonstrated. This selective approach is used to isolate the double‐quantum signal from a mixed two exciton state in a semiconductor quantum well. The removal of overlapping peaks allows analysis of the relevant peak‐shape and thus details of interactions with the environment and other carriers to be revealed. An alternative pulse ordering identifies a double‐quantum state associated only with GaAs defects, the signature of which has previously been confused with other interaction induced effects. The experimental approach described here provides access to otherwise hidden details of excitonic interactions and demonstrates that the manner in which the double‐quantum coherence is generated can be important and provide an additional control to help understand the many‐body physics in complex systems. image

DOI
10.1002/lpor.201600249

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Abstract Techniques for coherent multidimensional optical spectroscopy have been developed and utilised to understand many different processes, including energy transfer in photosynthesis and many‐body effects in semiconductor nanostructures. Double‐quantum 2D spectroscopy is one variation that has been particularly useful for understanding many‐body effects. In condensed matter systems, however, there are often many competing signal pathways, which can make it difficult to isolate different contributions and retrieve quantitative information. Here, a means of separating overlapping pathways while maintaining the fidelity of the relevant peak/s is demonstrated. This selective approach is used to isolate the double‐quantum signal from a mixed two exciton state in a semiconductor quantum well. The removal of overlapping peaks allows analysis of the relevant peak‐shape and thus details of interactions with the environment and other carriers to be revealed. An alternative pulse ordering identifies a double‐quantum state associated only with GaAs defects, the signature of which has previously been confused with other interaction induced effects. The experimental approach described here provides access to otherwise hidden details of excitonic interactions and demonstrates that the manner in which the double‐quantum coherence is generated can be important and provide an additional control to help understand the many‐body physics in complex systems. image
Heteronuclear multi-quantum spectroscopy is a powerful part of the NMR toolbox, commonly used to identify specific sequences of atoms in complex pulse sequences designed to determine the structure of complex molecules, including proteins. Optical coherent multidimensional spectroscopy (CMDS) is analogous to multidimensional NMR and many of the techniques of NMR have been adapted for application in the optical regime. This has been highly successful, with CMDS being used to understand energy transfer in photosynthesis and many body effects in semiconductor nanostructures amongst many other scientific breakthroughs. Experimental challenges have, however, prevented the translation of heteronuclear multi-quantum NMR to the optical regime, where capabilities to isolate signals in otherwise congested spectra, reduce acquisition times and enable more incisive probes of multi-particle correlations and complex electronic systems would have great benefit. Here we utilise a diffraction based pulseshaper to impose the two key avenues of selectivity required for the analogue of heteronuclear multi-quantum spectrocopy, - control of the individual pulse spectra, and control of the order and timing of interactions - while maintaining phase-locked excitation pulses. We utilise this approach to isolate the 2-quantum signal from a mixed two exciton state in a semiconductor coupled quantum well. The removal of other overlapping peaks allows analysis of the relevant peak shape and thus details of interactions with the environment and other carriers. An alternative pulse ordering also identifies a 2-quantum state associated only with a GaAs defect, the signature of which would otherwise be confused with other interaction induced effects. The experimental approach described here provides access to crucial details of excitonic interactions, which are important in a range of material systems
Simulations of two dimensional coherent photon echo (2D‐PE) spectra of self‐assembled InAs/GaAs quantum dots (QD) in different charged states are presented revealing the coupling between the individual mono‐exciton transitions and contributions of bi‐excitons . The information about the states is crucial for various application scenarios of QDs, like e.g. highly efficient solar cells. The simulations rely on a microscopic description of the electronic structure by high‐level atomistic many‐body pseudopotential calculations. It is shown that asymmetric diagonal peak shapes and double cross‐peaks are the result of state contributions to the PE signal by analyzing the contributions of the individual pathways excited state emission, ground state bleach and excited state absorption. The results show that from the detuned and contributions the bi‐exciton binding energies of the manifold are revealed in 2D‐PE signals.
Multidimensional analysis of coherent signals is commonly used in nuclear magnetic resonance to study correlations among spins. These techniques were recently extended to the femtosecond regime and applied to chemical, biological and semiconductor systems. In this work, we apply a two-dimensional correlation spectroscopy technique which employs double-quantum-coherence to investigate many-body effects in a semiconductor quantum well. The signal is detected along the direction k(1)+ k(2)- k(3), where k(1), k(2) and k(3) are the pulse wave vectors in chronological order. We show that this signal is particularly sensitive to many-body correlations which are missed by time-dependent Hartree-Fock approximation. The correlation energy of two-exciton can be probed with a very high resolution arising from a two-dimensional correlation spectrum, where two-exciton couplings spread the cross peaks along both axes of the 2D spectrum to create a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo (-k(1)+ k(2)+ k(3)).
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.
We propose a three-pulse coherent ultrafast optical technique that is particularly sensitive to two-exciton correlations. Two Liouville-space pathways for the density matrix contribute to this signal which reveals double quantum coherences when displayed as a two-dimensional correlation plot. Two-exciton couplings spread the cross peaks along both axes, creating a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo, in which two-exciton couplings show up along a single axis and are highly congested.
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.