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New Journal of Physics

Using localized double-quantum-coherence spectroscopy to reconstruct the two-exciton wave function of coupled quantum emitters

Felix Schlosser, Andreas Knorr, Shaul Mukamel, Marten Richter

Published Feb 5, 2013• 33 citations
Publisher

Abstract

Coherent multidimensional spectroscopy allows us to inspect the energies and the coupling of quantum systems. Coupled quantum systems—such as a coupled semiconductor quantum dot or pigments in photosynthesis—form delocalized exciton and two-exciton states. A technique is presented to decompose these delocalized wave functions into the basis of individual quantum emitters. This quantum state tomography protocol is illustrated for three coupled InAs quantum dots. To achieve the decomposition of the wavefunction, we combine the double-quantum-coherence spectroscopy with spatiotemporal control, which allows us to localize optical excitations at a specific quantum dot. Recently, a protocol was proposed for single exciton states (Richter et al 2012 Phys. Rev. B 86 085308). In this paper, we extend the method presented by Richter et al with respect to: the reconstruction of two-exciton states, a detailed analysis process of reconstruction and the effect of filtering to enhance the quality of the reconstructed wave function.

DOI
10.1088/1367-2630/15/2/025004

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Coherent multidimensional spectroscopy allows us to inspect the energies and the coupling of quantum systems. Coupled quantum systems—such as a coupled semiconductor quantum dot or pigments in photosynthesis—form delocalized exciton and two-exciton states. A technique is presented to decompose these delocalized wave functions into the basis of individual quantum emitters. This quantum state tomography protocol is illustrated for three coupled InAs quantum dots. To achieve the decomposition of the wavefunction, we combine the double-quantum-coherence spectroscopy with spatiotemporal control, which allows us to localize optical excitations at a specific quantum dot. Recently, a protocol was proposed for single exciton states (Richter et al 2012 Phys. Rev. B 86 085308). In this paper, we extend the method presented by Richter et al with respect to: the reconstruction of two-exciton states, a detailed analysis process of reconstruction and the effect of filtering to enhance the quality of the reconstructed wave function.
Quantum dots have been the focus of both fundamental and applied research due to their atomic-like properties. The delta-function-like density of states along with strong nonlinear optical properties have made quantum dots the focus of novel opto-electronic devices and of quantum computing proposals. The key issue for implementing quantum dots in devices such as quantum computers is the ability to coherently entangle separately localized quantum dot states. Using continuous wave coherent nonlinear optical spectroscopy techniques, this thesis focuses on creating coherent super-position states built from separately localized quantum dot states. The narrow bandwidths and mutual coherence of the applied laser fields allow for the creation of radiative and nonradiative coherences which can be understood from the coherent nonlinear optical response. The quantum dots under study are formed due to the width fluctuations of a thin quantum well. By applying nondegenerate mutually coherent fields on the sample in the traditional pump and probe geometry and homodyne detecting the nonlinear signal field, nonradiative coherences between two laterally coupled quantum dots are created and the coupling between their states examined. The coherent nonlinear optical response is compared with theoretical predictions based on the density matrix formalism for the interacting two exciton model. From this comparison, binding energies of the two-exciton bound state created with separately localized excitons is found to be on the order of 20 mueV for like-polarized excitons and on the order of 100 mueV for unlike-polarized excitons. A second order coherence between the ground and two-exciton state is also noted in the experimental data after comparison with theory. Further work attempting to study a vertically coupled quantum dot system was unsuccessful. The spectrum of a quantum dot is further understood from the comparison of the linear and nonlinear excited state spectra. Excited states which appear in both spectra imply a Coulomb interaction between them and their respective ground states. Coherent nonlinear optical signatures of excited states correlated with their linear excitation spectra are presented, and the importance of such states for a quantum computer read-out is described.
A detailed understanding of the population and coherence dynamics in optically driven individual emitters in solids and their signatures in ultrafast nonlinear-optical signals is of prime importance for their applications in future quantum and optical technologies. In a combined experimental and theoretical study on exciton complexes in single semiconductor quantum dots we reveal a detailed picture of the dynamics employing three-beam polarization-resolved four-wave mixing (FWM) micro-spectroscopy. The oscillatory dynamics of the FWM signals in the exciton-biexciton system is governed by the fine-structure splitting and the biexciton binding energy in an excellent quantitative agreement between measurement and analytical description. The analysis of the excitation conditions exhibits a dependence of the dynamics on the specific choice of polarization configuration, pulse areas and temporal ordering of driving fields. The interplay between the transitions in the four-level exciton system leads to rich evolution of coherence and population. Using two-dimensional FWM spectroscopy we elucidate the exciton-biexciton coupling and identify neutral and charged exciton complexes in a single quantum dot. Our investigations thus clearly reveal that FWM spectroscopy is a powerful tool to characterize spectral and dynamical properties of single quantum structures.
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
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)).