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Coherent ultrafast spectroscopy and manipulation of excitonic Q-bits

Final Report Summary - CUSMEQ (Coherent ultra-fast spectroscopy and manipulation of excitonic Q-bits)

The goal of the project was to establish a method for rapid and efficient characterisation of a coherent coupling in terms of mechanism and strength within a set of individual emitters in a semiconductor nanostructure, such as quantum dots, quantum dot molecules and quantum dots embedded in photonic resonators. The experimental basis of this method was heterodyne spectral interferometry - a previously developed tool that was shown to be efficient for extraction of coherent nonlinear response, like four-wave mixing (FWM), of individual quantum systems in a solid state structure. A major motivation of this research is the use of individual excitons in semiconductor nanostructures as qubits, with the coherent coupling allowing for quantum logic gates, for solid state ultrafast quantum information processing.

The project was set to be executed along the following objectives:

1. Training of the fellow (Dr Jacek Kasprzak) in the technique of heterodyne-detected single quantum dot transient four-wave mixing (SQDFWM).

This first task was completed during first six months of the project. The fellow was trained in the SQDFWM technique, by initially assisting in the experiments, and subsequently gained skills and autonomy in adjusting and managing the experiment, including the laser sources, cryogenic microscopy, and CCD detectors. He familiarised himself with the subsequent data analysis to retrieve the FWM spectral and temporal dynamics in amplitude and phase, two-dimensional four-wave mixing (2DFWM) diagrams, polarisation resolved data yielding the vectorial FWM field, real space imaging of the FWM signal, spectral and temporal filtering procedures.

For the reason of FWM signal strength, we have initially investigated individual excitons localised in monolayer islands of 5 nm and 7 nm thick GaAs/AlAs quantum wells, on which data of unprecedented quality were taken, yielding a variety of new results already at this initial stage of the fellowship.

By combining 2DFWM measurements with FWM imaging in real space we detected coherent coupling between spatially separated excitons. We have made a statistical analysis of the coupling strength versus distance. We compared FWM spatial imaging with photoluminescence (PL) imaging and demonstrated that the spatial resolution in FWM is 300 nm, below the one-photon diffraction limit, and almost factor of two below the one in PL.

By analysing the off-diagonal phase in 2DFWM we were able to distinguish between radiative coupling and biexcitonic (density) coupling. A biexcitonic mechanism was found in all cases, consistent with the distance dependence and the theoretically expected coupling strength as a function of detuning. We monitored the statistical build up of coherent coupling as function of monolayer island density continuously tuned via the average well thickness with sub-monolayer precision. At low densities, only coupling between excitons and biexcitons in spatial overlap is observed, and both states are localised to below 300 nm, the resolution of our setup. Increasing the fractional thickness, the island density increases, and the exciton states are both reducing their average distance and also show a spread in their individual spatial extension, with some states extending over a micrometer scale.

The formation of the quantum well polaritons at the high density region was an intriguing observation, hence we continued to pursue on this issue. We have performed spatial autocorrelation analysis of the FWM maps, which - by retrieval of the angle resolved auto-correlation width - characterised their spatial shape and extension in a more quantitative manner. Specifically, the width turned out to be larger along the diagonal, showing that the state extension is aligned along the [100] direction. Such a preferential direction could be explained by a misorientation of the sample substrate, giving rise to a preferential step edge direction.

We concluded that such a large extension of states is enabled by radiative coupling leading to formation of localised quantum well polaritons, allowing for coherent coupling between spatially separated exciton states. Based on these observations, an article was written, editorially accepted and to appear in Nature Photonics in 2010.

A detailed analysis of the biexciton features was performed in terms of binding energies and oscillator strengths. We found that the biexcitonic transitions always have a weaker transition dipole moment than the coupled excitonic transitions. We also found instances of several bound biexcitonic states coupled to a single exciton. This finding shows that in the investigated system the biexcitonic wavefunction is not described by a product state of the localised exciton wavefunction, as one would expect for a strongly confined QD exciton. Instead the Coulomb correlation energy is on the same order as the disorder potential, yielding biexcitonic states which contain a mixture of different exciton eigenstates.

The dipole moment ratio between excitonic and coupled biexcitonic transition gives a direct measure of the wave function fraction of the exciton product state in the biexciton. The non product-state nature also allows for multiple biexcitonic states coupled to a single exciton. Here, the FWM spatial mapping revealed co-localisation of an exciton and a corresponding biexciton. Quantitatively, such a co-localisation was characterised by performing energy-resolved auto-correlation studies. We have observed a peaked value of auto-correlation at the energy distance corresponding to the biexcitonic binding energy.

Because excitons are trapped in monolayer islands having a somewhat random shape, they show spectral features resulting from the local spatial anisotropy, such as a finestructure polarisation splitting, which is the result of the long-range exchange interaction between the two circularly polarised spin states of a single spatial exciton state. We have verified the coherent coupling between the two polarisation states of a fine-structure split exciton. We extended the FWM detection to a dual-polarisation version by splitting the signal in front of the spectrometer into two orthogonal linear polarised components. The data acquisition and analysis software was enhanced to determine the FWM signal in amplitude and phase for both polarisation components simultaneously, and thus to determine the spectrally and time-resolved polarisation state.

2. Investigation of the coupled system quantum dot exciton-microcavity photon under the strong coupling regime.

Measurements of the FWM signal from a single quantum dot - microcavity system in the strong coupling regime were performed already during the first part of the fellowship. Related data analysis and dissemination of the results were completed before the end of the project. The outcome of these experiments turned out to be particularly exciting and promising. The work that was performed should be considered as a pioneering one in the field of strongly coupled system in the solid state. We were able to distinguish transitions originating from the first and second rung of the Jaynes-Cummings ladder, demonstrating the quantum strong coupling regime in the system. By extracting the FWM in both amplitude and phase we are able to retrieve the signal both in temporal and spectral domain. In time domain we observed for the first time coherent oscillations between a single exciton and a photon mode.

The SQDFWM technique provided the unique possibility of decomposing the measured FWM spectrum into the signal originating from first and second rung transitions. By performing a comprehensive study as a function of the time delay we measured the coherent dynamics of the first and second rung states. Our experimental findings are supported by theoretical modelling within a local collaboration with Dr E. Muljarov (School of Physics and Astronomy, Cardiff University), who is an expert in modelling of FWM signals and phonon-induced dephasing in excitonic systems. Our results were recently published as a letter in the Nature Materials Magazine.

3. Coherent nonlinear spectroscopy of strongly confined GaAs/AlAs quantum dots

As planned, we investigated the hierarchically self-assembled GaAs/AlGaAs quantum dots grown by molecular beam epitaxy and in-situ AsBr3 etching [Phys. Rev. Lett. 92, 166104]. The samples were anti-reflex coated with a λ/4 layer of HfO2 to reduce surface reflections. Micro-photoluminescence characterisation measurements were performed on the sample. Thanks to our progress in the implementation of a new, rapid CCD camera system with high quantum efficiency in the infrared, the detection efficiency of the setup was improved by a factor of 2, and the saturation limit by a factor of about 50, rendering FWM measurements on individual transions of small oscillator strength feasible. We subsequently succeeded in measuring the FWM signal of these individual quantum dots, achieving a signal-to-noise ratio of the FWM intensity of ~100 after 20 minutes of integration time.

Towards the end of the project a comprehensive set of new results was obtained regarding: exciton and biexciton dephasing time, polarisation selection rules, fine structure splitting and related polarisation dynamics, two-dimensional FWM on the exciton-biexciton system, FWM imaging, higher order nonlinear effect, formation of single dot photon echo (inhomogeneous broadening due to spectral wandering), FWM induction via two-photon coherence. The analysis, interpretation, and publication of these results are subject of an on-going post-fellowship collaboration, the data analysis and the discussion carries on between the fellow (Kasprzak) and the PI (Prof. Langbein) and the related publications are being prepared. We expect these results to lead to at least two further significant publications.

4. Development of a high-resolution optical pulse shaper, creating from an incoming laser pulse four separate optical pulses, which are independently shaped in amplitude and phase on a 100 femtosecond to 20 picosecond time scale.

5. Use of coherent optical control of excitons confined within a single QD by the shaped optical pulses to demonstrate simple quantum computational operations on coupled exciton states.

The development of the pulseshaper was discussed as part of the training, and modelled with Zemax software. The missing essential equipment was selected and purchased. Further progress within task 2 and task 3 was delayed due to the development of the new lab facilities and the move of the experimental setup to the new lab space in December 2008. This was an essential move to ensure a smooth work flow of all the projects carried out in the Quantum Optoelectronics Group at Physics Department at Cardiff University. Furthermore, the CCD camera system (ISA CCD3500) used for the SQDFWM was failing in December 2008 and is beyond repair according to the manufacturer. It was replaced by a CCD system available within the group from a previous project, which implied a major change in the data acquisition software.

The new configuration of the SQDFWM setup was designed and assembled. An additional delay line was added to the setup to perform three pulse FWM measurements, which allow to measure not only to the coherent dynamics and coupling but also to the population dynamics and incoherent coupling via population transfer between individual excitons. A three-axis delay stage driver was bought to provide control over both delay stages present in the SQDFWM setup and a rotation stage for the pulse-shaper. The further development and completion of the pulse-shaper will be part of future projects in the group of Prof. Langbein.

6. Investigation of the coherent coupling in electrically controlled quantum dot molecules.
The sample design was discussed with J. Finley, TU Munich, and an initial electrically contacted sample with normal quantum dots was tested. However, considering the technical challenges of the other parts of the project, no further progress was made in this high risk part of the project.