Coherent Multi-Dimensional Spectroscopy (CMDS) is a powerful tool for examining electron coupling and dynamics in a wide range of condensed matter systems, including semiconductor nanostructures and biological light harvesting complexes. This technique utilises multiple phase locked laser pulses to excite and probe electronic transitions within the sample during various time periods. The phase and amplitude of the emitted signal are recorded using spectral interferometry. From the data a 2D and/or 3D spectrum can be generated which provides information including which states are coupled, the nature of the coupling, the homogeneous and inhomogenous linewidths, if peak broadening is correlated and the presence of many-body effects.

The spatial light modulator (SLM) based CMDS experiment in the Ultrafast Spectroscopy group is based on a design pioneered at the Massachusetts Institute of Technology. A SLM based beam shaper is used to split the input laser beam into four spatially separated and co-propagating beams. A SLM based pulse shaper is used to control the pulse time delays. As all pulses are incident on the same optics the pulses are phase locked. Three of the pulses are used to excite the sample, and the remaining pulse is used to perform spectral interferometry with the emitted signal. The signal is recorded as a function of the time delay between each of the excitation pulses. The multi-dimensional spectrum is then produced by Fourier transforming the detected signal as a function of the excitation pulse time delays. The ultrafast spectroscopy group at Swinburne is the only group in Australia with the experimental capability to perform coherent multi-dimensional spectroscopy.

Simple systems with well-defined and separated energy levels generally produce clear multi-dimensional spectra from which it is straight forward to identify the contributing quantum pathways. Such samples are well suited for examination using broadband CMDS. In more complex systems where spectral broadening leads to overlapping peaks in multi-dimensional spectra, it can be impossible to separate the contributing quantum pathways. Furthermore, in systems where many-body effects are important, such as semiconductor quantum wells, the excitation of the free-carrier continuum can alter the dynamics of excitons localised to the same quantum well. Such complexities can be significantly simplified by using pathway selective CMDS approach to isolate specific quantum pathways.

In our pathway selective CMDS experiment we use a spatial light modulator based pulse shaper to spectrally shape the excitation pulses. As all excitation pulses are incident on the SLM surface, the spectrum of each excitation pulse can be controlled, yet remain phase-locked. Applied to studying coupled excitons in asymmetric double quantum wells we show that this approach has multiple benefits, including unambiguous quantum pathway identification in multi-dimensional spectra and reduced noise levels on peaks corresponding to weakling coupled states compared to broadband 2D and 3D spectra containing peaks with amplitudes varying over several orders of magnitude.

This is an important first step towards quantitative CMDS for complex systems, without the need for multi-parameter fits of crowded 2D spectra.

It has been well-established that the relative orientation of transition dipoles can affect signal strengths in CMDS experiments. Furthermore, by controlling the polarization of each pulse certain pathways can be enhanced or eliminated. We have exploited the processes that underlie both of these facts to reveal structural information of some components of the light harvesting complex PC645. We are working towards enhancing this approach to obtain more and more detailed structural information in more complex systems.

We have developed a technique that determines the phase of the signal emitted in a coherent multi-dimensional spectroscopy experiment from spectrally resolved intensity data without phase stabilised excitation pulses. Using this technique it is possible to perform CMDS in situations where heterodyne detection is impractical, such as two-colour CMDS experiments. Two colour CMDS well suited for performing quantum pathway specific experiments, as well as for accessing spectral regions inaccessible by broadband laser sources.

Phase retrieval algorithms have proven to be effective in multiple areas of physics. In frequency resolved optical gating (FROG), which is a technique used for measuring ultra-short pulses, the algorithm recovers the pulse intensity I(t) and phase φ(t). The algorithm converges to the correct solution by applying constraints on what values the solution can take in time and frequency space based on the known time response of the signal, which depends on the FROG configuration used. In coherent diffractive imaging, where the phase information is required to perform the inverse Fourier transform to reconstruct the sample structure from its diffraction pattern, spatial constraints based on the dimensions of the sample and detector are used. The phase retrieval algorithm developed in our group draws on these two approaches by applying restrictions on the allowed time regions over which the signal should exist (based on causality), as well as using known information about the absorption and emission energies of the sample.

Comparisons between this non-interferometric technique and the more standard interferometric approaches have shown that non-interferometric CMDS can accurately retrieve the phase information and that the two techniques produce equivalent multi-dimensional spectra. We have used this technique to reveal coherent coupling in carotenoids from photosynthetic systems and to explore coherent coupling between spatially separated excitons in asymmetric double quantum wells.

Light-harvesting complexes are the molecules responsible for the initial stages of photosynthesis, where light from the Sun is converted into excited electronic states of the molecule. These excitations are then transferred within and between light-harvesting complexes towards a reaction centre where energy can be stored. The transfer processes necessarily occur on vanishingly short timescales, so that the energy can be reach the reaction centre before the excitation is quenched. Light-harvesting complexes have evolved to optimize the efficiency of these processes; however, the physical mechanisms behind the energy transfer are still not fully understood.

Recently it has been proposed that quantum mechanical coherence between excited states may play a significant role in energy transfer within the light-harvesting complex, Phycocyanin-645 (PC-645). Our work investigates these complexes we utilize a two-colour four-wave mixing experiment. The advantage of this experiment is that two spectrally narrow pulses (i.e. without any spectral overlap) are used to excite the complex, meaning that only coherences are probed, in isolation from other signals. Our work has used this technique to isolate decoherence times, which are typically difficult to measure in 2D spectroscopy. Further these experiments presented evidence for strong coupling between the electronic states and the phonon bath, which are suggested to be important for energy transfer within the complex.

Recently we have adapted polarization control to the two-colour experiment. This technique helps to separate signals from electronic coherence which typically have similar signatures to vibrational coherences in this type of experiment. For PC-645 a detailed picture of the energy landscape within this complex has been built up by using this approach across a range of pulse wavelengths.

We use two-colour vibronic coherence spectroscopy to observe long-lived vibrational coherences in the ground electronic state of carotenoid molecules, with decoherence times in excess of 1 ps. Lycopene and spheroidene were studied isolated in solution, and within the LH2 light-harvesting complex extracted from purple bacteria. The vibrational coherence time is shown to increase significantly for the carotenoid in the complex. Using this technique, we are also able to follow the evolution of excited state coherences and find that for carotenoids in the light-harvesting complex the S₂|S₀ superposition remains coherent for more than 70 fs. In addition to the implications of this long electronic decoherence time, the extended coherence allows us to observe the evolution of the excited state wavepacket. These experiments reveal an enhancement of the vibronic coupling to the first vibrational level of the C–C stretching mode and/or methyl-rocking mode in the ground electronic state 70 fs after the initial excitation. These observations open the door to future experiments and modelling that may be able to resolve the relaxation dynamics of carotenoids in solution and in natural light-harvesting systems.

We demonstrate how spectral shaping in coherent multidimensional spectroscopy can isolate specific signal pathways and directly access quantitative details. By selectively exciting pathways involving a coherent superposition of exciton states we are able to identify, isolate and analyse weak coherent coupling between spatially separated excitons in an asymmetric double quantum well. Analysis of the isolated signal elucidates details of the coherent interactions between the spatially separated excitons. With a dynamic range exceeding 10⁴ in electric field amplitude, this approach facilitates quantitative comparisons of different signal pathways and a comprehensive description of the electronic states and their interactions.

We utilize a three-dimensional (3D) visible spectroscopy to reveal and explore coherent coupling between excitons localized to GaAs quantum wells separated by barriers 4 and 6 nm wide. The coupled excitons were energetically separated by 43 meV, close to the longitudinal optical phonon energy, due to the different widths of the quantum wells to which they were localized. The ability to isolate coherence pathways in 3D spectroscopy has made it possible to not only identify weak coherent coupling, but also to explore the nature of the coupling through analysis of the peak shapes. This peak shape analysis showed inhomogeneous broadening of the excitons localized to different wells to be uncorrelated, as expected, while coupling between heavy-hole and light-hole excitons localized to the same well was shown to be correlated. To gain some insight into the coupling mechanism we explored the dependence of the coupling strength on the barrier width and hence spatial separation. Based on these results we discuss the possibility of phonon-assisted dipole coupling.

We demonstrate three-dimensional (3D) electronic spectroscopy of excitons in a double quantum well system using a three-dimensional phase retrieval algorithm to obtain the phase information that is lost in the measurement of intensities. By extending the analysis of two-dimensional spectroscopy to three dimensions, contributions from different quantum mechanical pathways can be further separated allowing greater insight into the mechanisms responsible for the observed peaks. By examining different slices of the complete three-dimensional spectrum, not only can the relative amplitudes be determined, but the peak shapes can also be analysed to reveal further details of the interactions with the environment and inhomogeneous broadening. We apply this technique to study the coupling between two coupled quantum wells, 5.7 nm and 8 nm wide, separated by a 4 nm barrier. Coupling between the heavy-hole excitons of each well results in a circular cross-peak indicating no correlation of the inhomogeneous broadening. An additional cross-peak is isolated in the 3D spectrum which is elongated in the diagonal direction indicating correlated inhomogeneous broadening. This is attributed to coupling of the excitons involving the two delocalised light-hole states and the electron state localised on the wide well. The attribution of this peak and the analysis of the peak shapes is supported by numerical simulations of the electron and hole wavefunctions and the three-dimensional spectrum based on a density matrix approach. An additional benefit of extending the phase retrieval algorithm from two to three dimensions is that it becomes substantially more reliable and less susceptible to noise as a result of the more extensive use of a priori information.

A video showing the the 3D spectrum in greater detail can be found here.