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Plasmonic nanostructures are considered promising candidates for essential components of integrated quantum technologies because of their ability to efficiently localize broad-band electromagnetic fields on the nanoscale. The resulting local near field can be understood as a spatial superposition of spectrally different plasmon-polariton modes due to the spectrally broad optical excitation, and thus can be described as a classical wave packet. Since plasmon polaritons, in turn, can transmit and receive non-classical light states, the exciting question arises to what extent they have to be described as quantum mechanical wave packets, i.e. as a superposition of different quantum states.
But how to probe, characterize and eventually manipulate the quantum state of such plasmon polaritons? Up to now, probing at room temperatures relied completely on analyzing quantum optical properties of the corresponding in-going and out-going far-field photon modes. However, these methods so far only allow a rather indirect investigation of the plasmon-polariton quantum state by means of transfer into photons. Moreover, these indirect methods lack spatial resolution and therefore do not provide on-site access to the plasmon-polariton quantum state. However, since the spectroscopic method of coherent two-dimensional (2D) nanoscopy offers the capability to follow the plasmon-
polariton quantum state both in Hilbert space and in space and time domain a complete characterization of the plasmon polariton is possible.
In this thesis a versatile coherent 2D nanoscopy setup is presented combining spectral tunability and femtosecond time resolution with spatial resolution on the nanometer scale due to the detection of optically excited nonlinear emitted electrons via photoemission electron microscopy (PEEM). Optical excitation by amplitude- and phase-shaped, systematically-modified and interferometric-stable multipulse sequences is realized, and characterized via Fourier-transform spectral interferometry (FTSI). This linear technique enables efficient data acquisition in parallel to a simultaneously performed experiment. The full electric-field reconstruction of every generated multipulse sequence is used to analyze the effect of non-ideal pulse sequences on the two-dimensional spectral data of population-based multidimensional spectroscopy methods like, e.g., the coherent 2D nanoscopy applied in this thesis. Investigation of the spatially-resolved nonlinear electron emission yield from plasmonic gold nanoresonators by coherent 2D nanoscopy requires a quasi-particle treatment of the addressed plasmon-polariton mode and development of a quantum model to adequately describe the plasmon-assisted multi-quantum electron emission from nanostructures. Good agreement between simulated and experimental data enables to connect certain spectral features to superpositions of non-adjacent plasmon-polariton quantum states, i.e, non-adjacent occupation-number states of the underlying quantized, harmonic oscillator, thus direct probing of the plasmon-polariton quantum wave packet at the location of the nanostructure.
This is a necessary step to locally control and manipulate the plasmon-polariton quantum state and thus of general interest for the realization of nanoscale quantum optical devices.
The goal of this thesis was the development and application of higher-order spectroscopic techniques. In contrast to ordinary pump–probe (PP) and two-dimensional (2D) spectroscopy, higher-order coherently detected spectroscopic methods measure a polarization that has an order of nonlinearity higher than three. The key idea of the techniques in this thesis is to isolate the higher-order signals from the lower-order signals either by their excitation frequency or by their excitation intensity dependence. Due to the increased number of interactions in higher-order spectroscopy, highly excited states can be probed. For excitonic systems such as aggregates and polymers, the fifth-order signal allows one to directly measure exciton–exciton annihilation (EEA). In polymers and aggregates, the exciton transport is not connected to a change of the absorption and can therefore not be investigated with conventional third-order techniques. In contrast, EEA can be used as a probe to study exciton diffusion in these isonergetic systems. As a part of this thesis, anisotropy in fifth-order 2D spectroscopy was investigated and was used to study geometric properties in polymers.
In 2D spectroscopy, the multi-quantum signals are separated from each other by their spectral position along the excitation axis. This concept can be extended systematically to higher signals. Another approach to isolate multi-quantum signals in PP spectroscopy utilizes the excitation intensity. The PP signal is measured at specific excitation intensities and linear combinations of these measurements result in different signal contributions. However, these signals do not correspond to clean nonlinear signals because the higher-order signals contaminate the lower-order multi-quantum signals. In this thesis, a correction protocol was derived that uses the isolated multiquantum signals, both from 2D spectroscopy and from PP spectroscopy, to remove the contamination of higher-order signals resulting in clean nonlinear signals. Using the correction on the third-order signal allows one to obtain annihilation-free signals at high excitation intensities, i.e., with high signal-to-noise ratio. Isolation and correction in PP and 2D spectroscopy were directly compared by measuring the clean third-order signals of squaraine oligomers at high excitation intensities. Furthermore, higher-order PP spectroscopy was used to isolate up to the 13th nonlinear order of squaraine polymers.
The demonstrated spectroscopic techniques represent general procedures to isolate clean signals in terms of perturbation theory. The technique of higher-order PP spectroscopy needs only small modifications of ordinary PP setups which opens the field of higher-order spectroscopy to the broad scientific community. The technique to obtain clean nonlinear signals allows one to systematically increase the number of interacting (quasi)particles in a system and to characterize their interaction energies and dynamics.
This thesis describes novel concepts for the measurement of the static and dynamic properties of the electronic structure of molecules and nanocrystals in the liquid phase by means of coherent fluorescence-detected spectroscopy in two and three frequency dimensions. These concepts are based on the systematic variation ("phase cycling") of a sequence of multiple time-delayed femtosecond excitation pulses in order to decode a multitude of novel nonlinear signals from the resulting phase-dependent fluorescence signal. These signals represent any permutation of correlations between zero-, one-, two-, and three-quantum coherences. To this end, two new phase-cycling schemes have been developed which can simultaneously resolve and discriminate several nonlinear signals of sixth order, including those of the fourth order of nonlinearity.
By means of the sixth-order signals recorded in this work, static properties of highly excited electronic states in molecules such as their energies, transition dipole moments, and relative displacement of electronic potential surfaces, as well as dynamic properties in terms of their relaxation kinetics, can be ascertained. Furthermore, it was shown that these signals are suitable for the characterization of exciton-exciton correlations in colloidal quantum dots and for the measurement of ultrafast exciton-exciton annihilation in molecular aggregates.
The experiments performed in this thesis mark an important step towards the complete characterization of the nonlinear response of quantum systems. In view of this, the concept of fluorescence-detected multiple-quantum coherence multidimensional spectroscopy introduced here offers a unified, systematic approach.
In virtue of the technical advantages such as the use of a single excitation beam and the absence of nonresonant contributions, the measurement protocols developed here can be directly transferred to other incoherent observables and to sample systems in other states of matter. Furthermore, the approaches presented here can be systematically extended to higher frequency dimensions and higher orders of nonlinearity.
An experimental setup for probing ultrafast dynamics at the diffraction limit was developed, characterized and demonstrated in the scope of the thesis, aiming for optical investigations while simultaneously approaching the physical limits on the length and timescale.
An overview of this experimental setup was given in Chapter 2, as well as the considerations that led to the selection of the individual components. Broadband laser pulses with a length of 9.3 fs, close to the transform limit of 7.6 fs, were focused in a NA = 1.4 immersion oil objective, to the diffraction limit of below 300 nm (FWHM).
The spatial focus shape was characterized with off-resonance gold nanorod scatterers scanned through the focal volume. For further insights into the functionality and limitations of the pulse shaper, its calibration procedure was reviewed. The deviations between designed and experimental pulse shapes were attributed to pulse-shaper artifacts, including voltage-dependent inter-layer as well as intra-layer LCD-pixel crosstalk, Fabry-Pérot-type reflections in the LCD layers, and space-time coupling. A pixel-dependent correction was experimentally carried out, which can be seen as an extension of the initial calibration to all possible voltage combinations of the two LCD layers.
The capabilities of the experimental setup were demonstrated in two types of experiments, targeting the nonlinearity of gold (Chapter 3) as well as two-dimensional spectroscopy at micro-structured surfaces (Chapter 4).
Investigating thin films, an upper bound for the absolute value for the imaginary part of the nonlinear refractive index of gold could be set to |n′′ 2 (Au)| < 0.6·10−16 m2/W, together with |n′ 2 (Au)| < 1.2·10−16 m2/W as an upper bound for the absolute value of the real part. Finite-difference time-domain simulations on y-shaped gold nanostructures indicated that a phase change of ∆Φ ≥ 0.07 rad between two plasmonic modes would induce a sufficient change in the spatial contrast of emission to the far-field to be visible in the experiment. As the latter could not be observed, this value of ∆Φ was determined as the upper bound for the experimentally induced phase change. An upper bound of 52 GW/cm2 was found for the damage threshold.
In Chapter 4, a novel method for nonlinear spectroscopy on surfaces was presented. Termed coherent two-dimensional fluorescence micro-spectroscopy, it is capable of exploring ultrafast dynamics in nanostructures and molecular systems at the diffraction limit. Two-dimensional spectra of spatially isolated hotspots in structured thin films of fluorinated zinc phthalocyanine (F16ZnPc) dye were taken with a 27-step phase-cycling scheme. Observed artifacts in the 2D maps were identified as a consequence from deviations between the desired and the experimental pulse shapes. The optimization procedures described in Chapter 2 successfully suppressed the deviations to a level where the separation from the nonlinear sample response was feasible.
The experimental setup and methods developed and presented in the scope of this thesis demonstrate its flexibility and capability to study microscopic systems on surfaces. The systems exemplarily shown are consisting of metal-organic dyes and metallic nanostructures, represent samples currently under research in the growing fields of organic semiconductors and plasmonics.
Coherent Multidimensional Spectroscopy in Molecular Beams and Liquids Using Incoherent Observables
(2018)
The aim of the present work was to implement an experimental approach that enables coherent two-dimensional (2D) electronic spectroscopy of samples in various states of matter. For samples in the liquid phase, a setup was realized that utilizes the sample fluorescence for the acquisition of 2D spectra. Whereas the liquid-phase approach has been established before, coherent 2D spectroscopy on gaseous samples in a molecular beam as developed in this work is in fact a new method. It employs for the first time cations in a time-of-flight mass spectrometer for signal detection and was used to obtain the first ion-selective 2D spectra of a molecular-beam sample. Additionally, a new acquisition concept was developed in this thesis that significantly decreases measurement times in 2D spectroscopy using optimized sparse sampling and a compressed-sensing reconstruction algorithm.
Characteristic for the variant of 2D spectroscopy presented in this work is the usage of a phase-coherent sequence of four laser pulses in a fully collinear geometry for sample excitation. The pulse sequence was generated by a custom-designed pulse shaper that is capable of rapid scanning by changing the pulse parameters such as time delays and phases with the repetition rate of the laser. The sample's response was detected by monitoring incoherent observables that arise from the final-state population, for instance fluorescence or cations. Phase cycling, i.e., signal acquisition with different combinations of the relative phases of the excitation pulses, was applied to extract nonlinear signal contributions from the full signal during data analysis.
Liquid-phase 2D fluorescence spectroscopy was established with the laser dye cresyl violet as a sample molecule, confirming coherent oscillations previously observed in literature that are originating from vibronic coherences in specific regions of the 2D spectrum.
The data set of this experiment was used subsequently to introduce optimized sparse sampling in 2D spectroscopy. An optimization algorithm was implemented in order to find the best sampling pattern while taking only one quarter of the regular time-domain sampling points, thereby reducing the acquisition time by a factor of four. Signal recovery was based on a new and compact representation of 2D spectra using the von Neumann basis, which required about six times less coefficients than the Fourier basis to retain the relevant information. Successful reconstruction was shown by recovering the coherent oscillations in cresyl violet from a reduced data set.
Finally, molecular-beam coherent 2D spectroscopy was introduced with an investigation of ionization pathways in highly-excited nitrogen dioxide, revealing transitions to discrete auto-ionizing states as the dominant contribution to the ion signal. Furthermore, the advantage of the time-of-flight approach to obtain reactant and product 2D spectra simultaneously enabled the observation of distinct differences in the multiphoton-ionization response functions of the nitrogen dioxide cation and the nitrogen oxide ionic fragment.
The developed experimental techniques of this work will facilitate fast acquisition of 2D spectra for samples in various states of matter and permit reliable direct comparison of results. Therefore, they pave the way to study the properties of quantum coherences during photophysical processes or photochemical reactions in different environments.