Quantum Electrodynamics of Macroscopic Systems
My main research fields are quantum optics and quantum electrodynamics in macroscopic systems. With the combination of classical electrodynamics with quantised fields and objects, I derive models describing interactions between them and their impact on physical scenarios. A special focus is on dispersion forces containing Casimir (between dielectric objects), Casimir-Polder (between a dielectric object and a polarisable particle), and van der Waals forces (between two polarisable particles) which are caused by the ground-state fluctuations of the electromagnetic fields. By considering the interactions between two particles, one also has to take into account the classical interactions caused by charges or permanent dipoles and their interactions with fluctuating dipoles which means that within the framework of quantum electrodynamics the complete spectrum of intermolecular forces is covered. Even that these research questions have a long history, there are a lot of unanswered questions which I want to address within my research, for instance:
What happens with the dispersion interactions on very short separations?
What is the impact of a solvent on a van der Waals bonded molecule?
When does a cluster of few atoms or molecules start to behave like a continuum?
What is the impact of interaction via dispersion forces on intramolecular forces?
Medium-assisted dispersion forces
One of my current main researches deals with the dispersion interactions close to an environment because most of the biological and chemical reactions take place in a solution or near an interface, for instance for catalysis. The impact of such an environment differs a lot depending on the physical scenario, for instance:
In solutions
A particle embedded in a solvent is a common situation for chemical reactions. Here, the particle and solvent molecules are getting very close to each other, that the balance of short-range repulsive forces (Pauli blocking) and long-range attractive forces (van der Waals forces) results in a binding distance that defines a vacuum bubble surrounding the particle. As the van der Waals interactions in terms of macroscopic Quantum Electrodynamics are expressed in an exchange of virtual photons, such photons have to pass the interface between the vacuum bubble and the solvent, which is one impact of the environment on the dispersion interactions. A second impact also occurs in a different situation, where a particle is
Near an interface
Beyond the Casimir-Polder interactions of the particle with the interface, a second important effect appears that can be described within the framework of macroscopic Quantum Electrodynamics – the spectroscopical impact on the particle. For simplicity, let’s consider an atom with a discrete atomic level. For a free atom, these levels are its eigenstates and couple with each other due to the presence of the interface. This results in an energy shift of the atomic states depending on the environmental material and their geometric arrangement. This is closely related to cavity quantum electrodynamics. Remarkably, this effect occurs for every possible environment, if it is a solid surface, a surrounding liquid or gas, a cavity, or an arrangement of atoms or molecules.
Fiedler, J., Spallek, F., Thiyam, P., Persson, C., Boström, M., Walter, M., Buhmann, S.Y. (2019): Dispersion forces in inhomogeneous planarly layered media: A one-dimensional model for effective polarizabilities. In: Phys. Rev. A 99, 062512.
Burger, F.A., Fiedler, J., Buhmann, S.Y. (2018): Zero-point electromagnetic stress tensor for studying Casimir forces on colloidal particles in media. In: EPL 121, 24004.
Fiedler, J., Thiyam, P., Kurumbail, A., Burger, F.A., Walter, M., Persson, C., Brevik, I., Parsons, D.F., Boström, M., Buhmann, S.Y. (2018): Effective Polarizability Models. In: J. Phys. Chem A 121, 9742-9751.
Applications of dispersion forces in natural systems
Dispersion forces, as the largest quantum mechanical effect, play a huge role in natural systems. The most common example is the gecko feet which glues on the slick surfaces due to Casimir-Polder forces. Motivated by that fact, I analyse the behaviour of water dissolved gases on a microscopic scale to reach statements about their macroscopic behaviour, such as escape dynamics. A further effect of dispersion forces on macroscopic systems is related to the thermodynamics of ice, rocks, gas hydrates in water, where the Casimir force determines the freezing and melting of surrounding ice layers.
Fiedler, J., Parsons, D.F., Burger, F.A., Thiyam, P., Walter, M., Brevik, I., Persson, C., Buhmann, S.Y., Boström, M. (2019): Impact of effective polarisability models on the near-field interaction of dissolved greenhouse gases at ice and air interfaces. In: Phys. Chem. Chem. Phys. 21, 21296-21304.
Boström, M., Corkery, R.W., Lima, E.R.A., Malyi, O.I., Buhmann, S.Y., Persson, C., Brevik, I., Parsons, D.F., Fiedler J. (2019): Dispersion Forces Stabilize Ice Coatings at Certain Gas Hydrate Interfaces That Prevent Water Wetting. In: ACS Earth Space Chem. 3, 1014-1022.
Thiyam, P., Fiedler, J., Buhmann, S.Y., Persson, C., Brevik, I., Boström, M., Parsons, D.F. (2018): Ice Particles Sink below the Water Surface Due to a Balance of Salt, van der Waals, and Buoyancy Forces. In: J. Phys. Chem. C 122, 15311-15317.
Sensors based on dispersion forces
The development of experiments measuring dispersion forces within the past decades provides a huge class of very accurate and precise measurement tools, such as the diffraction of matter waves at dielectric objects or atomic force microscopy experiments. The theoretical consideration of such experiments offers possibilities for inverse measurements. Especially, the experiments measuring retardation effects. There the spectral dielectric response function of a particle or a macroscopic object is mapped onto the spatial potential. Different experimental methods require different additional measuring algorithms or devices. For instance, considering the diffraction of matter waves results in a lack of information about the wave’s phase, which is solvable by an adaptation of the Hartmann-Shack sensor. With its help, the phase of the wavefront can be measured and together with the amplitude obtained from the interference pattern, the backpropagation is possible resulting in the spatial potential. Another scenario is the atomic force microscopy, where typically the Hamaker constant is measured, which depends on three dielectric functions: the substrate, the probe object, and the medium. A controlled repetition of such experiments with a change of one component can be used for the determination of one unknown response function. Here, we considered a two-component liquid as an environmental medium and showed that a unique mapping of the dielectric function onto the Hamaker constants at different concentrations is available.
Fiedler, J., Broer, W., Scheel, S. (2017): Reconstruction of Casimir-Polder interactions from matter-wave interference experiments. In: J. Phys. B: At. Mol. Opt. Phys. 50, 155501.
Fiedler, J., Persson, C., Buhmann, S.Y. (2020): Spectroscopy of Nanoparticles without Light. In: Phys. Rev. Applied 13, 014025.
Role of dispersion forces in matter-wave experiments
Matter waves are an interesting and exciting topic to study. Due to the wave-particle duality, every massive object can behave like a wave, which can, for instance, be observed in the appearance of interference patterns of atoms and molecules. Such investigations aim to test the transition between the classical and quantum-mechanical world by increasing the particle’s mass and measuring the vanishing of interference. Beyond such fundamental research questions, a wide range of applications is recently investigated as well, such as high-precision measurements of accelerations, microgravity, gravitational waves, or matter-wave lithography, where one aims to write nanostructures for electronic circuits with a higher transistor density compared to optically written structures. For all these investigations, the interactions between the matter wave and the environment play an important role due to wave propagation and coherence.
Bender, H., Stehle, C., Zimmermann, C., Slama, S., Fiedler, J., Scheel, S., Buhmann, S.Y., Marachevsky, V.N. (2013): Probing Atom-Surface Interactions by Diffraction of Bose-Einstein Condensates. In: Phys. Rev. X 4, 011029.
Brand, C., Fiedler, J., Juffmann, T., Sclafani, M., Knobloch, C., Scheel, S., Lilach, Y., Cheshnovsky, O., Arndt, M. (2015): A Green’s function approach to modeling molecular diffraction in the limit of ultra-thin gratings. In: Ann. Phys. (Berlin) 527, 580-591.
Hemmerich, J.L., Bennett, R., Reisinger, T., Nimmrichter, S., Fiedler, J., Hahn, H., Gleiter, H., Buhmann, S.Y. (2016): Impact of Casimir-Polder interaction on Poisson-spot diffraction at a dielectric sphere. In: Phys. Rev. A 94, 023621.
Gack, N., Reitz, C., Hemmerich, J.L., Könne, M., Bennett, B., Fiedler, J., Gleiter, H., Buhmann, S.Y., Hahn, H., Reisinger, T. (2020): Signature of Short-Range van der Waals Forces Observed in Poisson Spot Diffraction with Indium Atoms. In: Phys. Rev. Lett. 125, 050401.
Matter-wave lithography
The ability to pattern materials at ever-smaller sizes using photolithography is driving advances in nanotechnology. When the feature size of materials is reduced to the nanoscale, individual atoms and molecules can be manipulated to alter material properties dramatically. So far, the highest-resolution mask-based photolithography can generate patterns down to around 13 nm via Extreme ultraviolet. I investigate the ability of matter-wave diffraction to pattern specific target patterns. Beyond modelling the interactions between the beam particles and the dielectric masks, I work on inversion methods to relate the mask structure to the patterns via machine learning techniques.
Fiedler, J., Holst. B. (2022): An atom passing through a hole in a dielectric membrane: impact of dispersion forces on mask-based matter-wave lithography. In: J. Phys. B: At. Mol. Opt. Phys. 55, 025401.
Fiedler, J., Palau, A.S., Osestad, E.K., Parviainen, P., Holst, B. (2022): Realistic mask generation for matter-wave lithography via machine learning.