Comparison of two software toolboxes for the simulation of quantum systems in the context of coherent multidimensional spectroscopy

Abstract

Simulations are an indispensable tool in physics because they complement experiments, especially complex ones. Coherent multidimensional spectroscopy (CMDS) is such a complex experimental setup. In CMDS, the molecular system of interest interacts with two to four coherent laser pulses and the generated emission provides information about the energetic structure and the relaxation dynamics of the probed molecule.

The common technique to theoretically describe CMDS are perturbative expansions, in particular under the additional approximation that the pulses have zero width (duration). However, this approach doesn’t capture some phenomena observed in real-world spectroscopic experiments, for example it doesn’t account for pulse overlap artefacts. A more realistic modelling is achieved with explicitly propagating the density matrix of the system.

The issue with this, in turn, is that there exist many different simulation codes and toolboxes, which could impede the comparison and reproduction of simulation results. Kenneweg et al. (2024) therefore put forward their own quantum dynamics toolbox (QDT), a MATLAB-based toolbox that provides tools for simulating light-matter interactions, especially non-linear spectroscopic experiments with explicit density matrix propagation. The rationale is that its modularity will allow for widespread adoption. To test this new toolbox, this thesis compares it to QuTiP-based simulation code, by attempting to reproduce a result of a simulation script (Hedse et al. 2023) that simulates pulse overlap artefacts in double quantum coherence spectroscopy (a type of CMDS).

It was only possible to reproduce the results from Hedse et al. qualitatively, but not quantitatively. Several factors that could have potentially been responsible for the variations were investigated, but they were ruled out as the cause. This sheds a light on the difficulties one encounters when trying to reproduce simulation results on a different code bases, especially when the code is to complex to allow for line-wise comparison.

Popular Abstract

Unravelling the language of light and atoms!

How do most of us understand the world? By looking at things. If we want to look at small things, we can use a magnifying glass, and for even smaller things like bacteria, we can use a microscope, but how can we look at single atoms or atoms? There are several ways of doing that, but the one I am concerned with is called spectroscopy. Spectroscopy can look even at the parts of atoms, by probing what colours of light they absorb.

So, more generally speaking, I am trying to understand what happens when light is shone onto a material. For my work, we treat light as consisting of quantum particles, which means we say that a beam of light consists of many small particles, called photons, that together carry the energy of the beam. The energy of each light particle depends only on its colour: violet and blue means high energy, green and yellow medium energy, and red means low energy. On the other hand, these particles have ”wave-like” properties; however, these effects are not so important for my work. The main quantum effect I am concerned with is that one can only predict the probability of certain events to occur, not exactly when or where.

So, when we shine light onto a material, the atoms that make up that material, can absorb the energy stored in the light particles, i.e. photons. More precisely, the electrons orbiting the nuclei of the atoms in the atoms absorb the photon and gain energy and momentum. Because the electrons are not free but bound to the atoms, they cannot just ”fly a bit faster”, but instead they are only allowed to have certain discrete energies, like rungs on a ladder. This means that the absorption of the photon is only ”successful” if the energy that the photon carries matches the exact amount of energy that it needs to go from one orbit to another. Also, when an electron transits to an orbit with lower energy, it sends out a photon that carries the exact energy that is the difference between the previous, higher-energy orbit, and the new, lower-energy orbit.

Moreover, the restrictions as to which energies the electron can have depend on the kind of atom as well as with which other atoms the atom is together in a atom. Therefore, one can identify what atoms are present in a material as well as provide information about the structure of those atoms by shining light onto a sample and measuring which colours get absorbed and what colours of light the sample subsequently sends out, when the electrons fall back down to the lower-energy levels. This is exactly what spectroscopy does.

In my thesis, I work with so-called non-linear spectroscopy, which studies more complicated cases. In particular, I study how to better understand and model how short pulses of laser light interact with matter. However, when one is trying to describe more complicated phenomena, often we cannot calculate things exactly. Instead, we try to break things down and make approximative calculations, taking only the variables into account that we think have the biggest influence on the result. This way, we predict the most likely outcome of the experiment.

As experiments are often very time-consuming, attempts are being made to replace them with simulations. Software products have been developed for this purpose. I compare a new software to see whether it can reproduce results from an existing software and I try to explain deviations between the results.

• author: Schneider, Nils
• supervisor: Andreas Wacker
• organization: Mathematical Physics; Department of Physics
• course: FYSK04 20241
• year: 2024
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Spectroscopy, Simulation, CMDS, 2DES, MATLAB, python, qutip, Liouville–von Neumann equation, Density Matrix, Density Operator
• language: English
• id: 9169675
• date added to LUP: 2024-08-12 08:19:12
• date last changed: 2024-08-12 08:19:12