### Research team

Theory of quantum systems and complex systems

### Expertise

Theoretical physics, in particular quantum mechanics and many-body physics. The main areas of application are quantum gases, superfluidity and superconductivity, the quantum theory of the solid state, and quantumstatistical physics.

## Modeling and simulation with applications in finance, insurance and economics.

#### Abstract

The scientific target of this project is to develop, analyse and implement numerical methods for dealing with highly sophisticated mathematical models in finance and insurance, e.g., jump-diffusion models, free boundary problems, swing contracts, and high-dimensional systems. In particular, stochastic models will be implemented to tackle valuation, and network modelling will be developed to study systemic risk. This will also allow us to study the emergence of economic behaviour and opinions in local populations by using data-driven models of social networks, social influence, and opinion dynamics.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Many-polaron effects in a Bose-Einstein condensate.

#### Abstract

A Bose-Einstein condensate (BEC) can be thought of as a gas of atoms which undergoes a transition into a specific phase at very low temperatures. In this new phase the atomic gas exhibits various peculiar properties such as superfluidity, quantized vortices and many other phenomena not expected in normal gases. One such interesting problem is that of an impurity (usually an atom of a different species) moving through a BEC. This impurity will disturb the gas around it and create a dip of lower density which it will have to drag along. This will modify the properties of the impurity and for example change the effective mass, analogous to a person having more trouble walking on a trampoline and dragging along the deformation in the fabric. Such an impurity together with the dip in density as a whole is called a Bose-polaron. In 2016 two experiments first realized condensates that contained many Bose-polarons and gave rise to an active discussion in the theoretical community. It has been shown that for an accurate theoretical description of the polaron additional correction terms had to be taken into account which were not present in previous discussions. This has been recently done for a description of single Bose-polarons. In this research these correction terms will be included to describe a system of many polarons which in combination has not been done before. The results found here will also be extended to other atomic gases called ultracold fermionic gases.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Ichmoukhamedov Timour

#### Research team(s)

## Elementary excitations in Fermi systems: From cold atoms to condensed matter.

#### Abstract

When cooling down a system made of many interacting particles, one encounters new states of matter that display unique properties. Superconductors are metals whose resistivity suddenly drops at low temperature; similarly, superfluids are liquids or gases whose viscosity is much lower than in normal fluids. These phenomena rely on the same physical mechanism: at low temperature, the particles, instead of being distinguishable little balls, gather in a condensate, a quantum wave as big as the whole system. In systems made of fermionic particles (that is particles that cannot occupy the same quantum state, which include electrons, neutrons, protons and many atom nuclei), condensation may occur only if the particles first pair up. This kind of pair condensates are found in many different fields of physics, from solid-state physics with superconductors, to astronomy with neutron stars, and their study is equally crucial to the understanding of the fundamental laws of physics, and to the development of new technologies. I will try to better understand how these fermionic condensates in superconductors react to external perturbations, for instance laser pulses, with a special focus on the case when the perturbation has enough energy to break the pairs. Understanding this behavior will help predict the properties of the system as a function of temperature, and may help explain why some materials maintain their superconducting properties at higher temperatures than others.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Kurkjian Hadrien

#### Research team(s)

## Polaronic effects in superfluid Fermi gases.

#### Abstract

When a particle is placed in a medium consisting of other quantum particles, the interaction with this medium will lead to new effective properties for this particle. This was systematically studied for an electron in an ionic or polar lattice: the electron charge distorts the lattice, and the electron together with the lattice deformation is a new, heavier composite object called a polaron. This "polaronic effect" turns out to be ubiquitous in physical systems. Its most recent realization is the dressing of impurity atoms in a quantum gas of atoms cooled down to the nanokelvin regime where the gas turns into a superfluid, i.e. a state of matter exhibiting frictionless flow. The quantum gas embodiment of the polaron problem is particularly useful to study polaron physics since quantum gases are tunable and controllable to a high degree of precision by experimentalists. Hence, polarons can be brought into regimes hitherto inaccessible, where many-body theory can be tested in unprecedented ways. In that respect, superfluid Fermi gases show even more promise than superfluid Bose gases, as they possess a much richer and more tunable spectrum of elementary excitations that can dress the impurity atom. In this project, we will provide an in-depth study of the polaronic effects in these superfluid Fermi gases.This will lead not only to a better understanding of polaron physics, but also to new insights on the formation of superfluid Cooper pairs of fermionic atoms.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Ab-initio calculations for anharmonic polarons in hydrides.

#### Abstract

Hydrogen-rich materials or "hydrides" at high pressure reveal a host of interesting properties, among which record high critical temperatures for superconductivity. This recent discovery has put high-pressure hydrides in the spotlight. In this project, we focus on an aspect that makes these materials special: their very large phonon anharmonicity. Phonons are quantized lattice vibrations of the atoms in the crystal. When at atom is displaced out of its equilibrium position, it feels a restoring force that is usually approximated by a spring pulling it back to its lattice position. For hydrides, the force is no longer spring-like, but more complicated, and this is referred to as phonon anharmonicity. The electrons feel the lattice vibrations, and form an effective composite quasiparticle called a polaron, consisting of the electron taken together with the lattice deformation it induces. We combine the expertise of the Flemish partner, polaron physics, with that of the Austrian partner, first-principles calculation of phonons and electron-phonon interaction strength, to take into account phonon anharmonicity in the description of polarons in hydrides. This will lead to a better understanding of the normal state electronic and optical properties of the interesting class of materials that are the hydrides.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Post-quench prethermalization and thermalization dynamics in Bose gases: extension of the hierarchy of correlations method to the strongly interacting regime, multicomponent systems and finite temperature.

#### Abstract

When a gas of atoms is cooled close to absolute zero, it undergoes a transition to a Bose-Einstein condensate, a quantum mechanical state of matter characterized by frictionless flow or "superfluidity". In this project, we investigate what happens to such a superfluid when a parameter such as the interatomic interaction strength is suddenly changed or "quenched". In particular, the project focuses on how the Bose-Einstein condensate evolves towards the new equilibrium state. Several experimental observations, such as the existence of a prethermal steady state and universal dynamics, pose theoretical challenges that we plan to resolve by taking into account correlations between more than two atoms in our model. The behavior of strongly interacting ultracold atom gases is furthermore archetypical of a broad range of quantum many body systems ranging from neutron stars to superconductors. The research topic thus has many applications, and moreover touches on fundamental questions regarding the role of thermal equilibrium in quantum systems.#### Researcher(s)

- Promotor: Wouters Michiel
- Co-promotor: Tempere Jacques
- Fellow: Fernandes Lennart

#### Research team(s)

## Many-polaron effects in a Bose-Einstein condensate.

#### Abstract

A Bose-Einstein condensate (BEC) can be thought of as a gas of atoms which undergoes a transition into a specific phase at very low temperatures. In this new phase the atomic gas exhibits various peculiar properties such as superfluidity, quantized vortices and many other phenomena not expected in normal gases. One such interesting problem is that of an impurity (usually an atom of a different species) moving through a BEC. This impurity will disturb the gas around it and create a dip of lower density which it will have to drag along. This will modify the properties of the impurity and for example change the effective mass, analogous to a person having more trouble walking on a trampoline and dragging along the deformation in the fabric. Such an impurity together with the dip in density as a whole is called a Bose-polaron. In 2016 two experiments first realized condensates that contained many Bose-polarons and gave rise to an active discussion in the theoretical community. It has been shown that for an accurate theoretical description of the polaron additional correction terms had to be taken into account which were not present in previous discussions. This has been recently done for a description of single Bose-polarons. In this research these correction terms will be included to describe a system of many polarons which in combination has not been done before. The results found here will also be extended to other atomic gases called ultracold fermionic gases.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Ichmoukhamedov Timour

#### Research team(s)

## Dynamics and decay of solitons and solitonic vortices in superfluid Fermi gases.

#### Abstract

Ultracold quantum gases consist of a collection of magnetically trapped atoms cooled down to nanokelvin temperatures. At these ultralow temperatures, the laws of quantum mechanics, which are usually confined to the microscopic world of atoms and particles, now become apparent on the scale of the entire macroscopic cloud. This leads to remarkable behavior, such as flow without friction or "superfluidity". Superfluids are characterized by a complex order parameter. Phase defects in this order parameter are known as solitonic excitations, such as solitons and vortices. The former are localized density dips that propagate without changing their shape, with classical counterparts in water canals and optical fibers. The latter are quantized "whirlpools". Here, we will study these solitonic excitations in a Fermi quantum fluid by making use of a finite-temperature effective field theory that we developed specifically for these systems. Solitons in Fermi superfluids are experimentally seen to decay into vortices. We will model this decay and propose ways to stabilize solitons. We will also investigate collisions between solitonic excitations, and their spontaneous appearance when a gas is cooled rapidly. Finally, we will investigate how disorder and mixing of superfluids influence the properties of the solitonic excitations.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Van Alphen Wout

#### Research team(s)

## Modelling of thermo-optical properties of hydrogen at extreme pressures.

#### Abstract

Hydrogen is the simplest element in the universe. When it is at room temperature and atmospheric pressure, hydrogen takes the form of a gas. One can cool or pressurize this gas to turn it into a solid. Under these conditions, the solid hydrogen is an electrical insulator. However, nearly a century ago, it was predicted that putting a pressure of a quarter of a million times atmospheric pressure on solid hydrogen would turn it into a metal. This material was called metallic hydrogen, and physicists have been trying to create it ever since it was predicted to exist. Theoretical predictions also indicate that metallic hydrogen is a room-temperature superconductor, meaning that it can transport electricity without losses. Additionally, it would be a very powerful rocket fuel, and it would remain metallic even when the pressure is taken off. Recently, experiments by the Silvera research group at Harvard University indicate the first creation of metallic hydrogen in the lab. However, other research groups do not agree with this claim. In the proposed research, we attempt to theoretically model the experiment used by the Silvera research group to get a correct interpretation of their results. Furthermore, we will use this model and the experimental results to estimate material parameters of metallic hydrogen. Finally, we will theoretically develop an experiment that can measure whether the metallic hydrogen in the experiments is superconducting, as predicted by theory#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Houtput Matthew

#### Research team(s)

## Non-adiabatic dynamics of interacting quantum many-body systems

#### Abstract

Whether it's the heat produced in a car engine or the decoherence of a qubit, all losses stem from our lack of control on the microscopic degrees of freedom of the system. Since the early-days of thermodynamics, the adiabatic process has emerged as a universal way to minimize losses, leading to the concept of Carnot efficiency -- the cornerstone of modern thermodynamics. In spite of its conceptual importance, practical implications of the Carnot efficiency are limited since the maximal efficiency goes hand in hand with zero power. Similar issues appear in a seemingly different topic of adiabatic quantum computation, simulation and state preparation. Here the idea is to prepare an interesting state out of a state that is easy to prepare by slow switching a control parameter, in the hope not to excite the system. As in engines, this algorithm works in the adiabatic limit if the ramping rate is infinitesimally slow but leads to heating at finite ramping rates relevant for actual experiments. In this project we will investigate non-equilibrium phenomena in many-body quantum systems. Specifically, we intend to engineer non-adiabatic protocols that lead to the same result as the fully adiabatic protocol, albeit in finite time. For this purpose we will primarily build on the idea of transitionless driving. To deal with many-body quantum systems we will combine it with cutting edge numerical methods such as t-DMRG, phase-space methods and machine learning techniques.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Sels Dries

#### Research team(s)

## Unconventional atomic Fermi superfluids.

#### Abstract

In a superfluid, all particles, instead of being discernable little balls, gather in a single wave whose behaviour is very different from that of a normal fluid. When a superfluid rotates, swirls of quantized size form and arrange themselves in a lattice structure; sound propagates in a superfluid by twisting the macroscopic wave, rather than by compressing the fluid. We will study swirls and sound waves in two new kinds of superfluids recently realized in the lab using gases of atoms cooled down to nearly absolute zero and attracting each other with a strengh that can be magnetically adjusted. In a gas where 2 species of atoms are mixed in unequal proportions, the atoms of the minority form pairs with some atoms of the majority; the remaining unpaired atoms cause defects in the superfluid that self-arrange in an intriguing spatial pattern. We want to see how this pattern of defects reacts to swirls and sound waves. In a gas containing 3 species, threebody objects called trimers form. The nature of swirls and sound waves in this system is an entirely open problem, which would help understand how the collective behaviour of a fluid changes when its constituants interact 3-by-3, not just 2-by-2. Our study will answer fundamental questions relevant for many physical objects: cold gases, liquid Helium, superconductors and quarks. Meanwhile, it contributes to a better understanding of superfluids, objects nowadays widely used in the most advanced quantum technologies. -#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Dynamics and decay of solitons and solitonic vortices in superfluid Fermi gases.

#### Abstract

Ultracold quantum gases consist of a collection of magnetically trapped atoms cooled down to nanokelvin temperatures. At these ultralow temperatures, the laws of quantum mechanics, which are usually confined to the microscopic world of atoms and particles, now become apparent on the scale of the entire macroscopic cloud. This leads to remarkable behavior, such as flow without friction or "superfluidity". Superfluids are characterized by a complex order parameter. Phase defects in this order parameter are known as solitonic excitations, such as solitons and vortices. The former are localized density dips that propagate without changing their shape, with classical counterparts in water canals and optical fibers. The latter are quantized "whirlpools". Here, we will study these solitonic excitations in a Fermi quantum fluid by making use of a finite-temperature effective field theory that we developed specifically for these systems. Solitons in Fermi superfluids are experimentally seen to decay into vortices. We will model this decay and propose ways to stabilize solitons. We will also investigate collisions between solitonic excitations, and their spontaneous appearance when a gas is cooled rapidly. Finally, we will investigate how disorder and mixing of superfluids influence the properties of the solitonic excitations.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Van Alphen Wout

#### Research team(s)

## Polarons in oxides: hamiltonian description and ab-initio treatment

#### Abstract

Polarons are quasiparticles that originate from the coupling between charge carriers and the lattice phonon field. They are of fundamental importance for many practical applications involving charge transfer, conduction and optical excitation. The strength of the electron-phonon coupling determines shape, type, size and characteristics of the polaron: in the short-range strong-coupling regime the polaron size is similar to the lattice constant, when the coupling decreases, the polarons becomes large and a continuum approximation is possible. Although the theoretical basis of polaron physics has been established in the 1950s, a unified treatment of small and large polarons at the same level of theory is still missing. The continuum many-body Hamiltonian description of Frohlich works for large polarons, whereas the basic features of small polarons are better captured by ab-initio calculations. The first goal of this project is to reformulate, design and test an ab-initio and model Hamiltonian approach that will allow a unified theoretical description of small and large polarons within the same theoretical framework. The second objective is to apply our new framework to realistic problems in materials science, specifically, to transition metal oxides.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

#### Project website

## Dynamics and decay of solitons and solitonic vortices in superfluid Fermi gases.

#### Abstract

Ultracold quantum gases consist of a collection of magnetically trapped atoms cooled down to nanokelvin temperatures. At these record low temperatures, the laws of quantum mechanics, usually confined to the microscopic world of single atoms and particles, now dictate the behavior of the entire macroscopic cloud. This leads to remarkable behavior, such as flow without friction or "superfluidity". The main aim of this project is to investigate theoretically how solitary waves travel through a superfluid. These solitary waves, or "solitons", have classical counterparts in water canals and optical fibers, where they propagate without changing their shape. Here, we will study the solitons in a quantum fluid, where they are experimentally seen to decay into quantized whirlpools or "solitonic vortices". For this purpose, we will use and expand a finite-temperature effective field theory developed specifically for superfluid quantum gases. With it, we will model soliton decay and propose ways to stabilize solitons. We will also investigate collisions between solitons, and the interaction between solitons and vortices. We focus on fermionic superfluids, where the atoms form Cooper pairs that in turn lead to superfluidity. Two important effects frustrate this pairing: the presence of an imbalance in the populations of the pairing atoms, and the presence of disorder potentials. We will investigate how solitons behave in superfluids where these two effects hamper the superfluidity.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Van Alphen Wout

#### Research team(s)

#### Project website

## Superfluidity and superconductivity in multicomponent quantum condensates.

#### Abstract

Both superconductors and fermionic superfluids are characterized by frictionless coherent flow, respectively of electron pairs and fermionic atom pairs. Usually, there is only one 'species' of electron pair in a superductor, and analogously only one type of atomic pair in a fermionic superfluid. Recently systems with mixtures of multiple species of pairs have caught the attention of researchers, as it became clear that the interplay of the different types of pairs leads to new behavior that was not expected on the basis of systems with only one type of pair. These systems are called 'multiband' superconductors or superfluids, and in this project we will set up the theoretical tools to model their behavior from the microscopic level up to the level of the macroscopic coherent behavior. With these tools we will systematically investigate how properties (such as critical field and temperature) and important flow patterns (such as vortex matter and solitons) are affected by the multiband nature of the system, and how this multiband nature can be engineered through quantum confinement. Moreover, we seek to characterize new quantum states emerging from the coupling between the different types of pairs.#### Researcher(s)

- Promotor: Tempere Jacques
- Co-promotor: Milosevic Milorad

#### Research team(s)

## Emergent Phenomena in Multicomponent Quantum Condensates.

#### Abstract

Quantum effects usually only matter at the microscopic scale. However, in superconductors and superfluids these quantum effects appear on a macroscopic level, leading to surprising properties such as frictionless or lossless flow. The macroscopic quantum state arises from the collective behavior of a large number of microscopic particles (Bose-Einstein condensation). In the case of fermionic particles these must first pair up. Neutral particles lead to superfluidity, charged ones to superconductivity. Both cases are described by the same underlying mathematical formalism. The discovery of superfluidity in magnesium diboride in 2001 marked the appearance of a new class of macroscopic quantum systems, the so-called multiband systems. They are characterized by multiple types of pairs, leading to a mixture of quantum condensates. This mixing of different types of quantum fluids within the confines of a single fluid or solid leads to a rich set of novel phenomena. Experimentally not only multiband superconductors have been realized but also multiband superfluids. The goal of the project is to study the interplay between these multiple quantum condensates and to quantify the effects of mixing. We aim to develop and extend the mathematical formalism to the multiband case, and to develop efficient solvers for the non-linear field equations characteristic for this formalism. This will be applied to study a wide range of macroscopic quantum phenomena, both for multiband superfluids and for multiband superconductors.#### Researcher(s)

- Promotor: Tempere Jacques
- Co-promotor: Vanroose Wim

#### Research team(s)

## Solitons and vortex patterns in superfluid Fermi gases.

#### Abstract

Trapped clouds of atoms can be cooled down to nanokelvin temperatures and reach the quantum mechanical state known as 'superfluidity'. A superfluid can flow coherently (like a laser), and without friction (like a superconductor). Many flow phenomena that are known for classical fluids, like solitary waves and vortices, have their quantum counterparts in superfluids. The aim of this project is to study solitary waves and collections of these vortices, in dilute atomic superfluids consisting of fermionic atoms. Fermionic atoms have to pair up in order to become superfluid, so the interplay of the coherence and the interatomic interaction is paramount. This is in contrast to bosonic atoms, which can become superfluid without pairing up. The fermionic system only became experimentally available a few years ago. These experiments also reveal that the properties in dilute fermionic superfluids differ from what is known in superfluid helium and in superconductors. To do investigate these properties, we developed tailored extensions of the techniques used to described superconductors, and combine them with recent theoretical models for fermionic superfluids obtained in the TQC lab where this research will take place. With our approach, we aim to understand and explain how the differences in superflow between bosonic and fermionic superfluids arise.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Verhelst Nick

#### Research team(s)

## Non-equilibrium dynamics and thermalization of quantum many-body systems.

#### Abstract

Since Kepler's observation of the regularities in the planetary motion, physics has been concerned with the study of all kinds of regularities in nature. Each of these regularities satisfies a set of rules, the laws of nature. 'The elements of the behavior which are not specified by the laws of nature are called initial conditions. These, then, together with the laws of nature, specify the behavior as far as it can be specified at all' (E.P. Wigner, Nobel lecture, 1963). When systems grow bigger the number of initial conditions grows accordingly, in contrast to the laws which remain as simple as always. New laws emerge, i.e. the laws of thermodynamics, from our ignorance of all the initial conditions. Thermodynamic equilibrium is reached, when we reach the state of maximal ignorance. The field of non-equilibrium thermodynamics is concerned precisely with the process of evolving towards equilibrium. The emergence of non-equilibrium thermodynamics from the microscopic laws has been well established in classical systems. However, nature is intrinsically quantum mechanical, and the main aim of this project is to provide a theoretical description of quantum many-body systems out of equilibrium. For this purpose, we primarily build on Wigner's description of quantum mechanics, and combine this with Feynman's path integral theory to study the time evolution, equilibration, thermalization of quantum many-body systems.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Sels Dries

#### Research team(s)

## Spin-orbit coupling in ultracold Fermi gases.

#### Abstract

One of the latest achievements with ultracold atoms has been the ability to create artificial spin-orbit coupling. The goal of my project is to theoretically describe the properties of spinorbit coupling in ultracold gases, and to predict new phenomena that can be observed experimentally in the near future.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Devreese Jeroen

#### Research team(s)

## Probing itinerant ferromagnetism with ultracold quantum gases.

#### Abstract

The goal of this project is to improve the description of itinerant ferromagnetism using path integral formalism. First, the formalism will be verified with existing mean-field theories. Next, fluctuations around the mean field will be taken into account. This improves the description of strong interactions. In the third part, the interplay between itinerant ferromagnetism and the competing fermionic pairing processes (i.e. superfluidity) will be studied.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Vermeyen Enya

#### Research team(s)

## Investigation of strongly-correlated states of photons in the presence of artificial gauge fields.

#### Abstract

In our project we plan to investigate the interplay between the artificial gauge fields imposed on photons and the effective inter-photonic interactions with an eye to the inherenlty non-equilibrium nature of these systems. In the first place, expanding on our previous work [16,17], we will explore the possibility to excite edge-like modes in a few-particle system of photons. Obeserving the analogues of chiral edge states of the quantum Hall physics and understanding the effects of interactions would be complementary to the studies which have been conducted for non-interacting photons. In doing this, we will also try to think of simpler configurations than have been thought of by considering the state-of-the-art experimental techniques.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Umucalilar Rifat Onur

#### Research team(s)

## Quantum turbulence in atomic and solid state Bose-Einstein condensates.

#### Abstract

This project aims at a theoretical analysis of these quantum fluids in the turbulent regime. Theories for turbulence in superfluid helium will be adapted to account for a larger vortex core size. Interestingly, additional key observables, such as the spatial and temporal coherence, can be measured. We will develop theoretical descriptions for these quantities in order to characterize the turbulent state in these novel quantum fluids.#### Researcher(s)

- Promotor: Wouters Michiel
- Co-promotor: Tempere Jacques

#### Research team(s)

## Quantum simulation of polaronic effects in quantum gases.

#### Abstract

The focus of the proposed project is on the quantum simulation and study of impurities strongly coupled to an environment, in particular a trapped quantum gas. These quantum mechanical quasi-particles play a key role in the dynamics of the macroscopic quantum liquid. This can be related to the general framework derived first for polarons in the context of solid state physics.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Quantum mechanical effects in the optical response of metallic .

#### Abstract

This project represents a research agreement between the UA and on the onther hand IWT. UA provides IWT research results mentioned in the title of the project under the conditions as stipulated in this contract.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Van den Broeck Nick

#### Research team(s)

## Probing itinerant ferromagnetism with ultracold quantum gases.

#### Abstract

The goal of this project is to improve the description of itinerant ferromagnetism using path integral formalism. First, the formalism will be verified with existing mean-field theories. Next, fluctuations around the mean field will be taken into account. This improves the description of strong interactions. In the third part, the interplay between itinerant ferromagnetism and the competing fermionic pairing processes (i.e. superfluidity) will be studied.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Vermeyen Enya

#### Research team(s)

## Lattice models for quantum gases with spin imbalance.

#### Abstract

My research consists of a theoretical study of ultracold Fermionic gases with spin imbalance. At sufficiently low temperatures, these systems can become superfluid. My main goal is to study the formation of exotic forms of superfluidity (supervloeibaarheid).#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Devreese Jeroen

#### Research team(s)

## Localization and response properties of one or more impurities in a Bose-Einstein condensate.

#### Abstract

It has been shown that the system of an impurity in a Bose-Einstein condensate can be described by the Frölich Hamiltonian. This generic model has many applications in different branches of physics. One of these is the well known polaron in solid state physics which consists of an electron coupled to the phonons of the crystal. Despite the many applications there are still some important outstanding issues about the strong coupling regime of the model. The main reason these haven't been solved yet is that the strong coupling regime doesn't appear in solids. We look at this particular model in an ultra cold gas because in these it is possible to very accurately tune some of the aspects of the experiment, as for example the interaction strength between particles. This will allow us to make measurements in the regime of strong coupling for the first time. The purpose of the project is to develop the theoretical description for this system. We will calculate the response properties for arbitrary coupling and also the effect of multiple impurities. Doing the predictions we will always keep the experiment in mind which will allow us to probe the strong coupling properties of the model.#### Researcher(s)

- Promotor: Tempere Jacques
- Fellow: Casteels Wim

#### Research team(s)

## Matching the functional properties of nanoparticles and nanowires.

#### Abstract

This project aims at a continuing integration and optimalization of the unique expertise available in the WOG consortium, regarding the preparation, the structural and physical characterization and the theoretical modeling of nanowires and nanoparticles, forming the building blocks in the developmment of nanotechnological applications. Specifically, theoretical modeling techniques will be developed to describe and model the functional properties of interacting and non-interacting nanoparticles and -wires.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Strong-coupling phenomena for impurity atoms interacting with condensate fluctuations.

#### Abstract

In short, cold atomic gases appear as a new and potent way to investigate an essential problem in many-body physics: particles (strongly) coupled to a bath of bosons. This basic problem falls precisely in the expertise of our research group, so we do not want to miss out on this opportunity to valorize previous results. We plan to develop the path-integral treatment so that it describes the polaronic effect in cold atomic gases on three levels: ground state properties, response properties, and multipolaron effects.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Dynamic effects in coupled superconductor-ferromagnet nanosystems.

#### Abstract

The main objective of this project is to investigate experimentally and theoretically the physical properties of coupled, mutually influencing, superconductor-ferromagnet nanosystems. We will study the different contributions of the ubiquitous electromagnetic coupling and the more fragile exchange coupling. This will include the back-coupling from the superconductor to the (soft) magnetic system. A complementary theoretical approach will be developed by studying more general systems like cold atomic gases, for which the physical description can be mapped onto the S/F hybrids systems and vice versa.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Optical confinement phenomena in plasmonic nanomaterials with predesigned electromagnetic properties.

#### Abstract

The principal objective of this project is to investigate and control the optical confinement phenomena through mastering the plasmonic excitations in individual metallic nanoparticles and study negative refractive index materials composed of nano-engineered arrays of metallic and superconducting nanoresonators. This goal will be achieved by using the following nanoengineered systems, which also eventually will improve the limitations of existing NRI: (i) to broaden considerably the negative magnetic permeability (¿<0) interval, by using nanostructured multilayers and nanostructured hybrid structures [metal/dielectric/metal]n and single layers where several resonance frequencies will be superimposed. The resonant frequencies in a multilayer will be the same within the layer but different from layer to layer. In a single plane version a 2D superposition of the cells with different resonances will be used. (ii) to increase the frequency for which the negative index occurs up to a visible range. Different techniques can be implemented to achieve this goal as is highlighted in the section Design and Methodology. (iii) to reduce absorption at the frequencies below the superconducting gap, these systems will be made from both normal metallic and superconducting films.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Design of new models and techniques for high performance financial applications.

#### Abstract

In the past decennia the international financial markets are witnessing a huge increase in the trading of more and more complex products, such as exotic options and interest products, and this growth is only amplifying. For the exchanges and banks it is of crucial importance to be able to price these products accurately, and as fast as possible. The simulation of the current, sophisticated pricing models is, however, very time consuming with classical techniques such as Monte Carlo methods or binomial trees, and practical pricing formulas are often not at hand. This project is concerned with new models and techniques for robustly and efficiently pricing modern financial products. We investigate two complementary approaches: the first is based on partial differential equations and the second on quantum mechanical path integrals. In the first approach, we will consider operator splitting methods and meshfree methods for the effective numerical solution of these, often multi-dimensional, equations. In the second approach, path integral formulas for financial products will be studied by using the present theory concerning physical multi-particle systems and the comonotonicity coefficient. The obtained models and computational techniques will continually be mutually validated.#### Researcher(s)

- Promotor: In't Hout Karel
- Co-promotor: Cuyt Annie
- Co-promotor: De Schepper Ann
- Co-promotor: Tempere Jacques

#### Research team(s)

## Path-integral techniques for prizing of financial options.

#### Abstract

In this project we develop and apply many-body path integral techniques to derive prizing formulae for financial options for which till now no analytic prizing formulae are available. This is achieved by transferring recent breakthroughs in path integration applied from the context of many-body physics to the context of financial models with stochastic volatility.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Superfluid properties of mixtures of ultracold atomic gases.

#### Abstract

The first aim of this project is to set up a microscopic quantum-kinetic theory for the dilute Bose gas that -is capable of making a distinction between the superfluid and dissipative dynamics ; -is valid at arbitrary temperatures ; -is in agreement with experimental observations; -is satisfying all necessary conservation laws and the second principle of thermodynamics.#### Researcher(s)

- Promotor: Tempere Jacques
- Co-promotor: Brosens Fons

#### Research team(s)

## Nanoscale condensate and flux confinement in superconductors.

#### Abstract

Two main important new topics will be focussed upon : - nanoscale evolution of Tc and gap in individual 3D structures; - controlling vortex patterns and achieving vortex manipulation in superconductors and S/F hybrids with nanoscale pinning centers and magnetic field techniques.#### Researcher(s)

- Promotor: Peeters Francois
- Co-promotor: Tempere Jacques

#### Research team(s)

## Superfluidity of fermionic atoms in a magnetic trap.

#### Abstract

In this project, a theoretical investigation will be made on the artificial interactions between fermionic atoms in a magnetic trap, and how these interactions affect the properties of the gas as concerns the stability of the gas in the trap and the realisation of fermionic superfluidity. The properties of the superfluid state of the trapped fermionic atoms will be investigated and properties suited for the detection of this superfluidity will be identified.#### Researcher(s)

- Promotor: Tempere Jacques

#### Research team(s)

## Application of new methods for confined many-fermion and many-boson systems to confined atomic gases and multielectron bubbles in helium.

#### Abstract

This project focuses on two specific and complementary confined many-body systems: atoms in magnetic traps and electrons in a multielectron bubble. These timely subjects are ideally suited to apply and develop the many-body methods introduced during my previous research and based on the expertise present in the laboratory TFVS where I propose to perform this project. Previous publications, establishing the methods to be used and exploring the systems to be studied testify to the realizabily of the proposed project. For both systems, collaborations with leading experimental groups will enrich and valorize the theoretical results.#### Researcher(s)

- Promotor: Brosens Fons
- Fellow: Tempere Jacques

#### Research team(s)

## Statistics and dynamics of confined fermion systems.

#### Abstract

The recent trends in research and the experiments to come in the domain of the confined atomic fermion gasses and electron bubbles will allow researchers in the near future to observe many-fermion systems in regimes and under physical conditions which up to now were not accessible. These new developments will certainly extend the frontiers of our knowledge of these systems. The aim of the present project is to develop a theoretical framework for these experiments, to predict the new phases and phenomena which will come within reach of the experimentalists, and to formulate the theory of many-electron systems for regimes and under conditions which hitherto were essentially left unconsidered.#### Researcher(s)

- Promotor: Brosens Fons
- Co-promotor: Devreese Jozef
- Co-promotor: Tempere Jacques

#### Research team(s)

## Path-integral treatment of the dynamics of confined many-boson and many-fermion systems.

#### Abstract

The aim of the project is twofold: firstly to develop a path-integral many body theory for the description of the dynamical effects and the response for confined many-boson and many-fermion systems, and secondly to apply this theory to actual experimental developments in the field of Bose-Einstein condensation (boson system) and quantum dots (fermion system, boson-fermion mixtures).#### Researcher(s)

- Promotor: Devreese Jozef
- Fellow: Tempere Jacques

#### Research team(s)

## The role of periodic paths in the path-integral formulation of the quantum theory, applied to field theoretical problems of solid state physics.

#### Abstract

Gutzwillers trace-formula allows to construct a propagator using an expansion of the action-integral in the neighbourhood of the classical paths. The aim of this project is the study of this method and its application to problems of the solid state physics, especially to the polaron problem.#### Researcher(s)

- Promotor: Devreese Jozef
- Fellow: Tempere Jacques

#### Research team(s)

## The role of periodic paths in the path-integral formulation of the quantum theory, applied to field theoretical problems of solid state physics.

#### Abstract

Gutzwillers trace-formula allows to construct a propagator using an expansion of the action-integral in the neighbourhood of the classical paths. The aim of this project is the study of this method and its application to problems of the solid state physics, especially to the polaron problem.#### Researcher(s)

- Promotor: Devreese Jozef
- Fellow: Tempere Jacques

#### Research team(s)

## The role of periodic paths in the path-integral formulation of the quantum theory, applied to field theoretical problems of solid state physics.

#### Abstract

Gutzwillers trace-formula allows to construct a propagator using an expansion of the action-integral in the neighbourhood of the classical paths. The aim of this project is the study of this method and its application to problems of the solid state physics, especially to the polaron problem.#### Researcher(s)

- Promotor: Devreese Jozef
- Fellow: Tempere Jacques