Research
Summary
Quantum dynamics is the motion of electronic or other quantum degrees of freedom in non-equilibrium conditions. In a material, quantum dynamics controls the response of said material to perturbations. When the perturbations are weak, the response is connected to the quantum fluctuations around its equilibrium structure, a fact that constitutes the backbone of linear response theory. When perturbations are strong, however, equilibrium properties cannot help us to understand the response. We then need to resort to more powerful techniques based on real-time quantum evolution. The physical behaviors that emerge are complex, and often exhibit fascinating fingerprints of the quantum nature of the dynamics.
In the QUDYMA group we specialise in the exploration of the response of quantum materials, with a focus on low-dimensional systems, when pushed aways from equilibrium. Our projects often start by developing a solid understanding of equilibrium structure, described with a variety of tools that include ab-initio approaches and effective models. We can then perturb the system under study using the large toolbox of numerical and analytic techniques at our disposal, most of them developed in-house. The development of these tools is also an important part of our research activity.
Notable fields of study of interest to us include attosecond science in 2D materials, out-of-equilibrium superconductivity, topological materials and computational dynamics.
Open research topics
Attosecond science in 2D materials
Our work in the field of attosecond science explores processes at attosecond timescales involving quantum degrees of freedom in condensed matter systems. By understanding these processes we aim to unveil ways to control the properties of quantum materials (e.g., 2D layers and heterostructures, topological insulators, strongly-correlated systems, etc.) at these ultrashort times. In this domain, the tool of choice is strong laser fields, which can drive crystals to a highly non-equilibrium regime. New transient properties such as high-harmonic generation emerge in response to attosecond-resolved optical techniques, and novel measurement techniques such as transient absorption spectroscopy become possible. By controlling the form of the lightwave on a sub-cycle timescale, we steer the coherent electron motion, manipulating quantum properties on few-femtosecond timescales, i.e., faster than the typical dephasing mechanisms at room temperature.
Main line leaders: Alvaro Jimenez-Galán, Antonio Picón and Rui Silva
Out-of-equilibrium superconductivity
Controlling electronic motion using light on attosecond timescales is just one extreme example of quantum electron dynamics. Many other quantum dynamical phenomena of fascinating complexity and promising applications can be found in condensed matter systems. One instance of particular interest to us is out-of-equilibrium superconductivity.
In superconducting systems, electrons form a superconducting condensate that is endowed with a macroscopic quantum-mechanical phase. It is responsible for spectacular phenomena, such as supercurrents and magnetic levitation. In time-dependent scenarios, this phase becomes a dynamic degree of freedom, like e.g. in the ac-Josephson effect.
We explore the interplay of external driving, the condensate and the electronic quasiparticles in out-of-equilibrium superconducting systems, with a particular eye on topological effects. The typical timescales of superconductor dynamics are very different from those of attosecond physics, but the underlying theoretical formalism (real-time Keldysh Green functions) is similar. We use this fact to explore connections between these fields.
Main line leaders: Elsa Prada and Pablo San-Jose
Hybrid nanostructures and the search for Majorana bound states
Topological materials, topological superconductors, hybrid nanostructures, full-shell nanowires
Main line leader: Elsa Prada
Computational modelling of quantum materials
Understanding quantum dynamics far from equilibrium is a daunting task in all but the simplest model systems. At QUDYMA we aim to understand real materials and devices that our experimental colleagues also study in the lab. This requires powerful numerical techniques that can deal with the complexity of the quantum world under arbitrary perturbations. We combine established ab-initio codes with our own simulation libraries, developed in-house. This becomes a necessity when exploring the frontier of quantum many-body dynamics in novel materials, as the numerical cost of the simulations is often enormous, so incorporating new state-of-the-art algorithms and approaches is a must.
Developing and maintaining these state-of-the-art tools using modern High-Performance Computing (HPC) approaches is a huge research project in its own right. We have currently three main packages under active development: ATATA, EDUS and Quantica.jl, and some older ones in maintenance mode (MathQ, IWERIA, TimeProp) .
ATATA
Main Developer: Rui Silva
EDUS
A code to simulate the electron dynamics of a material induced by a laser pulse. The code is designed to model state-of-the-art ultrafast experiments, and is particularly efficient for simulating X-ray spectroscopy.
Main Developer: Antonio Picón
An open-source domain-specific language (DSL) written in Julia. It allows to define arbitrary tight-binding models, and to compute and visualise general electronic structure and transport properties for them. Its guiding design principles are performance, extensibility and composability. It is a registered Julia package (also available directly from Github). It has complete documentation and also a recorded demo in Youtube.
Main Developer: Pablo San-Jose