The following link contains a list of the the proposed topics for a Master’s thesis.

COSMOLOGY AND GRAVITATION

Cosmology describes the origin of the physical universe and its evolution until now. Even though one of its foundations is Einstein’s General Theory of Relativity (GR), which is the best tool we have to understand gravitation, it must ultimately be explained by fundamental physics (see below in FIELDS AND PARTICLES). Gravitation is one of the key subjects in theoretical physics, and one that has provided us with most mysteries lately: dark matter and dark energy are two of the most exciting and less understood phenomena in our Universe.In a more fundamental level,the theory that merges quantum mechanics and gravitation is one of the major conceptual challenge for theoretical physics. In our group we investigate formal aspects of GR, andtheories beyond GR, such as supergravity or superstrings, in order to advance in understanding the nature of gravity. We also work in Cosmology, from theoretical cosmology, including Cosmological Inflation and the Landscape, to more observational cosmology, using probes such as Gravitational Waves, Cosmic-Microwave-Background, Baryon-Acoustic-Oscillations and Supernova.

FIELDS AND PARTICLES

The standard model of particle physics is one of the most successful theories in physics, it has explained a wide variety ofexperimental results.The discovery of the Higgs boson has been one of its recent successes. The standard model is a Quantum Field Theory (QFT), and most attempts to go beyond the Standard model to explain new phenomena (like, for example, dark matter) are also developed as a QFT. As mentioned above, the study ofCosmology, or more specifically, of physics of the Early Universe, encompasses both gravitation and particle physics. It is therefore a very exciting subject, which uses the actual Universe as a laboratory to test and understand the particle physics at very high energies. In our group we investigate QFT, most notably in relation to cosmology. Topics such as Inflation, the Landscape of string theory, topological defects, or Quantum anomalies, help us understand the physics governing the physics of the early Universe.

SUPERSYMMETRY, SUPERGRAVITY and STRING THEORY

The research in this field use intensively the modern mathematical method to understand the nature of fundamental interaction from the first principles, which are understood as principles of symmetry. String theory, also known under the name of M-theory, provides a quantum description of gravity and is a candidate for the role of unified theory of all fundamental interactions. Its essential ingredient is supersymmetry, which can be understood, roughly speaking, as symmetry between elementary particles of matter and quanta of fundamental interactions (this is usually stated as ‘symmetry between fermions and bosons’). Its low energy limits are described by supergravity, the multidimensional supersymmetric generalizations of the Einstein General Relativity. It also includes a set of multidimensional supersymmetric extended objects, strings, membranes and higher ‘p-branes’, some of which are now used as a basis to search for a realistic ‘Brane World’ model for our Universe. Besides providing a convenient framework to search for the explanation of the properties of our Universe and fundamental interactions, String theory produced a number of by-product results which strongly influenced the development of other fields of research. The most exemplar case is the so-called gauge-gravity correspondence which has an important applications for studying quark-gluon plasma, complicated solid state systems and hydrodynamics.Our current interest include the investigation of the duality symmetries and other properties of supergravity, superstring and multiple p-brane systems, as well as related issues of higher spin theories.

THEORETICAL CONDENSED MATTER

A primary goal of the research of the theoretical and computational materials physics is to understand and predict material properties at the most fundamental level using atomistic first principles and quantum-mechanical calculations. In particular, we apply first-principles electronic structure calculations to investigate a wide range of properties arising in materials, from optical, electronic and magnetic excitations, to superconductivity. Our current interests include the following lines: new materials and physical properties under pressure, electronic correlation, superconductivity, spin-orbit induced anomalous spin structure at surfaces, and anharmonicity.

QUANTUM INFORMATION

Processing information with systems that preserve quantum coherence offers important advantages over classically-based computations. This is so because of the parallelism implicit in the superposition principle (many paths are followed at once so many computations are done simultaneously) and the rich structure of the quantum qubit compared to the binary, classical bit. Problems that cannot be addressed with a classical computer could be solved using a quantum computation. Implementing a quantum computer is not a trivial task because of the need to develop algorithms and fundamental theory (software) and the need to find the appropriate physical platform or “architecture’’ to implement the logical operations reliably (hardware). This implies finding good qubits, easy to manipulate and ready to interact among themselves in fast logic gates keeping quantum coherence. Our activity in this field is manifold: We work on fundamental aspects, such as the theory of entanglement, as well as on close collaborations with different laboratories to improve and implement elementary operations -used as well in simulations or other quantum technologies- in different architectures.

QUANTUM SIMULATIONS

Quantum simulations represent an evolution of the concept of the universal quantum simulator proposed by R. Feynman at the beginning of the ’80. Though initially conceived as the platform for a quantum computer, nowadays a quantum simulator is – in a wider sense – a controllable quantum system that can mimic the behavior of other physical systems or permits the implementation of specific theoretical quantum models. Our activity covers different kinds of quantum simulations: analog – when the quantum simulator is designed to have the same Hamiltonian of the system that one wants to simulate; digital – consisting in the implementation of a sequence of elementary gates resulting in an evolution similar to the original model; digital-analog, a combination of the previous cases. In particular, we work with different physical systems that, thanks to the modern quantum technologies, have proven to be excellent platforms for quantum simulations. These include, among others, quantum photonics, superconducting circuits, trapped ions, and ultracold atoms.

QUANTUM TECHNOLOGIES

Quantum-based technologies are really everywhere in our modern society (the transistor, micro-chip, laser, or GPS are all quantum devices). However in recent times the term “quantum technologies’’ refers to new -existing or projected- devices or operations associated with a “second quantum revolution’’. This second wave of applications of quantum phenomena includes prominent fields such as communications and cryptography, metrology and sensors. These applications are at different stages of development. For example our society -in particular bank transactions, power companies, communications, transport- “ticks’’ already thanks to atomic quantum clocks, a field where research and development keeps improving the accuracy at an impressive pace. Many other precise measurements (for example leading to accurate navigation if GPS is not available), or sensors that will govern one day the “internet of things’’, are being developed or will be developed soon. Big companies such as Intel, Google, Microsoft, Toshiba, Bosch, or IBM as well as Governments around the world are investing heavily on quantum technologies. The EU in particular has just launched the “quantum technologies flagship’’, a 1 billion euro initiative to support quantum technologies. Our activity is right now centered on the use of entanglement to develop accurate measurements (quantum metrology), as well on the design of fast and reliable elementary operations, the building blocks for quantum control and manipulations.

## Research

## MASTER THESIS TOPICS

The following link contains a list of the the proposed topics for a Master’s thesis.

## COSMOLOGY AND GRAVITATION

Cosmology describes the origin of the physical universe and its evolution until now. Even though one of its foundations is Einstein’s General Theory of Relativity (GR), which is the best tool we have to understand gravitation, it must ultimately be explained by fundamental physics (see below in FIELDS AND PARTICLES). Gravitation is one of the key subjects in theoretical physics, and one that has provided us with most mysteries lately: dark matter and dark energy are two of the most exciting and less understood phenomena in our Universe. In a more fundamental level, the theory that merges quantum mechanics and gravitation is one of the major conceptual challenge for theoretical physics. In our group we investigate formal aspects of GR, and theories beyond GR, such as supergravity or superstrings, in order to advance in understanding the nature of gravity. We also work in Cosmology, from theoretical cosmology, including Cosmological Inflation and the Landscape, to more observational cosmology, using probes such as Gravitational Waves, Cosmic-Microwave-Background, Baryon-Acoustic-Oscillations and Supernova.

## FIELDS AND PARTICLES

The standard model of particle physics is one of the most successful theories in physics, it has explained a wide variety of experimental results. The discovery of the Higgs boson has been one of its recent successes. The standard model is a Quantum Field Theory (QFT), and most attempts to go beyond the Standard model to explain new phenomena (like, for example, dark matter) are also developed as a QFT. As mentioned above, the study of Cosmology, or more specifically, of physics of the Early Universe, encompasses both gravitation and particle physics. It is therefore a very exciting subject, which uses the actual Universe as a laboratory to test and understand the particle physics at very high energies. In our group we investigate QFT, most notably in relation to cosmology. Topics such as Inflation, the Landscape of string theory, topological defects, or Quantum anomalies, help us understand the physics governing the physics of the early Universe.

## SUPERSYMMETRY, SUPERGRAVITY and STRING THEORY

The research in this field use intensively the modern mathematical method to understand the nature of fundamental interaction from the first principles, which are understood as principles of symmetry. String theory, also known under the name of M-theory, provides a quantum description of gravity and is a candidate for the role of unified theory of all fundamental interactions. Its essential ingredient is supersymmetry, which can be understood, roughly speaking, as symmetry between elementary particles of matter and quanta of fundamental interactions (this is usually stated as ‘symmetry between fermions and bosons’). Its low energy limits are described by supergravity, the multidimensional supersymmetric generalizations of the Einstein General Relativity. It also includes a set of multidimensional supersymmetric extended objects, strings, membranes and higher ‘p-branes’, some of which are now used as a basis to search for a realistic ‘Brane World’ model for our Universe. Besides providing a convenient framework to search for the explanation of the properties of our Universe and fundamental interactions, String theory produced a number of by-product results which strongly influenced the development of other fields of research. The most exemplar case is the so-called gauge-gravity correspondence which has an important applications for studying quark-gluon plasma, complicated solid state systems and hydrodynamics.Our current interest include the investigation of the duality symmetries and other properties of supergravity, superstring and multiple p-brane systems, as well as related issues of higher spin theories.

## THEORETICAL CONDENSED MATTER

A primary goal of the research of the theoretical and computational materials physics is to understand and predict material properties at the most fundamental level using atomistic first principles and quantum-mechanical calculations. In particular, we apply first-principles electronic structure calculations to investigate a wide range of properties arising in materials, from optical, electronic and magnetic excitations, to superconductivity. Our current interests include the following lines: new materials and physical properties under pressure, electronic correlation, superconductivity, spin-orbit induced anomalous spin structure at surfaces, and anharmonicity.

## QUANTUM INFORMATION

Processing information with systems that preserve quantum coherence offers important advantages over classically-based computations. This is so because of the parallelism implicit in the superposition principle (many paths are followed at once so many computations are done simultaneously) and the rich structure of the quantum qubit compared to the binary, classical bit. Problems that cannot be addressed with a classical computer could be solved using a quantum computation. Implementing a quantum computer is not a trivial task because of the need to develop algorithms and fundamental theory (software) and the need to find the appropriate physical platform or “architecture’’ to implement the logical operations reliably (hardware). This implies finding good qubits, easy to manipulate and ready to interact among themselves in fast logic gates keeping quantum coherence. Our activity in this field is manifold: We work on fundamental aspects, such as the theory of entanglement, as well as on close collaborations with different laboratories to improve and implement elementary operations -used as well in simulations or other quantum technologies- in different architectures.

## QUANTUM SIMULATIONS

Quantum simulations represent an evolution of the concept of the universal quantum simulator proposed by R. Feynman at the beginning of the ’80. Though initially conceived as the platform for a quantum computer, nowadays a quantum simulator is – in a wider sense – a controllable quantum system that can mimic the behavior of other physical systems or permits the implementation of specific theoretical quantum models. Our activity covers different kinds of quantum simulations: analog – when the quantum simulator is designed to have the same Hamiltonian of the system that one wants to simulate; digital – consisting in the implementation of a sequence of elementary gates resulting in an evolution similar to the original model; digital-analog, a combination of the previous cases. In particular, we work with different physical systems that, thanks to the modern quantum technologies, have proven to be excellent platforms for quantum simulations. These include, among others, quantum photonics, superconducting circuits, trapped ions, and ultracold atoms.

## QUANTUM TECHNOLOGIES

Quantum-based technologies are really everywhere in our modern society (the transistor, micro-chip, laser, or GPS are all quantum devices). However in recent times the term “quantum technologies’’ refers to new -existing or projected- devices or operations associated with a “second quantum revolution’’. This second wave of applications of quantum phenomena includes prominent fields such as communications and cryptography, metrology and sensors. These applications are at different stages of development. For example our society -in particular bank transactions, power companies, communications, transport- “ticks’’ already thanks to atomic quantum clocks, a field where research and development keeps improving the accuracy at an impressive pace. Many other precise measurements (for example leading to accurate navigation if GPS is not available), or sensors that will govern one day the “internet of things’’, are being developed or will be developed soon. Big companies such as Intel, Google, Microsoft, Toshiba, Bosch, or IBM as well as Governments around the world are investing heavily on quantum technologies. The EU in particular has just launched the “quantum technologies flagship’’, a 1 billion euro initiative to support quantum technologies. Our activity is right now centered on the use of entanglement to develop accurate measurements (quantum metrology), as well on the design of fast and reliable elementary operations, the building blocks for quantum control and manipulations.