Skip to content

Research

I have a varied set of research interests within what I broadly call Quantum Matter. These include strongly correlated materials, impurity models, topological phases of matter and quantum information. However, the main focus of my research has been on open quantum systems driven away from thermal equilibrium by the contact with environments (baths) at different thermodynamic potentials (chemical potential or temperature) which yield thermodynamic flows of particles and/or energy.

My publications are available on:

More information about my research topics is given below.

Non Equilibrium Quantum Matter

Most phases of matter known today are for materials at thermal equilibrium or so close to it that predictions can be made based on linear response. This implies that fluctuation-dissipation relations have to be obeyed. Overcoming these restrictions requires to step away from equilibrium. In the last decade, the study of isolated quantum many-particle systems, taken away from equilibrium by quenching or periodic driving, emerged as a new dynamic field of research. An alternative way to attain a non-equilibrium state requires coupling a system with its environment by connecting external macroscopic reservoirs at different thermodynamic potentials. Transport of otherwise conserved quantities such as energy, charge or spin typically ensues. Understanding the nonequilibrium dynamics of a quantum system coupled to its environments is of central importance for the possible improvement of current technologies such as nuclear magnetic resonance, electronic and optical spectroscopy, and inelastic neutron scattering. It is also a key ingredient for a coherent manipulation of quantum states, for classical and quantum information processing, sensing, and metrology.

Non-equilibrium Quantum Criticality
Critical systems, i.e. systems in the vicinity of a continuous phase transition, are particularly susceptible to perturbations and are therefore natural starting points to look at novel non-equilibrium phenomena.

Quenches and work distributions
The evolution subsequent to an abrupt change of a parameter reveals a complex set of interesting phenomena that may encode simple and universal properties about a quantum system.

Universal signatures of dynamics of quantum systems
Identifying universal dynamic properties of quantum flows will ultimately lead to a classification of non-equilibrium phases of matter.

Non-equilibrium transport though Magnetic Impurities

Non-equilibrium Steady-States

QUANTUM MATERIALS

Although matter ultimately follows the laws of quantum mechanics, most materials admit an effective classical description. This is because the variables, relevant at low energies, are often made of collective excitations that radically differ from higher energy degrees of freedom. Materials that require a deeper appeal to quantum laws - broadly dubbed quantum materials (QM) - are rather exceptional. The study of their exotic states has been central not only to condensed matter physics but also to the fields of cold atomic gases and quantum optics. Examples of strongly-correlated QM are high-temperature superconductors, heavy-fermion compounds, exotic magnetic systems, and quantum Hall states. Quantum effects also have to be considered in some weakly correlated systems such as graphene and its higher dimensional counterparts - Weyl and nodal loop semimetals, and to explain the properties of topological insulators and superconductors.

Topological Phases of Matter
Topology can be used to describe properties of materials that are robust to perturbations. States with different topological orders cannot be continuously changed into each other without passim by a phase transition. Therefore topological properties are naturally useful  to classify phases of matter.
Disorder driven multifractality transition in Weyl nodal loops. 
Dirac points merging and wandering in a model Chern insulator.
Entanglement entropy and entanglement spectrum of triplet topological superconductors

Hybrid quantum-classical models

There are systems made of different degrees of freedom that have radically different time scales. Sometimes, one set of these variables can be modeled as having a classical character. This greatly simplifies the analysis and allows to effective study quantum phases with numerically exact methods.
Classical and quantum liquids induced by quantum fluctuations. (2010)
Temperature-driven gapless topological insulator. (2019)
Interaction-tuned Anderson versus Mott localization. (2016)

Impurity models

An impurity (also called zero-dimensional system) is a generic designation of system with a few degrees of freedom in contact with a bath. Despite their apparent simplicity the physics of these systems is rich when strong correlation are included giving rise to the Kondo effect, several kinds of phase transitions, etc...

Superconductivity

Superconductors remain one of the most fascinating materials with important technological applications. Although a great deal is known on how superconductivity works in some compounds, new materials with novel properties and some of the old ones are a source interesting puzzles.

Impact of Atomic-Scale Contact Geometry on Andreev Reflection (2017)
Dissipation in a Simple Model of a Topological Josephson Junction (2014)
Interplay of classical and quantum capacitance in a one dimensional array of Josephson junctions (2014)
Theoretical Description of the Superconducting State of Nanostructures at Intermediate Temperatures: A Combined Treatment of Collective Modes and Fluctuations (2012)
Experimental observation of thermal fluctuations in single superconducting Pb nanoparticles through tunneling measurements (2011)

Strongly-Interacting Electronic Phases 

Some electronic system where the electron-electron interactions are large behave quite differently that normal metals or insulators. Their collective excitations can be rather exotic. Quantum spin liquid are one of these examples, there are an unusual phase of matter. Quantum spin liquids are characterized by long-range quantum entanglement, fractionalized excitations, and absence of magnetic order.

QUANTUM INFORMATION

Quantum information refers loosely to a set of processes (algorithms) and setups (devices) used to process information with systems obeying the laws of quantum mechanics. The ultimate goal of quantum information is to be able to build and operate an quantum computer that will outperform the existing ones that are based on classical principles. The search for better devices and algorithms poses some practical and theoretical physical challenges.

Adiabatic Quantum Computation

Adiabatic quantum computing is a model of computation that uses quantum dynamics under adiabatic conditions to perform universal quantum computation. The core idea consist of finding the ground-state of a classical optimization problem using adiabatic quantum evolution that makes use of tunneling. This is a very physical idea that can be tested in simplified models that highlight the relations with quantum phase transitions.
Adiabatic computation : A toy model.
Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model.

Entanglement Classification

Entanglement is a unique feature of quantum systems at the heart of their contra-intuitive nature. Entangled degrees of freedom cannot be described independently of the state of the others. Systems can be entangled in many different ways. Classifying and describing these forms of entanglement will allow us to better understand the quantum world.
Entanglement and Hilbert space geometry for systems with a few qubits
Entanglement in the Symmetric Sector of n Qubits

Quantum Walks

Quantum walks are the quantum counterpart of classical random walks. They have been used in the design of algorithms of several quantum algorithms. Generalized quantum walk protocols with biased quantum coins arranged in periodic and aperiodic sequences may yield ballistic, sub-ballistic and diffusive spreading.
Aperiodic Quantum Random Walks.