- Simulation of quantum computers: The fundamental block of a quantum computer, the “qubits“, are two-level systems that can be found in a superposition of two states. Thanks to this natural parallelism, quantum computers can perform alogirthms, like the Shor’s algorithm, which can solve problems that cannot be solved on a classical computer. An important question is how to simulate a quantum computer on a classical device, and/or how to verify the result of a quantum calculation. We will address this question using ideas from many-body systems, and in particular the concept of Floquet engineering and emergent phases in periodically driven quantum systems.
Driven quantum systems: When a quantum system is cooled to very low temperatures, it mostly occupies its lowest-energy eigenstate, or “ground state”. This state is qualitatively different from any other state and in particular, it allows to identify distinct quantum phases of matter. One fundamental question is what happens when a ground state is periodically driven by an external drive. Will the ground state keep its unique quantum properties? In this project, we will study this fascinating question by considering the example of a quantum spin chain, whose ground state can be numerically computed. The main tool of our analysis will be the key concept of “entanglement entropy”, which can be used to distinguish equilibrium ground states from excited states.
Spin-waves in superconductors: Superconductor are not just good metals: their resistance is exactly zero. In recent years it was found that superconducting materials can often show additional types of order, such as charge and spin density waves. In these states, the electrons spontaneously form an ordered pattern, which is often incommensurate to the lattice organization of the atoms. Some authors believe that these types of density waves are unrelated to superconductivity and can occur in normal metals as well. We will critically review this statement by comparing experimental observations with simple models of metals (Fermi liquid).
- Matter-wave interferometers: Ultracold atoms currently hold the promises for the detection of extremely weak forces and accelerations. For instance, they may be used in submarines for navigation purposes. These devices are analogous to common optical interferometers, but use quantum matter waves instead of light. Their precision is often determined by interactions among the atoms that scramble the quantum phase of the atoms and limit the sensitivity of the interferometer. In this project, we will consider a novel mechanism that can restore the sensitivity of the interferometer. Our proposal is inspired by the quantum zeno effect and can be used to lock the phase of the interferometer.
Older projects (some of them might still be relevant)
- Imaginary Resonances: Small systems of masses and springs are characterized by a finite set of “normal modes” and their corresponding “eigenfrequencies”. When excited at integer multiples of these frequencies, the system experiences a “resonance” and becomes unstable. In the presence of dissipation (friction), the eigen-frequencies acquire an imaginary part, which reduces the region of stability. Previous works indicate that small imaginary contributions are not sufficient to completely remove the resonances. But what happens when the imaginary part is larger than the real one, or when the latter is even absent?
Quantum Optics: We generically think of the light as a continuous flux of light. This approach is used in classical optics and is extremely successful in the case of free propagation in the vacuum and in dielectric materials. When the light interacts with isolated atoms, one instead realizes that its energy is quantized in photons with a well-defined energy. This description is for instance needed to understand the behavior of a laser. In our study, we will consider a minimal model of a laser, but considering the behavior of photons inside a cavity that contains a small number of atoms. Due to the limited Hilbert space of the problem we will be able to apply numerically-exact diagonalization methods.
Phenomenological description of superconductors: High-temperature superconductors are considered as on the major puzzles of condensed matter physics. Several model exist on the market, but none of them seems to correctly describe the actual experimental data. We will consider one such model and we will compare its predictions with the actual data of a scanning tunneling microscope. Our goal is quantify the agreement between theory and experiment and to verify the existence of a global maximum for this quantity, using a multi-variable optimization method.
Periodic Drives: We are all used to the fact that periodic machines, or engines, dissipate energy (in the winter we even enjoy this effect by heating our vehicle with air passing through the engine). This is a direct consequence of the second principle of the thermodynamics , stating that a periodic motion is always accompanied by a non-negative loss of motion. For quantum systems, such as electrons rotating around the nucleus, it is not uncommon to observe periodic orbits in which the energy loss is exactly zero. The goal of our research is to develop semi-classical methods allowing us to bridge between the quantum and classical word.