2019-01-18

ION HANCU

ION HANCU

2019-01-29

MARIA MAFFEI

MARIA MAFFEI

2019-02-13

BORIS BOURDONCLE

BORIS BOURDONCLE

2019-02-15

JORDI MORALES DALMAU

JORDI MORALES DALMAU

2019-02-22

FRANCESCO RICCI

FRANCESCO RICCI

2019-03-06

CLARA GREGORI

CLARA GREGORI

2019-03-26

ALEXIA SALAVRAKOS

ALEXIA SALAVRAKOS

2019-04-12

SENAIDA HERNANDEZ SANTANA

SENAIDA HERNANDEZ SANTANA

2019-04-15

DAVID RAVENTÓS RIBERA

DAVID RAVENTÓS RIBERA

2019-04-16

PETER SCHMIDT

PETER SCHMIDT

2019-04-29

CALLUM O’DONNELL

CALLUM O’DONNELL

2019-05-02

LUCIANA VIDAS

LUCIANA VIDAS

2019-05-03

HANYU YE

HANYU YE

2019-05-10

TANJA DRAGOJEVIC

TANJA DRAGOJEVIC

2019-05-17

FLAVIO BACCARI

FLAVIO BACCARI

2019-06-04

MARTINA GIOVANNELLA

MARTINA GIOVANNELLA

### Exact Diagonalization Studies of Quantum Simulators

Dr DAVID RAVENTÓS RIBERA

**April 15th, 2019**

**DAVID RAVENTÓS RIBERA**

**Quantum Optics Theory**

ICFO-The Institute of Photonic Sciences

ICFO-The Institute of Photonic Sciences

Understand and tame complex quantum mechanical systems to build quantum technologies is one of the most important scientific endeavour nowadays. In this effort, Atomic, molecular and Optical systems have clearly played a major role in producing proofs of concept of several important applications. Notable examples are Quantum Simulators for difficult problems in other branches of physics i.e. spin systems, disordered systems, etc., and small sized Quantum Computers. In particular, ultracold atomic gases and trapped ion experiments are nowadays at the forefront in the field.

This fantastic experimental effort needs to be accompanied by a matching theoretical and numerical one. The main two reasons are: 1) theoretical work is needed to identify suitable regimes where the AMO systems can be used as efficient quantum simulators of important problems in physics and mathematics, 2) thorough numerical work is needed to benchmark the results of the experiments in parameter regions where a solution to the problem can be found with classical devices.

In this dissertation, we present several important examples of systems, which can be numerically solved. The technique used, which is common to all the work presented in the dissertation, is exact diagonalization. This technique works solely for systems of a small number of particles and/or a small number of available quantum states. Despite this limitation, one can study a large variety of quantum systems in relevant parameter regimes. A notable advantage is that it allows one to compute not only the ground state of the system but also most of the spectrum and, in some cases, to study dynamics.

The dissertation is organized in the following way. First, we provide an introduction, outlining the importance of this technique for quantum simulation and quantum validation and certification. In Chapter 2, we detail the exact diagonalization technique and present an example of use for the phases of the 1D Bose-Hubbard chain. Then in Chapters 3 to 6, we present a number of important uses of exact diagonalization. In Chapter 3, we study the quantum Hall phases, which are found in two-component bosons subjected to artificial gauge fields. In Chapter 4, we turn into dynamical gauge fields, presenting the topological phases which appear in a bosonic system trapped in a small lattice. In Chapter 5, a very different problem is tackled, that of using an ultracold atomic gases to simulate a spin model. Quantum simulation is again the goal of Chapter 6, where we propose a way in which the number-partitioning problem can be solved by means of a quantum simulator made with trapped ions. Finally, in Chapter 7, we collect the main conclusions of the dissertation and provide a brief outlook.

**Monday April 15, 11:00. ICFO Auditorium**

Thesis Advisor: Prof Dr Maciej Lewenstein

Co-Advisor: Dr. Bruno Julia

Thesis Advisor: Prof Dr Maciej Lewenstein

Co-Advisor: Dr. Bruno Julia