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NOSLEN SUAREZ

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VALERIA RODRÍGUEZ-FAJARDO

VALERIA RODRÍGUEZ-FAJARDO

2018-02-26

BENJAMIN WOLTER

BENJAMIN WOLTER

2018-03-19

JOANNA ZIELINSKA

JOANNA ZIELINSKA

2018-03-23

QUAN LIU

QUAN LIU

2018-03-28

LARA LAPARRA

LARA LAPARRA

2018-04-03

GUILLAUME CORDIER

GUILLAUME CORDIER

2018-05-22

KEVIN SCHÄDLER

KEVIN SCHÄDLER

2018-06-14

MIRIAM MARCHENA

MIRIAM MARCHENA

2018-06-19

CARLOS ABELLAN

CARLOS ABELLAN

2018-07-02

LUKAS NEUMEIER

LUKAS NEUMEIER

2018-07-24

SHAHRZAD PARSA

SHAHRZAD PARSA

2018-07-25

PAU FARRERA

PAU FARRERA

2018-07-31

BARBARA BUADES

BARBARA BUADES

2018-09-06

SIMON COOP

SIMON COOP

2018-09-13

NICOLAS MARING

NICOLAS MARING

2018-09-19

IVAN SUPIC

IVAN SUPIC

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ANIELLO LAMPO

ANIELLO LAMPO

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CÉSAR CABRERA

CÉSAR CABRERA

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FLORIAN CURCHOD

FLORIAN CURCHOD

2018-10-18

JOSEP CANALS

JOSEP CANALS

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ROLAND TERBORG

ROLAND TERBORG

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KAVITHA KALAVOOR

KAVITHA KALAVOOR

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MIGUEL MIRELES

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JIL SCHWENDER

JIL SCHWENDER

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JOSÉ RAMÓN MARTÍNEZ

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LIJUN MENG

LIJUN MENG

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NICOLÁS MORELL

NICOLÁS MORELL

2018-12-18

JUNXIONG WEI

JUNXIONG WEI

### 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