Theses
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2018-01-23
NOSLEN SUAREZ
2018-02-26
BENJAMIN WOLTER
2018-03-23
QUAN LIU
2018-03-28
LARA LAPARRA
2018-05-22
KEVIN SCHÄDLER
2018-06-14
MIRIAM MARCHENA
2018-06-19
CARLOS ABELLAN
2018-07-02
LUKAS NEUMEIER
2018-07-24
SHAHRZAD PARSA
2018-07-25
PAU FARRERA
2018-07-31
BARBARA BUADES
2018-09-06
SIMON COOP
2018-09-13
NICOLAS MARING
2018-09-19
IVAN SUPIC
2018-10-02
ANIELLO LAMPO
2018-10-10
CÉSAR CABRERA
2018-10-11
FLORIAN CURCHOD
2018-10-18
JOSEP CANALS
2018-10-19
ROLAND TERBORG
2018-10-24
MIGUEL MIRELES
2018-10-26
KYRA BORGMAN
2018-11-12
JIL SCHWENDER
2018-12-12
LIJUN MENG
2018-12-17
NICOLÁS MORELL
2018-12-18
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


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