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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

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CLARA GREGORI
CLARA GREGORI

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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

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LUCIANA VIDAS
LUCIANA VIDAS

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HANYU YE
HANYU YE

2019-05-10
TANJA DRAGOJEVIC
TANJA DRAGOJEVIC

2019-05-17
FLAVIO BACCARI
FLAVIO BACCARI

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MARTINA GIOVANNELLA
MARTINA GIOVANNELLA

2019-07-02
OZLEM YAVAS
OZLEM YAVAS

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ALESSANDRO SERI
ALESSANDRO SERI

2019-07-11
RENWEN YU
RENWEN YU

2019-09-06
ALEXANDER BLOCK
ALEXANDER BLOCK

2019-10-04
MARCO PAGLIAZZI
MARCO PAGLIAZZI

2019-10-07
RINU MANIYARA
RINU MANIYARA

2019-10-15
ALEJANDRO POZAS-KERSTJENS
ALEJANDRO POZAS-KERSTJENS
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
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