01HFYUU

A.A. 2023/24

2023/24

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The course aims at providing the theoretical basis necessary to understand and describe the physics of condensed matter. The student will learn how to apply the laws of quantum mechanics to study the functioning mechanism of solid-state quantum devices, with applications in the area of quantum sensing, quantum communication and quantum computing. During the first part of the course, the basics of solid-state physics are presented, while the second part deals with the physics of low-dimensional nanostructures such as quantum wells, multi-quantum wells, quantum wires and quantum dots. Finally, the course addresses quantum phenomena such as superconductivity, the Hall effect and others, that are currently exploited for the realization of qubits and quantum devices.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

The availability of devices exploiting quantum effects is at the basis of the development of quantum electronics and quantum computing. The development of physical structures where quantum states can be prepared and manipulated is nowadays an active research field where new ideas, device concepts and physical implementations are developing day by day. Quantum engineers must be able to understand the operation principle of the main quantum devices as well as acquire the competences needed to keep the pace with the fast evolution in this field. The “Quantum devices” course is the introductory course of the Master Degree in Quantum engineering, first addressing the transition from the “classic devices” picture to the to “quantum devices” one. The course provides the theoretical background to understand and model the operation principles of the main quantum devices. It specifically aims at linking new electron device concepts to specific material properties of semiconductor and other nanotechnologies materials, allowing quantum operation. The course serves as the basis for the subsequent courses of the Master Degree, dedicated to qubit electronics, quantum communications and quantum computing.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The course aims at providing the theoretical basis necessary to understand and describe the physics of condensed matter. The student will learn how to apply the laws of quantum mechanics to study the functioning mechanism of solid-state quantum devices, with applications in the area of quantum sensing, quantum communication and quantum computing. During the first part of the course, the basics of solid-state physics are presented, while the second part deals with the physics of low-dimensional nanostructures such as quantum wells, multi-quantum wells, quantum wires and quantum dots. Finally, the course addresses quantum phenomena such as superconductivity, the Hall effect and others, that are currently exploited for the realization of qubits and quantum devices.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

The availability of devices exploiting quantum effects is at the basis of the development of quantum electronics and quantum computing. The development of physical structures where quantum states can be prepared and manipulated is nowadays an active research field where new ideas, device concepts and physical implementations are developing day by day. Quantum engineers must be able to understand the operation principle of the main quantum devices as well as acquire the competences needed to keep the pace with the fast evolution in this field. The “Quantum devices” course is the introductory course of the Master Degree in Quantum engineering, first addressing the transition from the “classic devices” picture to the to “quantum devices” one. The course provides the theoretical background to understand and model the operation principles of the main quantum devices. It specifically aims at linking new electron device concepts to specific material properties of semiconductor and other nanotechnologies materials, allowing quantum operation. The course serves as the basis for the subsequent courses of the Master Degree, dedicated to qubit electronics, quantum communications and quantum computing.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The students are expected to learn how to apply the principles of quantum physics to study, describe and predict the physical properties of condensed matter both at the micro and nanoscale. Main anticipated achievements are: - Knowledge of solid-state structure - Knowledge of electronic and optical properties of solids and nanostructures - In-depth knowledge of quantum charge conduction in nanostructures - Knowledge of the effects related to quantum coherence and ballistic regime of electrons in nanostructures - Knowledge of superconductivity - Ability to evaluate the effect of confinements on the electronic motion in nanostructures - Ability to evaluate band structures in low-dimensional systems - Ability to apply quantum condensed matter physics for the realization of solid-state qubits and quantum sensors - Ability to use physics-based models for the prediction of materials and nanostructures properties.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Expected knowledge: - Understand and discuss the quantum limitation to device scaling in the framework of the current technological scenario - Acquire the mathematical and theoretical background to model quantum effects in electron devices ad in particular quantum confinement and quantum tunnelling - Understand and discuss the operation of advanced classic devices, highlighting the role of quantum effects - Understand and discuss the operation of the main quantum devices, and in particular quantum dots and resonant tunnel devices - Understand and discuss the fundamental physical properties relevant to quantum devices: spin, polarization, superconductivity - Understand the basic knowledge of superconducting quantum circuits. Expected competences and skills - Describe the FinFET operation and derive the characteristics in terms of analytical models - Describe the JLNT operation and derive the characteristics in terms of analytical models - Describe the TFET operation and derive the characteristics in terms of analytical models - Describe heterostructure devices - Describe the tunnel junctions characteristics in terms of analytical models - Describe Quantum blockade devices and Single electron transistors - Describe superconducting Quantum circuits and Qubit and SQUID operations in these quantum circuits - Develop codes to model FinFETs, TFETs, resonant diodes, single electron transistors - Compare devices in terms of quantum effects, operation and applications.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The students are expected to learn how to apply the principles of quantum physics to study, describe and predict the physical properties of condensed matter both at the micro and nanoscale. Main anticipated achievements are: - Knowledge of solid-state structure - Knowledge of electronic and optical properties of solids and nanostructures - In-depth knowledge of quantum charge conduction in nanostructures - Knowledge of the effects related to quantum coherence and ballistic regime of electrons in nanostructures - Knowledge of superconductivity - Ability to evaluate the effect of confinements on the electronic motion in nanostructures - Ability to evaluate band structures in low-dimensional systems - Ability to apply quantum condensed matter physics for the realization of solid-state qubits and quantum sensors - Ability to use physics-based models for the prediction of materials and nanostructures properties.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Expected knowledge: - Understand and discuss the quantum limitation to device scaling in the framework of the current technological scenario - Acquire the mathematical and theoretical background to model quantum effects in electron devices ad in particular quantum confinement and quantum tunnelling - Understand and discuss the operation of advanced classic devices, highlighting the role of quantum effects - Understand and discuss the operation of the main quantum devices, and in particular quantum dots and resonant tunnel devices - Understand and discuss the fundamental physical properties relevant to quantum devices: spin, polarization, superconductivity - Understand the basic knowledge of superconducting quantum circuits. Expected competences and skills - Describe the FinFET operation and derive the characteristics in terms of analytical models - Describe the JLNT operation and derive the characteristics in terms of analytical models - Describe the TFET operation and derive the characteristics in terms of analytical models - Describe heterostructure devices - Describe the tunnel junctions characteristics in terms of analytical models - Describe Quantum blockade devices and Single electron transistors - Describe superconducting Quantum circuits and Qubit and SQUID operations in these quantum circuits - Develop codes to model FinFETs, TFETs, resonant diodes, single electron transistors - Compare devices in terms of quantum effects, operation and applications.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

Classical Physics. Basic knowledge of quantum mechanics.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

• Elementary physics (mechanics, thermodynamics, wave optics, fluidics, elements of structure of matter) • Elements of circuit theory and electronics (amplification, filtering, analog to digital conversion, …) • Elements of electronic devices (diode, BJT and CMOS transistor, band-gap concept): if this knowledge is not present the students will be asked to follow a self-learning activity with dedicated teaching material (slides, notes and video) + 10 hours in class.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

Classical Physics. Basic knowledge of quantum mechanics.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

• Elementary physics (mechanics, thermodynamics, wave optics, fluidics, elements of structure of matter) • Elements of circuit theory and electronics (amplification, filtering, analog to digital conversion, …) • Elements of electronic devices (diode, BJT and CMOS transistor, band-gap concept): if this knowledge is not present the students will be asked to follow a self-learning activity with dedicated teaching material (slides, notes and video) + 10 hours in class.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

- Condensed matter structure: crystalline and amorphous materials. Direct and reciprocal lattice. Point defects in crystals (F-centers). (6 hours) - Electrons in solids: the Sommerfeld model, Bloch theorem, bands and Fermi surfaces. Semiconductors and doping. (9 hours) - Phonons in condensed matter. Electron-phonon interaction. (6 hours) - 2-dimensional electron gas (2DEG). Quantum devices based on 2DEG. Quantum Transport in two dimensions. Quantum Hall Effects and Quantum Spin Hall Effect. (10.5 hours) - Quantum wells and multi-quantum wells, quantum wires and quantum dots, with application as qbits. Quantized conductance, tunnelling transport, the Aharonov-Bohm effect, and the Coulomb blockade effect. (12 hours) - Topological insulators. (3 hours) - Introduction single photon sources and quantum sensors. (3 hours) - Superconductivity: the macroscopic quantum state (MQM, macroscopic quantum model), flux quantization, Josephson effect and junctions, SQUID RF and DC (10.5 hours)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Introduction (group A) - Advanced concepts on ballistic and quantum transport (5h). - Modelling Techniques for nanoscale devices: variability, statistical analysis, noise (3h theory + 2h lab) Introduction (group B) - Basics of semiconductors, band theory, electron transport (1.5 h) - The pn junction (3 h) - MOSFET transistors (5.5 h) From classic devices to quantum devices (23h) - Limits of device scaling, quantum effects in classic devices (3h) - Advanced MOSFETs, FINFETs (6h + 3h lab) - Nano transistors: JNTs, nanowires (2h) - Tunnel transistors (TFET) (6h + 3h lab) Quantum devices (19.5h) - Heterostructure devices and quantum confinement: quantum wells, quantum dots (1.5h) - Tunnel junctions, resonant tunnel devices, tunnelling models (3h + 3h lab) - Coulomb blockade device and single electron transistors (3h + 3h lab) - Silicon based qubits: basic concepts, spin, polarization (3h + 3h lab) Introduction to superconducting quantum circuits (7.5h): - the quantum Hamiltonian of a network of devices (3h) - LC resonator, transmission line, nonlinear resonator (Qubit), loops with Josephson junctions (SQUIDs) (4.5h)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

- Condensed matter structure: crystalline and amorphous materials. Direct and reciprocal lattice. Point defects in crystals (F-centers). (6 hours) - Electrons in solids: the Sommerfeld model, Bloch theorem, bands and Fermi surfaces. Semiconductors and doping. (9 hours) - Phonons in condensed matter. Electron-phonon interaction. (6 hours) - 2-dimensional electron gas (2DEG). Quantum devices based on 2DEG. Quantum Transport in two dimensions. Quantum Hall Effects and Quantum Spin Hall Effect. (10.5 hours) - Quantum wells and multi-quantum wells, quantum wires and quantum dots, with application as qbits. Quantized conductance, tunnelling transport, the Aharonov-Bohm effect, and the Coulomb blockade effect. (12 hours) - Topological insulators. (3 hours) - Introduction single photon sources and quantum sensors. (3 hours) - Superconductivity: the macroscopic quantum state (MQM, macroscopic quantum model), flux quantization, Josephson effect and junctions, SQUID RF and DC (10.5 hours)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Introduction (group A) - Advanced concepts on ballistic and quantum transport (5h). - Modelling Techniques for nanoscale devices: variability, statistical analysis, noise (3h theory + 2h lab) Introduction (group B) - Basics of semiconductors, band theory, electron transport (1.5 h) - The pn junction (3 h) - MOSFET transistors (5.5 h) From classic devices to quantum devices (23h) - Limits of device scaling, quantum effects in classic devices (3h) - Advanced MOSFETs, FINFETs (6h + 3h lab) - Nano transistors: JNTs, nanowires (2h) - Tunnel transistors (TFET) (6h + 3h lab) Quantum devices (19.5h) - Heterostructure devices and quantum confinement: quantum wells, quantum dots (1.5h) - Tunnel junctions, resonant tunnel devices, tunnelling models (3h + 3h lab) - Coulomb blockade device and single electron transistors (3h + 3h lab) - Silicon based qubits: basic concepts, spin, polarization (3h + 3h lab) Introduction to superconducting quantum circuits (7.5h): - the quantum Hamiltonian of a network of devices (3h) - LC resonator, transmission line, nonlinear resonator (Qubit), loops with Josephson junctions (SQUIDs) (4.5h)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The course consists of theoretical lectures and class practices. The latter include simple problem-solving activities and small computer program coding, with strict connections to theoretical lectures.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

The course is divided into three parts: 1) Introduction: 10 hours 2) Course body: 42.5 hours (33.5 theory + 9 lab) 3) Seminar part on superconducting quantum circuits: 7.5 hours The introduction is different for students coming from curricula providing a solid background on semiconductor devices (group A) and those who have no or insufficient knowledge in this field (group B). Before the course start, a preliminary assessment of the basic knowledge of semiconductor theory and the operation of elementary electron devices will be made by a multiple-choice quiz. Students will be then divided into groups A and B according to the quiz result, also taking into account their own choice. Students from group A will complement the preparation on electron devices with advanced topics on technological variability and quantum electron transport. These concepts, despite not necessary for the rest of this course, are of great relevance for a deeper understanding of quantum device fabrication and modelling issues. Students from group B will instead follow a specific path to bridge the gap in the basic electron device operation and modelling. The main course and seminar parts are instead common to all students. The course consists of lectures and lab sessions. Lectures cover the topics detailed in the Course Topics section and are delivered using slides on graphical tablet. The slides will be available to students in pdf format on the POLITO website at the beginning of the course. Laboratory practice sessions include software exercises where the students can work “hands on”, developing codes in MATLAB and/or using external software (NanoHub), to implement the theoretical concepts in significant case studies. The seminar dedicated to superconducting quantum circuits is tightly connected to similar parts specifically inserted in the courses of “Quantum Condensed Matter Physics “ and “Fundamentals of technological processes”, dedicated to the theory of superconductivity and the superconductor technology, respectively.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The course consists of theoretical lectures and class practices. The latter include simple problem-solving activities and small computer program coding, with strict connections to theoretical lectures.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

The course is divided into three parts: 1) Introduction: 10 hours 2) Course body: 42.5 hours (33.5 theory + 9 lab) 3) Seminar part on superconducting quantum circuits: 7.5 hours The introduction is different for students coming from curricula providing a solid background on semiconductor devices (group A) and those who have no or insufficient knowledge in this field (group B). Before the course start, a preliminary assessment of the basic knowledge of semiconductor theory and the operation of elementary electron devices will be made by a multiple-choice quiz. Students will be then divided into groups A and B according to the quiz result, also taking into account their own choice. Students from group A will complement the preparation on electron devices with advanced topics on technological variability and quantum electron transport. These concepts, despite not necessary for the rest of this course, are of great relevance for a deeper understanding of quantum device fabrication and modelling issues. Students from group B will instead follow a specific path to bridge the gap in the basic electron device operation and modelling. The main course and seminar parts are instead common to all students. The course consists of lectures and lab sessions. Lectures cover the topics detailed in the Course Topics section and are delivered using slides on graphical tablet. The slides will be available to students in pdf format on the POLITO website at the beginning of the course. Laboratory practice sessions include software exercises where the students can work “hands on”, developing codes in MATLAB and/or using external software (NanoHub), to implement the theoretical concepts in significant case studies. The seminar dedicated to superconducting quantum circuits is tightly connected to similar parts specifically inserted in the courses of “Quantum Condensed Matter Physics “ and “Fundamentals of technological processes”, dedicated to the theory of superconductivity and the superconductor technology, respectively.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

H. Ibach and Hans Lüth, Solid-State Physics: An Introduction to Principles of Materials Science, Springer 2009. T. Ihn, Semiconductor Nanostructures: Quantum States and Electronic Transport, Oxford Unix. Press, 2012. J. Davies, The physics of low-dimensional semiconductors, Cambridge Univ. Press, 2012. M. Tinkham, Introduction to superconductivity, McGraw-Hill, 2° edition, 1996. T. P. Orlando and K. A. Delin, Foundations of applied superconductivity, Addison-Wesley, 1991. Lectures notes produced by the teacher will be available on-line at the course web page.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

The teaching material includes the on slides for the lectures and the course notes. It will be distributed in pdf format by the teachers, and uploaded on the POLITO website before the course start. Some optional additive readings (i.e. fundamental historical papers, whitepapers, review papers, manuals, …) will be proposed by the teachers on the same above mentioned repository. Guidelines for the software Lab activity include notes and software templates.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

H. Ibach and Hans Lüth, Solid-State Physics: An Introduction to Principles of Materials Science, Springer 2009. T. Ihn, Semiconductor Nanostructures: Quantum States and Electronic Transport, Oxford Unix. Press, 2012. J. Davies, The physics of low-dimensional semiconductors, Cambridge Univ. Press, 2012. M. Tinkham, Introduction to superconductivity, McGraw-Hill, 2° edition, 1996. T. P. Orlando and K. A. Delin, Foundations of applied superconductivity, Addison-Wesley, 1991. Lectures notes produced by the teacher will be available on-line at the course web page.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

The teaching material includes the on slides for the lectures and the course notes. It will be distributed in pdf format by the teachers, and uploaded on the POLITO website before the course start. Some optional additive readings (i.e. fundamental historical papers, whitepapers, review papers, manuals, …) will be proposed by the teachers on the same above mentioned repository. Guidelines for the software Lab activity include notes and software templates.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

**Modalità di esame:** Prova scritta (in aula);

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

**Modalità di esame:** Prova orale obbligatoria;

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

**Exam:** Written test;

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

**Exam:** Compulsory oral exam;

...

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The Quantum Condensed Matter Physics exam consists of a written test aiming at addressing the degree of understanding achieved by the students on the subjects explained during the lectures (see expected learning outcome above). No supporting material is allowed during the exam. The exam aims at assessing the comprehension of the quantum condensed matter and nanophysics phenomema and to discuss the application of these concepts to quantum devices. When writing the exam sheet the student has to show that he/she is able to rigorously discuss and present the physical models introduced during the lectures, highlighting the approximations behind each model. The written test includes multiple-answer questions, statements (to be assessed as true or false) and two open questions covering all the course’s subjects. The maximum mark of questions/statements is 12/30, that of open questions is 18/30. The total allotted time is 90 min. The written test is passed with a score of at least 18/30. The final score will be obtained by averaging with the score obtained for the Electrons Devices part of the course.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Criteria, rules and procedures for the examination The exams aims at assessing the ability of the student to 1) describe each quantum device analysed during the course in terms of operation principles, modelling and fabrication techniques 2) compare quantum devices with classic counterparts, highlighting the advantages and the challenges for their exploitation 3) compare the various quantum devices and their exploitation in the current electronics scenario 4) present and discuss the codes developed during the software lab 5) describe the basic ideas of superconducting quantum circuits Points 1) and 4) are essential to pass the exam. Points 2)-3)-5) are evaluated with growing marks in terms of depth of understanding and synthesis capability. The exam is oral with both open questions and short exercises. The total allotted time is 30-40 minutes for each student. No books, notes or any other didactic material is allowed. The exam results are communicated directly to the students at the end of the exam session.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

**Exam:** Written test;

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

**Exam:** Compulsory oral exam;

Quantum Condensed Matter Physics/Quantum Devices (Quantum Condensed Matter Physics)

The Quantum Condensed Matter Physics exam consists of a written test aiming at addressing the degree of understanding achieved by the students on the subjects explained during the lectures (see expected learning outcome above). No supporting material is allowed during the exam. The exam aims at assessing the comprehension of the quantum condensed matter and nanophysics phenomema and to discuss the application of these concepts to quantum devices. When writing the exam sheet the student has to show that he/she is able to rigorously discuss and present the physical models introduced during the lectures, highlighting the approximations behind each model. The written test includes multiple-answer questions, statements (to be assessed as true or false) and two open questions covering all the course’s subjects. The maximum mark of questions/statements is 12/30, that of open questions is 18/30. The total allotted time is 90 min. The written test is passed with a score of at least 18/30. The final score will be obtained by averaging with the score obtained for the Electrons Devices part of the course.

Quantum Condensed Matter Physics/Quantum Devices (Quantum Devices)

Criteria, rules and procedures for the examination The exams aims at assessing the ability of the student to 1) describe each quantum device analysed during the course in terms of operation principles, modelling and fabrication techniques 2) compare quantum devices with classic counterparts, highlighting the advantages and the challenges for their exploitation 3) compare the various quantum devices and their exploitation in the current electronics scenario 4) present and discuss the codes developed during the software lab 5) describe the basic ideas of superconducting quantum circuits Points 1) and 4) are essential to pass the exam. Points 2)-3)-5) are evaluated with growing marks in terms of depth of understanding and synthesis capability. The exam is oral with both open questions and short exercises. The total allotted time is 30-40 minutes for each student. No books, notes or any other didactic material is allowed. The exam results are communicated directly to the students at the end of the exam session.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.

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Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY

Corso Duca degli Abruzzi, 24 - 10129 Torino, ITALY