An introduction to Quantum Mechanics, Quantum Optics and Quantum Science
To introduce students to key concepts in quantum mechanics, quantum optics and quantum science. For students with a working knowledge of mathematical physics who are interested in quantum systems, quantum communication & computing.
Upon successful completion of this course, students will be able to:
Explain foundational concepts in quantum mechanics and quantum optics, including wave-particle duality, quantum interference, and quantum states.
Describe the mathematical tools used in quantum science, such as linear algebra, Hermitian and unitary operators, and density matrices, and apply them to simple quantum systems.
Compare and contrast different types of quantum states (e.g., Fock, coherent, squeezed, thermal) and their relevance to quantum technologies.
Analyze the principles and applications of quantum entanglement, measurement, and quantum information, including cryptography, teleportation, and quantum communication.
Evaluate the role of quantum technologies in metrology and computation, including quantum sensing, quantum algorithms, and error correction.
Discuss current research topics in quantum science through seminar presentations and journal club participation, demonstrating critical engagement with primary literature.
This course will introduce key introductory concepts in quantum mechanics, quantum optics and quantum science. It is designed to provide a foundation for the more advanced courses in quantum science and technology offered at OIST. Topics will include: Wave particle duality, quantum interference, quantum states and their evolution, quantum cryptography, communication, computation and metrology. While sufficient mathematics knowledge is required to do well in the course, the focus is less on a rigorous mathematical approach than on covering a broad range of concepts and applications of quantum systems and technologies.
Topic 1: The Phenomena of Quantum Mechanics
- Particles and Waves
- Wave particle duality
- Quantum interference
Topic 2: Mathematical Prerequisites
- Linear Algebra
- Hermitian operators
- Projection operators and complete sets of states
- Unitary operators and Pauli matrices
- Traces of operators
- Density operators
Topic 3: Entanglement and Measurement
- Composite systems and partial traces
- Superposition and entanglement
- Measurement of quantum states
Topic 4: Quantum states and their characteristics
- Fock states
- Coherent states
- Squeezed states
o Application: Detecting gravitational waves
- Thermal states
Topic 5: Quantum states and their characteristics
- N00N states
- Distinguishing nonorthogonal quantum states
- Quantum state tomography
- Phase space distributions
Topic 6: Hamiltonians and Dynamics
- Simple Hamiltonians
- Quantum Dynamics
- Master equations
Topic 7: Quantum bits
- Quantum bits
- Entangled states
- EPR, Bell inequalities, and Local Realism
- Quantum information measures
Topic 8: Quantum cryptography
- Quantum non cloning
- Quantum random numbers generation
- Quantum key distribution
Topic 9: Advanced quantum communication
- Transmitting information with photons
- Quantum teleportation
- Quantum dense coding
- Quantum entanglement distribution
Topic 10: Quantum metrology
- Phase measurement: Heisenberg and Standard Quantum limits
- Quantum sensing
Topic 11: Quantum computation
- What is quantum computation?
- Quantum error correction
Topic 12: Quantum algorithms
- Deutch algorithm
- Search Algorithm
- Shor’s Algorithm
[*Topics covered will change depending on the class and their background]
Homework: 50%, Seminar/Journal Club on Hot topic: 50%
undergraduate quantum mechanics and linear algebra
Quantum Computation and Quantum Information, by M.A. Nielsen and I.L. Chuang (2010). Cambridge University Press
Introduction to Quantum Computing, by Ray LaPierre (2021). Springer Cham