ECE 406

• Electromagnetic fields quantization; non-classical light; quantum correlations
• Quantum nonlinear optics
• Open quantum systems; input-output formalism; Master equation
• Atom-light interaction; cavity-QED
• Optical quantum computing
• Superconducting quantum circuits
• Mechanical quantum systems
• Quantum measurement

Quantum mechanics

“Quantum Optics,” by D. F. Walls and G. J. Milburn

“Introductory Quantum Optics,” by C. Garry and P. Knight.

“Quantum Optics: An Introduction,” by M. Fox.

To introduce students with fundamental physics of quantum optics and related analytical methods. To apply the concepts and methods in quantum optics to analyze quantum systems and platforms for quantum sensing, quantum computing, and quantum networking.

A. By the midterm, the students should be able to do the following:

• Be familiar with identities of operators. Calculate expectation values and variance of observable using operators. (1)
• Understand the procedure of quantization of harmonic oscillators. Be familiar with creation and annihilation operators. (1)
• Understand the procedure of electromagnetic field quantization. (1)
• Understand the properties of Fock states and coherent states. (1)
• Understand the properties of squeezed states. (1)
• Understand the properties of beamsplitters. Analyze quantum light transmission through beamsplitters and circuits involving beamsplitters. (1,2)
• Understand the concept of correlation functions. Calculate first and second-order correlation functions of classical and quantum light. (1)
• Understand photon correlation measurements. Analyze photon statistics based on the second-order correlation function. (1,2)
• Analyze single-mode nonlinear optical systems and understand associated quantum optical effects. (1,2)
• Analyze two-mode nonlinear optical systems and understand associated quantum optical effects. (1,2)
• Analyze basic optical circuits for quantum logic gates. (1,2,6)

B. By the end of the course, the students should be able to do all of the items listed under A, plus the following:

• Understand the input-output formalism. Analyze open quantum systems, such as waveguide-coupled lossy optical cavities, using the input-output formalism. (1,7)
• Analyze physics of quantum optomechanics using the input-output formalism. (7)
• Understand Master equation. Analyze open quantum systems, such as damped harmonic oscillators, using Master equation. (1,7)
• Calculate correlation functions using quantum regression theorem. (1)
• Understand and analyze the physics related to atom-field interaction using Jaynes-Cummings model, including Rabi splitting, spontaneous decay and dephasing, Purcell effect, photon anti-bunching. (1,7)
• Analyze the cavity-QED system. Understand the application of cavity-QED systems for CNOT gate and entanglement between quantum emitters. (1,2,7)
• Be aware of several practical cavity-QED platforms, in particular solid-state platforms. (1,2,6,7)
• Understand the quantization of LC resonators. Analyze Josephson junctions and basic superconducting qubits. (1,6)
• Understand properties of weak continuous measurement. (1)
• Understand and analyze quantum non-demolition measurement. Design optical circuits for quantum non-demolition measurement of field quadratures. (1,2,7)