2022 Quantum Physics in Optical Response of Materials

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Academic unit or major
Graduate major in Materials Science and Engineering
Nakamura Kazutaka 
Class Format
Lecture    (Livestream)
Media-enhanced courses
Day/Period(Room No.)
Mon1-2()  Thr1-2()  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

This course gives fundamentals of quantum mechanical description for interaction between light and matter. The students learn description of quantum state using state vectors, equation of motions with three pictures, harmonic oscillators, coherent states. In addition, recent research results of coherent control will be presented.

The aim of this course is to understand the light matter interaction using quantum mechanical description.

Student learning outcomes

By the end of this course, students will be able to:
1) describe photo induced process in materials by using quantum mechanics
2) solve typical problems on light-matter interaction.


Quantum mechanics, light matter interaction, non-linear spectroscopy, Ultrafast Phenomena, Laser

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

After the lecture on topics, the exercise are sometimes presented. By solving problems in exercise terms, students can evaluate their understanding.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Time evolution of quantum state Learn the equation of motion for a quantum system i.e. Shrodinger, Heisenberg, and Interaction pictures. Learn the equation of motion for a quantum system i.e. Shrodinger, Heisenberg, and Interaction pictures. A quantum system is described using a state vector.
Class 2 Density operator Learn how to describe the system with a density matrix; time evolution of density matrix and Feynman diagram.
Class 3 Light interaction in two-level system Lean the interaction of light pulse with a simple two-level system.
Class 4 Double-sided Feynman diagrams Learn how to use the Double-sided Feynman diagrams for optical nonlinear optical processes.
Class 5 Harmonic oscillator Describe harmonic oscillator as quantum mechanics and learn on creation/annihilation operators and number states.
Class 6 Time evolution in harmonic oscillator Study time evolution of superpositions states in a harmonic oscillator
Class 7 Coherent state Describe harmonic oscillator as quantum Learn the coherent states; definition and character.
Class 8 Squeezed state Learn the squeezed states; definition and character.
Class 9 One dimensional lattice vibration Learn the .lattice vibration in one dimensional chain
Class 10 Field quantization and phonon Learn the field quantization of one-dimensional lattice vibration and phonon.
Class 11 Coherent phonons: Experiment of ultrafast spectroscopy Learn the coherent phonons and experiment with ultrafast spectroscopy.
Class 12 Coherent phonons: Theory Learn how to treat coherent phonon with quantum mechanics
Class 13 Time evolution of coherent-phonon amplitude Learn the time evolution of coherent-phonon amplitude
Class 14 Summary of lecture and check understanding Check each understanding on the quantum descriptin for the light matter interaction.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


I am planning to lecture along the book "Quantum Phononics" by K. Nakamura (Springer, 2019).
However, students can study using the following reference books instead of the above book.

Reference books, course materials, etc.

"Modern Quantum Mechanics" by J.J. Sakurai and J.J. Napolitano (Pearson Education Limited 2014) ISBN 10:1-292-02410-0
"Introductory Quantum Optics" by C. C. Gerry and P. L. Knight (Cambridge University Press, 2005) ISBN 978-0-521-52735-4
"Quantum Field Theory of Solids" by H. Harken (North-Holland Publishing, 1976)
"Principles of Nonlinear optical spectroscopy" by S. Mukamel (Oxford University Press 1995) ISBN 0-190509278-3

Assessment criteria and methods

Students are evaluated whether they understand the quantum description of the light matter interaction based on the score of the test and exercises.

Related courses

  • MAT.A203 : Quantum Mechanics of Materials
  • PHY.Q435 : Quantum Information

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are required to take the credits on "Quantum Physics" or "Quantum Chemistry" or related subjects in undergraduate courses.

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