Radiation-Matter Interaction: applications to Condensed Matter
Mathieu Gallart & François Fras (IPCMS)
This advanced optics class presents some fundamental aspects of light–matter interaction in condensed matter in order to understand and model how the response of charges to the electromagnetic field at the microscopic scale is responsible for optical properties of matter at the macroscopic scale. Students will be taught from basic concepts of the classical linear optical response of a medium to more advanced quantum optics such as field quantization or Bloch equation. They will learn to model optically–induced transition between electronic states in matter. We will highlight the connection between electronic structure and characteristic response of generic systems (atoms and molecules, metal, semiconductors or dielectric, crystalized and amorphous materials). The theoretical tools that will be introduced (semi–classical approximation, time dependent perturbations,
density matrix…) remain essential in numerous fields of physics. At the end of this course, students should be able to understand and interpret optical properties of condensed matter. They will master the fundamental tools that are essential to model light–matter interaction different systems that they will encounter during their future research. These skills will be useful not only to use optics as a characterization tool (interpretation of absorption or emission spectra…) but also to understand and model physical systems specifically designed for state–of–the–art optical applications (single photon sources, micro–cavity optics, nano–photonics).
Contents:
I- Phenomenological models of light-matter interaction
1- Classical model of an atomic dipole – Drude-Lorentz model
Free evolution, forced motion, susceptibility, dielectric function & refractive index
2- Einstein coefficients
Rate equations, relations between coefficients, dynamics
II- Single atom in a classical electromagnetic field
1- Introduction
2- Hamiltonian
Coulomb gauge, quantum Hamiltonian, Göppert-Mayer Gauge, electric-dipole Hamiltonian
3- Perturbative approach
Probability of transition under the influence of a sinusoidal E.M-field, resonance, validity of approximation, comparison with Einstein model
4–Non-pertubative approach in the case of a two-level system
Two-level system in interaction with an E.M-field, Rabi oscillations, Coherent transients and π/2 pulses
III- Density matrix treatment of a two-level system
1- Introduction
2- Essentials of the density-matrix
Definition, properties
3 Application to a two-level system – optical Bloch equations
Derivation of OBE, free evolution, driven system, analytical solutions
4- Bloch vector
The two level-system seen as a spin ½, definition of the Bloch vector, geometrical representation
5- Applications
Free evolution, driven system
IV Field quantization
1- Quantization of e single mode field
Single mode in a cavity, Eigenvalues & eigenstates, 1.4 Interpretation; 1.5 Expression of the quantized fields
2- Multimode quantization
Generalization, quantum fluctuations
3- Interaction with a quantized field – spontaneous emission
Atom + field Hamiltonian, spontaneous emission scheme, perturbative treatment, matrix element of the electric-dipole operator, density of final states, expression of the spontaneous emission rate, Purcell effect
V- Optical transition in atoms, the case of hydrogen
1- Introduction
2- Eigenstate & eigenfunctions
3- Optical transitions
Linearly polarized light, circularly polarized light
4- Fine structure
Spin-orbit coupling, Anomalous Zeeman effect
5- Applications
Double resonance method, optical pumping
VI Spectroscopy of diatomic molecules
1- Eigenstates of the H2+ molecule
Hamiltonian & Schrödinger equation, electronic equation, nuclear motion
2- Selection rules
Optical transitions, Vibration-rotation transitions, intersystem crossing & phosphorescence
VII- Optics of semiconductors & their nanostructures
1- Electronic states and band structure
Crystal structure, electronic states, fine structure, Bloch theorem, dispersion, effective mass
2- Band to band optical transitions
Calculation of the matrix element of the dipole operator, selection rules, absorption rate
3- Excitons
Experimental evidence, definition, Hamiltonian, center of mass, relative motion, wavefunction, excitonic absorption spectrum
4- Spontaneous emission
Spontaneous emission rate, photoluminescence, excitonic complexes, phonon replica,
5- Nanostructures
Growth, electronic properties, envelope function equation, quantum wells, confinement potential, eigenstates & eigenfunctions, density of states, inter-band transitions, quantum well excitons, effect of with fluctuations & inhomogeneous broadening, application: light emitting diode, quantum dots, self-assembled quantum dots & nanocrystals, density of states, simple analytical models of self-assembled QDs and nanocrystals, band to band transitions, size effect & emission energies, inhomogeneous broadening, single dot spectroscopy, multi-excitonic states, blinking of nanocrystals, single photon emission