Topics of the Lectures 

Lecture 1 - 27/09/2023 

Introduction to the course. The photoelectric effect, revisited. Semi-classical approach to light-matter interaction. Time-dependent pertubation theory. The Fermi's Golden Rule.  

REFERENCES: Introductory slides (click here!),  Lamb and the photoelectric effect  (click here!), GK: Ch. 4 (4.1-4.2).  

Lecture 2 - 29/09/2023 

Photon-counting statistics with a coherent beam of light: "quantum" and "semi-classical" approaches. Poissonian distribution. Semi-classical theory of photodetection. 

Photocounting statistics of a fluctuating field: the Mandel formula. Classification of light by photon statistics: Poissonian, Super-Poissonian, and sub-Poissonian light.

REFERENCES: FOX: Ch. 5 (5.1,  5.2, 5.3, 5,4 , 5,5 , 5.8) -  LOU: Ch. 3 (3.9) -  Undergradutate experiment: photon-counting statistics  (click here!)

Lecture 3 - 11/10/2023 

Discharge lamps and a model for chaotic light sources.  Stochastic processes: definition of stationary and ergodic processes. Intensity fluctuations of chaotic light: calculation of the probability distribution and its variance. 

REFERENCES: LOU: Ch. 3 (3.6, 3.9)

Lecture 4 - 13/10/2023 

Mandel formula applied to a chaotic light source: from Bose-Einsterin to Poissonian distribution. Further details on the Mandel formula and its connection to the second order correlation function:  Mandel Q paramenter. Thermal light and and the super-Poissonian carachter of balck-body radiation. Degradation of photon statistics by optical losses. Quantum theory of photodetection. Experiments demonstrating the existence of sub-poissonian sources of light: Frank-Hertz experiment in space-charge limited-current regime; Experiments performed with a beam of single atoms. 

REFERENCES: FOX: Ch. 5 (5.5, 5.6) - LOU: Ch. 3 (3.9)  - Paper on the Franck-Hertz experiment (click here!) - Paper on the "single" atom experiment (click here!)

Lecture 5 - 18/10/2023 

Classical theory of the beam splitter. The Michelson and the Mach-Zender interferometer. Coherence and degree of first order coherence.  Calculation of the degree of first order coherence function for 1) a coherent source of light with constant intensity 22) chaotic light sources with different broadening mechanisms: Collision broadening, lifetime broadening, Doppler broadening. Link between the degree of first order coherence and the frequency spectrum (the Wiener-Khintchine therorem).

REFERENCES: FOX: Ch. 2 (2.2,  2.3) -  LOU: Ch. 3 (3.2, 3.3, 3.4, 3.5) 

Lecture 6 - 20/10/2023 

Degree of second order coherence. Hanbury-Brown and Twiss interferometer. Calculation of the second order correlation function for  a coherent source of light with constant intensity and for chaotic light sources. Connection between the first order and second order correlation functions. Calculations of the bounds of the second order correlation function (for any classical light source). New definition of light sources according to the value of the second order  correlation function at zero time delay: Photon bunching and antibunching.  Experimental demonstrations of photon antibunching. Kimble experiment with "single atoms". Experiments with single "artificial atoms".  Triggered single photon sources. The differences between the two classifications of non-classical light sources: photon antibunching vs. sub-poissonian photon statistics. Calculation of the Mandel Q parameter for chaotic light sources with collision broadening.

REFERENCES: FOX: Ch. 6 (6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7) -  LOU: Ch. 3 (3.7, 3.9).  Slides presented during the lecture (click here!)  Kimble experiment (click here!) - Michler experiment (click here!) - Photon Antibunching vs. sub-poissonian photon statistics (up to equation  4, click here!)

Lecture - 25/10/2023 

CANCELLED

Lecture 7 - 27/10/2023 

How to quantize the electromagnetic field. Hamilton's equations. Potential theory for the classical electromagnetic field.  Coulomb gauge and the Helmotz theorem. The quantum harmonic oscillator: review of the basic concepts and formulas using the raising and lowering operators.

REFERENCES:  LOU: Ch. 4 (4.1, 4.2, 4.3, 4.4) 

Lecture 8 - 03/11/2023 

Quantization of the electromagnetic field.  Fock states. Multi-mode and single-mode states. Fock state or photon number states. Discusssion about the concept of "photon". The quadrature operators in the classical and quantum pictures. Quantum noise. Vaccum fluctuations. Fock state as highly non-classical states of light.

REFERENCES:  LOU: Ch. 4 (4.4), Ch. 5 (5.1, 5.2) 

Lecture 9 - 08/11/2023 

Coherent or quasi-classical states.  Discussion of the main properties of coherent states: expectiation value of the electric field and noise for a coherent state. Phase-space pticture of coherent states. Displacement operator.  Generatio of coherent states.

REFERENCES:  LOU: Ch. 5 (5.3), GK: Ch. 3 (3.1-3.6) 

Lecture 10 - 10/11/2023 

Quadrature squeezing and squeezed states. Squeeze operator. Squeezed vaccum state. Decomposition into Fock states. Statistical properties of the squeezed vacuum state.

Introduction to the practical experience: Research seminar on " Sources of Single Photons Based on Semiconductor Quantum Dots" from Dr. Michele Rota. 

REFERENCES: LOU: Ch. 5 (5.5, 5.6), GK: Ch. 7 ( 7.1).  Slides (click here)

Lecture 11 - 14/11/2023 - Practical experience - Lab Nanophotonics 

Practical experience "Hanbury-Brown and Twiss experiment: Estimating the degree of second-order coherence for a single-photon source and a laser".

REFERENCES:  Slides (click here)

Lecture 12 - 15/11/2023 

Squeezed coherent state: Definition and main properties.  Amplitude- and phase-squeezed coherent states: From super-poissonian to sub-poissonian statistics. Application of squeezed states in gravitational-wave interferomenters (only qualitative discussion). Pure states and statistical mixtures. Introduction to the density operator: main properties. Thermal states and chaotic light states: Probability distributions and density operators. Photon statistics and representation  of thermal states and chaotic light states in the phase-space picture.  

REFERENCES: LOU: Ch. 4 (4.6), Ch. 5 (5.4), GK: Ch. 2 (2.5)  Ch.7 (7.1). Paper on the "Measurement of the quantum states of squeezed light", click here!  Paper on the gravitational-wave interferometer: click here

Lecture 13 - 17/11/2023 

Quantum mechanics of the beam splitter. Input-output relations. Single-photon input: the appearance of entanglement. Coherence state at the input port of the beam splitter. Discussion and summary of the the properties of the different excitations of the electromagnetic field studied in the previous lectures. Short summary of the different classification of the light beams: classical and non-classical light. Intensity measurements in the quantum picture. The photon intensity operator. Quantum degree of first and second order coherence. Calculation of the second order correlation functionfor the the different excitations studied in the previous lectures (only single mode).  

REFERENCES:  LOU: Ch 4 (4.11), Ch. 5 (5.7, 5.8, 5.10), GK:Ch. 5 (5.2, 5.4) , Ch. 6 (6.1, 6.2) 

Lecture 14 - 22/11/2023 

Second order correlation function "before and after" the beam splitter.  Two single photon states at the input of a beam splitter: The Hong-Ou-Mandel effect. The classical Mach- Zender interferometer: input-output relations. The quantum Mach-Zender interferometer. Interferometry with a single photon.  The Grangier experiment. Interaction-free measurements.

REFERENCES:  LOU: Ch. 5 (5.8), GK: Ch. 6 (6.2, 6.3, 6.4) . Paper on the Hong-Ou-Mandel effect, click here! Paper on the Grangier experiment, click here!

Lecture 15 - 24/11/2023 

Balanced homodyne detection. Multimode and continuous-mode quantum optics. Formalism for the continuous-mode theory.  Continuous-mode photon number states. Photon wave packets.  Calculation of the intensity at the detector. 

REFERENCES:  LOU: Ch. 6(6.1, 6.2, 6.3, 6.11). Ch. 7 (7.3). See also lecture notes.

Lecture 16 - 29/11/2023 

Continuous-mode photon number states. Probability of photon-detection.  Mach-Zender interferometry with continuos-mode single-photon states: differences with resepct to the case of single-mode states. More insights on the Hong-Ou-Mandel: Time-resolved two-photon interference. 

REFERENCES:  LOU: Ch. 6(6.6-6.8).  Time-resolved two-photon interference, click here! Quantum beat of two single photons,  click here!

Lecture 17 - 01/12/2023 

Introduction to the light-matter (atom) interaction. The interaction Hamiltonian in the semi-classical approach.  The "length" gauge. The case of a weak interaction: time-dependent perturbation theory. Light-atom interaction: the two-level atom. The case of strong interaction: The Rabi model with no detuning. 

REFERENCES:  LOU: Ch. 2(2.1, 2.2). GK: Ch. 4 (4.1, 4,2, 4.4). FOX: Ch. 9 (9.5.1) 

OPIS survey , click here!

Lecture 18 - 05/12/2023 - 12:00-14:00 - Aula C, Dipartimento di Chimica, Cannizzaro building (2 hours)

Again on the Rabi model: the case with detuning. The rotating frame of the atom and of the field.  Optical Bloch equations. Spontaneous emission. Damping of the Rabi oscillations. Experimental observation of Rabi oscillations (experiments of Gibbs).

REFERENCES:  LOU: Ch. 2(2.7, 2.8). See also Ch. 5.2, 5.3 of D.A. Steck "Quantum and Atom Optics". Paper on the Gibbs experiments, click here.

Lecture 19 - 13/12/2023 

Steady-state solutions of the optical Bloch equations. Resonance fluorescence spectroscopy.  Power broadening of the atomic transitions. Bloch Sphere and Bloch vector. Dynamics of the two-level system on the Bloch sphere. 

REFERENCES:  FOX: Ch. 9 (9.6). LOU: 2.8. See also Ch. 5.4, 5.5.1, 5.5.2, 5.5.3, 5.6, 5.7,1  of D.A. Steck "Quantum and Atom Optics". 

Lecture 20 - 15/12/2023 

Full quantum treatment of light-matter interaction. Second quantization of the atomic Hamiltonian. Rotating wave approximation. Full Hamiltonian in the Schoedinger and in the Dirac (interaction) picture. Matrix elements, absorption, emission and the appearance of spontaneous emission. The Jaynes-Cummings model.  Quantized Rabi oscillations. Vacuum Rabi oscillations. Interaction between a two-level system and a coherent state. Collapse and revival of Rabi oscillations. Experimental demonstration of quantized Rabi Oscillations as well as collapese and revival or Rabi oscillations. 

REFERENCES:  LOU: 4.9, 4.10,  GK: Ch. 4 (4.5) Ch. 10 (10.3). See also Ch. 6.1 and 6.2 of "Quantum Optics", by M-S. Zubairy and M. O. Scully,  Cambridge University Press.  Paper on the experimental demonstration of quantum Rabi Oscillations, click here.

Lecture 21 - 20/12/2023 

Cavity quantum electrodynamics: distinction between strong and weak coupling regimes. Damping of vacuum Rabi oscillations. Weisskopf-Wigner theroy of spontaneous emission in free space. Calculation of the photon decay rate. Calculation of the single photon "wavefunction" for the case of spontaneous emission.

REFERENCES:  See Ch. 6.3 of "Quantum Optics", by M-S. Zubairy and M. O. Scully,  Cambridge University Press and Ch. 11.1, 11.2, 11.3, 11.4 of D.A. Steck "Quantum and Atom Optics". 

Lecture 22 - 22/12/2023 

Calculation of the transition rate for an atom in free-space using perturbation theory.  Fundamental properties of Fabry-Perot cavities and resonant modes.  Weak coupling regime: Calculation of the transition rate for an atom in a single-mode cavity. The Purcell effect. Experimental demonstration of the Purcell effect using "artificial atoms" in semiconductor micro cavities.  

REFERENCES:  FOX: Ch. 10 (10.1, 10.2),  Paper on the experimental demonstration of the Purcell effect, click here!