Description

Short description:

1 General concepts and theoretical background (10h)

• Using the Schrödinger equation: Free Evolution & interaction Picture; the Wigner-Weisskopf model (= coupling of a single state to a continuum of states): Markov approximation, Fermi Golden Rule, exponential population decay, Lorentzian spectral shape. The bath of independent harmonic oscillators; Application to spontaneous emission (exercise).

• Using the density operator formalism: interaction picture and partial trace: the Quantum Master Equation (QME) in the Born and Markov approximations; bath correlation functions.

• The Redfield and Lindblad formulations of the QME; Decoherence by population transfer and/or pure dephasing.

• Illustration on simple models (exercise): bath correlation functions; the open 2-level system; the open harmonic oscillator, expectation values of operators

• Quantum-classical correspondence (Wigner & P-distribution), quantum regression theorem, Wiener Khinchin theorem, noise spectral density, standard quantum limit on detection, shot noise

2 Application to light-matter interaction. I. Condensed phase (4h)

• The « molecular » (or « condensed-phase ») Hamiltonian : Born-Oppenheimer separation between electronic and vibrational degrees of freedom; the two-state molecule / spin-boson model. Interaction with light and Condon approximation: ex: fluorescence emission from a cold/hot molecule.

• Light-matter interaction & Linear response: dipole-dipole correlation function and lineshape function; vibrational motions, bath fluctuations & electronic decoherence: Pure dephasing.

3 Application to light-matter interaction. II. Quantum technologies (4h)

• Circuit QED (Blais, Rev. Mod. Phys 2021): quantization of LC oscillator; need for a nonlinearity: Kerr Oscillator; Jaynes-Cummings model, dispersive regime, Schrieffer-Wolff transformation, coupling to environment (qubit decay/dephasing time);

• Purcell effect/filter, control and read-out, signal-to-noise ratio, measurement induced dephasing, example: dissipation engineering for cooling and state preparation of a qubit.

Syllabus

Key topics:

• Bath & system-bath coupling; master equation, quantum regression theorem, noise spectra

• Electron-phonon coupling; linear response theory, dipole-dipole correlation function, lineshape function, pure dephasing.

• Jaynes Cummings Model, superconducting circuits, qubit measurement, dissipation engineering

Contacts

Responsable(s) de l'enseignement

• Jeremie Leonard

Responsable(s) de l'enseignement

• Anja Metelmann

MCC

Les épreuves indiquées respectent et appliquent le règlement de votre formation, disponible dans l'onglet Documents de la description de la formation.

Régime d'évaluation

CT (Contrôle terminal, mêlé de contrôle continu)

Coefficient

1.0

Évaluation initiale / Session principale - Épreuves

Seconde chance / Session de rattrapage - Épreuves