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Open quantum systems
Master PhysiqueParcours Physics of Quantum and Soft Condensed Matter
ComposanteFaculté de physique et ingénierie
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.