Office Hours: TBA
Synopsis: All quantum systems
interact with their environment, be it through unwanted interactions with a noisy
bath of thermal and quantum fluctuations, or because we want to
observed the system through a quantum measurement. This
class will cover the foundations of open quantum systems and its
relationship to classical nonequilibrium statistical
physics. New features arise in quantum mechanics --
entanglement and negative probabilities -- with profound
implications. With a foundation in open quantum
systems, we will address fundamental processes in quantum
mechanics: dissipation, decoherence, and measurement.
Jan. 17 |
Introduction to
Open Quantum Systems:
Dissipation, Irreversibility, Decoherence, Measurement |
Lecture
#1 |
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Jan. 19 |
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Lecture #2 | |
Jan. 24 |
Qubit Dynamics: Rabi
Oscillations |
Lecture #3 | |
Jan. 26
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Qubits : Phenomenological Damping - Bloch equations |
Lecture #4 | |
Jan. 31 |
Bosons: Simple harmonic oscillator
Fock states, coherent states, Boson algebra |
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Feb.2 |
Introduction to Phase Space
Representations
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Feb. 7 |
Quasiprobability
functions Wigner (W),
Husumi (Q), and Glauber (P)
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Feb. 9 |
Dynamics in Phase Space |
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Feb. 14 |
Tensor product structure and entanglement
Schmidt decomposition |
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Feb. 16 |
Intro to open quantum system
dynamics: Quantum operations, CP maps, Kraus Representation |
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Feb. 21 |
Quantum Channels for qubits |
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Feb.
23 |
Irreversible bipartite system-reservoir interaction. Markov
approximation - Lindblad Master Equation
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Feb. 28 |
Derivation of the Lindblad Master Equation Born-Markov approximation |
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Mar. 2 |
Continuation
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Mar. 7
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Examples of Master Equation Evolution: Damped two-level atom |
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Mar. 9
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Damped Simple
Harmonic Oscillator
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Mar. 13-17 |
Spring Break |
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Mar. 21 | Stochastic Processes |
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Mar. 23 |
Brownian Motion and Langevin Equation
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Mar. 28 |
Heisenberg
-Langevin Equations
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Mar. 30 |
Fokker-Planck Equation | ||
Apr. 4 |
Damped Simple Harmonic Oscillator
in Phase Space
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Apr. 6 |
Continuation |
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Apr. 11 |
The Truncated Wigner
Approximation |
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Apr. 13 |
Quantum Trajectories I Measurement theory |
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Aprl. 18
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Quantum Trajectories II Quantum Monte-Carlo Wave Function Algorithm |
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Apr. 20
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Different Unravelings of the Master Equation |
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Apr. 25
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The Stochastic Schrodinger Equation. Quantum State Diffusion |
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Apr. 27 |
QND measurement and and the Stochastic Schrodinger Equation |
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May 2 |
Slack
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May 4
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Slack |
Problem Set #1 |
Problem Set #2
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Problem Set #3
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Problem Set #4
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Problem Set #5
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