Credit: P. Grangier, "Make It Quantum and Continuous", Science (Perspective) 332, 313 (2011)
Office Hours: Wed. TBA
Quantum
optics is a broad and varied subject that deals with the study, control, and
manipulation of quantum coherence associated with electromagnetic fields. This
includes nonclassical optical media, the basic interaction of photons and
atoms, and the nonclassical nature of the electromagnetic field itself.
Quantum optics is the natural arena for experimental tests of the foundations
of quantum mechanics and measurement, especially in the context of open,
nonequilibrium quantum systems. Most recently, developments in theory and
experiment have led to the possibility of applying the coherent control of
quantum optical systems to perform completely new information-processing
paradigms such as quantum communication and quantum computation.
Quantum Optics II (Physics 581)
- Quantum optical particles and waves (discrete and continuous variables)
- Foundations of entanglement and quantum maps
- Open quantum systems and decoherence
- Quantum trajectories and continuous measurement
- Fundamental paradigms in quantum optics (cavity QED, ion and neutral atom
traps, entangled light)
- Applications in quantum information science (quantum communication,
computation, metrology)
"Recommended" Texts (none required):
* Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light - Gryberg, Aspect, Fabre
* Quantum Optics - Scully and Zubairy,
* Quantum Optics, by R. Y. Chiao and J. C. Garrision
* Quantum Optics, by M. Fox
We will not be following any of these texts directly . They all have strengths in different areas and are good to have on your bookshelf.
Grading:
* Problem Sets (5-8 assignments) 75%
* Final Project 25%
* Problem sets will be available on the web, about every other week. Generally assignments will be due in class, Wednesdays.
Phys. 581: Quantum Optics II
I. Nonclassical Light
A. Nonlinear
optics and nonclassical light.
B. Squeezed
states.
C. Homodyne
detection.
D. Phase space methods -- Quasiprobability distributions, P-Glauber, Q-Husimi,
W-Wigner functions.
E.
Correlated twin photons.
II. Foundations
A. Bipartite entanglement.
B. EPR and
Bell’s Inequalities, finite and infinite dimensional systems.
C.
Completely-positive map, Kraus operators, and POVMs.
III. Open quantum systems
A. System-reservoir interactions.
B. Born-Markoff approximation and the Lindblad Master Equation.
C.
Phase-space representation: Fokker-Planck equation.
D.
Heisenberg-Langevin equation.
IV. Continuous measurement
A. Quantum trajectories – different unravelings of the Master Equation.
B. Quantum Monte-Carlo wave functions.
C. The
stochastic Schrödinger equation.
V. Applications in quantum information processing
A. Quantum communication
B. Quantum
computation
C. Quantum
metrology
Jan. 17 |
Review: Particles, Waves, Coherence, Density Matrix |
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Jan. 22 |
Review: Quantum Fields |
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Jan. 24 |
Review: Nonclasiscal Light - Glauber Theory
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Jan. 29 |
Continuous variables: Squeezed states, general properties |
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Jan. 31 |
Quadratures, shot noise, and homodyne detection
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Feb. 5 |
Introduction to nonlinear optics and the generation of nonclassical light |
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Feb. 7 |
Three Wave Mixing Production of Squeezed Sates |
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Feb. 12 |
On Travel: No Lecture |
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Feb. 14 |
On Travel: No Lecture |
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Feb. 19 |
Introduction to Phase Space Representations
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Feb. 21 |
Continuation |
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Feb. 26 |
Continuation |
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Feb. 28
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Quasiprobability functions Wigner (W), Husmi (Q), and Glauber (P) |
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MAKE-UP Mar. 1 |
Tensor product structure and entanglement
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Mar. 5 |
Schmidt decomposition
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Mar. 7 |
No Lecture -- Travel to March Meeting
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Mar, 12-16
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Spring Break |
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Mar. 19
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Entanglement in quantum optics - particles and waves |
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Mar. 21
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Parametric Conversion I Type I phase matching: Time energy entanglement |
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Mar. 22 MAKEUP
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Parametric Conversion II Spatial mode and polarization entnaglement Two-mode squeezing and CV entanglement |
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Mar. 26 |
Tests of Bells Inequalities in Quantum Optics |
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Mar. 28 |
Intro to open quantum systems: Quantum operations, CP maps, Kraus Representation
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Mar. 29 MAKEUP
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Irreverisble bipartite system-reservoir interaction. Markov approximation - Lindblad Master Equation |
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Apr. 2 |
Derivation of the Lindblad Master Equation Born-Markov approximation
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Apr. 4 |
Examples of Master Equation Evolution: Damped two-level atom |
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Apr. 9 |
Damped Simple Harmonic Oscillator
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Apr. 11 |
Fokker-Planck Equation and Decoherence |
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Apr. 16 |
Quantum Trajectories I Measurement theory |
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Apr. 18 |
Continuation Nonlinear Stochastic Jump Equation |
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Aprl. 19 MAKEUP
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Quantum Trajectories II Quantum Monte-Carlo Wave Function Algorithm |
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Apr. 23 |
Quantum Trajectories III Different Unravelings of the Master Equation
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Apr. 25
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On Travel: No Lecture |
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Apr. 30 |
Continuation |
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May 2 |
The Stochastic Schrodinger Equation. Quantum State Diffusion
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QND measurement and and the Stochastic Schrodinger Equation |
Problem Set #1 |
Problem Set #2 |
Problem Set #3 |
Problem
Set #4
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Problem
Set #5
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