Quantum Aspects Of Optical Communications Assignment


Physics 581 Fall 2014

Quantum Optics II


University of New Mexico

Department of Physics and Astronomy

Instructor: Prof. Ivan H. Deutsch
Lectures: Tues. and Thurs. 5:15-6:30 PM, P&A Room 184

Office Hours: Wed. 10:00-11:00, Room 23

Teaching Assistants: Bob Keating

Problem Session: 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.

In this year long course will develop the tools necessary to analyze these problems and apply them to contemporary research problems.  Topics to be studied include:

Quantum Optics I (Physics 566)

- Quantum and classical coherence
- Atom-photon coupling and atomic coherence
- The quantum electromagnetic vacuum
- Nonclassical light and photon statistics

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)


On this page:


General Information


"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.




* 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, Tuesdays.




Tentative Syllabus


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.


III. Continuous measurement

            A. Quantum trajectories – different unravelings of the Master Equation.

            B. Quantum Monte-Carlo wave functions.

            C. The stochastic Schrödinger equation.

            D. Quantum filtering theory.


IV. Fundamental Paradigms of quantum optics

            A. Cavity QED (from atoms to superconductors)

            B. Ion traps.

            C. Cold neutral atom ensembles.

            D. Correlated photons and squeezed states.


V. Applications in quantum information processing

            A. Quantum communication

            B. Quantum computation

            C. Quantum metrology




Review: Quantum Optics, Coherence, and Quantum Fields


Continuous variables: Squeezed states, general properties


Quadratures, shot noise, and homodyne detection

Podcast 3

Introduction to nonlinear optics and the generation of nonclassical light



Linear optics, three-wave mixing

No Podcast -- Sorry

Production of Squeezed Sates

Parametric Downconversion

Quasiprobability functions

Wigner (W), Husmi (Q), and Glauber (P)

Podcast 7


Tensor product structure and entanglement

Lecture 5

Podcast 8


No lecture -- SQuInT

Entanglement and different degrees of freedom

Podcast 10

Entanaglement in quantum optics - particles and waves

Twin photon pairs and two-mode squeezing

Podcast 12



Test of Bell's Inequalities in Quantum Optics

Podcast 13


Intro to open quantum systems:

Quantum operations, CP maps, Kraus Representation

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation


Podcast 16


Apr. 1


Apr. 5

Examples of Master Equation Evolution:

Damped two-level atom, damped SHO

Podcast 19

Fokker-Planck Equation and Decoherence

Heisenberg-Langevin formulation of open quantum systems


Podcast 21

Quantum Trajectories I

Master equation: quantum jump picture



Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm


Quantum Trajectories III

Different Unravelings of the Master Equation


Quantum Trajectories IV

Quantum State Diffusion

Continuous Measurement -- The Stochastic Schrödinger Equation

Case study -- Spin squeezing

Podcast 28




Problem Sets




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