Physics 581 Spring 2018

Quantum Optics II

Credit: P. Grangier, "Make It Quantum and Continuous", Science (Perspective) 332, 313 (2011)

 

University of New Mexico

Department of Physics and Astronomy

 
Instructor: Prof. Ivan H. Deutsch
Lectures: Mon. and Wed. 12:30-1:45 PM, P&A Room 5

Office Hours: Wed. TBA

 
Teaching Assistant: Karthik Chinni
 

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)

 

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.

 

 

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, 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.

 

IV. Applications in quantum information processing

            A. Quantum communication

            B. Quantum computation

            C. Quantum metrology

 


 

Lectures
Notes in .pdf, Video in .mp4 (Quicktime).

 

Jan. 17

 

Review: Particles, Waves, Coherence, Density Matrix

 

 

Jan. 22

 

Review: Quantum Fields, Nonclassical Light - Glauber Theory

 

 

Jan. 24

 

Continuous variables: Squeezed states, general properties

 

 

Jan. 29

 

Quadratures, shot noise, and homodyne detection

 

 

Jan. 31

 

Introduction to nonlinear optics and the generation of nonclassical light

 

 

 

Feb. 5

 

Production of Squeezed Sates

 

 

 

Feb. 7

 

Parametric Downconversion

 

 

Feb. 12

 

On Travel: No Lecture

 

 

Feb. 14

 

On Travel: No Lecture

 

 

Feb. 19

Quasiprobability functions

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

 

 

 

Feb. 21

 

Continuation

 

 

Feb. 26

 

Tensor product structure and entanglement

Schmidt decomposition

 

Feb. 28

 

Entanaglement in quantum optics - particles and waves

 

 

 

Mar. 5

 

Twin photon pairs and two-mode squeezing

 

Mar. 7

 

Tests of Bells Inequalities in Quantum Optics

 

 

Mar, 12-16

 

Spring Break

 

Mar. 19

 

Intro to open quantum systems:

Quantum operations, CP maps, Kraus Representation

 

 

Mar. 21

 

Irreverisble bipartite system-reservoir interaction.

Markov approximation - Lindblad Master Equation

 

Mar. 26

 

Examples of Master Equation Evolution:

Damped two-level atom, damped SHO

 

 

 

Mar. 28

 

Fokker-Planck Equation and Decoherence

 

 

Apr. 2

 

Heisenberg-Langevin formulation of open quantum systems

Fluctuation-dissipation

 

Apr. 4

 

Quantum Trajectories I

Measurement theory

 

 

Apr. 9

 

Quantum Trajectories II

Quantum Monte-Carlo Wave Function Algorithm

 

 

 

Apr. 11

 

Quantum Trajectories III

Different Unravelings of the Master Equation

 

 

Apr. 16

The Stochastic Schrodinger Equation.

Quantum State Diffusion

 

 

Apr. 18

QND measurement and and the Stochastic Schrodinger Equation.

Case-Study: Spin Squeezing

 

 

 

 

Apr. 23

 

QND measurement and and the Stochastic Schrodinger Equation.

Case-Study: Spin Squeezing

 

 

 

Apr. 25

 

On Travel: No Lecture

 

 

Apr. 30

 

 

 

May 2

 

 

 

May 97

   

 

May 9