9772

Q-Representation of Number States

Quasi-probability densities represent the density operator of optical fields. Here the special quasi-probability densities are plotted as functions of and for the first eleven photon numbers . The complex variable is an eigenvalue of the non-Hermitian annihilation operator . The number state of the field is an energy eigenstate of the same field also. This means that in these plots the optical fields can be characterized by exactly photons.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

As usual in quantum optics, the density operators of light fields can be represented by normalized real-valued functions. There are three types of functions: , and are the P-representation (Glauber-Sudarshan representation), the Q-representation and the Wigner-Weyl distribution, respectively. For example, the diagonal elements of the density operator define the Q-representation: is a real, well-behaved, non-negative definite and bounded function of the complex variable ; . The set of states forms the basis of coherent states, the eigenstates of the annihilation operator . Note that the quasi-probability densities are not genuine probability densities, but they are suitable to calculate expectation values (mean values) of ordered operator products. In our case, expectation values of antinormal ordered operator products can be calculated with the help of the Q-representation.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+