Notebook

Latex Headers¶

Ensure proper support for certain latex notation
Code below

$$\newcommand{\ket}[1]{\left|{#1}\right\rangle}$$$$\newcommand{\bra}[1]{\left\langle{#1}\right|}$$$$\newcommand{\braket}[2]{\left\langle{#1}\middle|{#2}\right\rangle}$$$$\newcommand{\adagger}[0]{\hat{a}^{\dagger}}$$$$\newcommand{\ahat}[0]{\hat{a}}$$$$\newcommand{\bdagger}[0]{\hat{b}^{\dagger}}$$$$\newcommand{\bhat}[0]{\hat{b}}$$$$\newcommand{\cdagger}[0]{\hat{c}^{\dagger}}$$$$\newcommand{\chat}[0]{\hat{c}}$$$$\newcommand{\ddagger}[0]{\hat{d}^{\dagger}}$$$$\newcommand{\dhat}[0]{\hat{d}}$$$$\newcommand{\edagger}[0]{\hat{e}^{\dagger}}$$$$\newcommand{\ehat}[0]{\hat{e}}$$$$\newcommand{\fdagger}[0]{\hat{f}^{\dagger}}$$$$\newcommand{\fhat}[0]{\hat{f}}$$

TEXT: Introduction to single photons¶

SPDC
Hanbury Brown-Twiss & Second order coherence $g^{(2)}$
1. classical
2. quantum
Single photon interference

Spontaneous Parametric Down-Conversion (SPDC)¶

Need to find/make some images

Review Article First, let's take a high level overview of what SPDC is. SPDC occurs when a pump photon is converted into 2 photons of less energy. Traditionally, one output photon is called the signal and the other is called the idler. This conversion adheres to energy conservation and momentum conservation. Our system is degenerate in wavelength: both output photons have the same wavelength.

Energy Conservation

images from hc photonics

Momentum Conservation

(image frome review paper)

Recall that momentum is a vector, so the magnitude and direction need to be maintained. This is why we see that the signal and idler photons are non-colinear (they travel in different directions): their sum still matches the pump photons.

Matching the momentum is an essential part of generating SPDC. As you recall, $$\overrightarrow{k} = \frac{2\pi n}{\lambda}$$ where $n$, the index of refraction, is a function of $\lambda$, the wavelength of the light.

Different types of SPDC

SPDC is divided into different types based on the polarization of the pump and signal and idler photons. For our experiment, we'll only be using type 1 SPDC. (image from HC Photonics)

SPDC in quED

(from quTools Manual)

Walk through the math to show how it's quantum
Uses of SPDC

In [7]:

from IPython.display import Video
Video("testvideo.mov")

Out[7]:

Hanbury Brown-Twiss¶

Following Loudon, let's walk through the HBT experiment for a single photon.

Set-up the experiment following Loudon¶

Second order time coherence¶

Work out the quantum and show the results for coherent light and Fock states. Present the results for other light sources.

HBT experiment with SPDC