Lectures on Quantum Optics and Quantum Information

Quantization of the Electromagnetic Field
• For each wave vector:
This equation is similar to the one describing the evolution of a
harmonic oscillator with frequency , which can be described
by a vector a, function of p (position) and q (momentum).
• By analogy, we introduce an operator a
and define a field operator :
We can also define the quadrature operators:
Where and can be identified to
the creation and annihilation operators for
harmonic oscillators
• By considering Fourier-limited wavepackets, it can be shown finally for one mode
(one dimension quantized harmonic oscillator) :
Total number
of photons