Hi. I am going to start my MSc in a couple of months majoring in nonlinear quantum optics. I have a good basic in quantum mechanics, but have never looked at quantum optics before. My topic will be to investigate quantum properties of nonlinear optical coupler but i have problem with the construction of the Hamiltonian for interacting optical fields. For starting, i start with two mode nonlinear optical coupler(adsbygoogle = window.adsbygoogle || []).push({});

H= hω(a1b1+a2b2)+hωg(a1^2 b1^2+a2^2 b2^2) + hk(a1b2+b1a2)

h=planck constant (h bar)

ω=angular frequency

an= creation operator associated with the optical mode

bn=annihilation operator associated with the optical mode

g=nonlinear susceptibility

k= coupling constant

I will really appreciate it if anyone can explain the physical meaning of this Hamiltonian and how do we construct such equation to describe the system.

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# Construction of Hamiltonian for interacting optical fields

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