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- Characteristic Functions in Quantum Optics for linear amplifiers/attenuators

Hi everyone,

I am following along with the MIT OCW quantum optical communication course. I have a question about this chapter, concerning the linear attenuators and amplifiers.

Specifically, the chapter mentions that they are not going to get ##\rho_{out}##, but I am interested in this.

More specifically, I am curious about the number of photons detected from the output <n|##\rho_{out}##|n>, which I know will be a function of the arbitrary input state <n|##\rho_{in}##|n>.

I am at the point where I have the antinormal characteristic function ##\chi_{out}(\eta,## ##\eta^*)=\chi_{in}(\eta \sqrt{G}##, ##\eta^*\sqrt{G})## for an arbitrary gain ##G>1##. How do I proceed from here to get <n|##\rho_{out}##|n>? Do I just take the operator-valued inverse fourier transform, as suggested earlier in the course? If so, I don't know how to do this, so if someone could provide some help in this calculation for a non-coherent state I would appreciate it.

Cheers,

W

I am following along with the MIT OCW quantum optical communication course. I have a question about this chapter, concerning the linear attenuators and amplifiers.

Specifically, the chapter mentions that they are not going to get ##\rho_{out}##, but I am interested in this.

More specifically, I am curious about the number of photons detected from the output <n|##\rho_{out}##|n>, which I know will be a function of the arbitrary input state <n|##\rho_{in}##|n>.

I am at the point where I have the antinormal characteristic function ##\chi_{out}(\eta,## ##\eta^*)=\chi_{in}(\eta \sqrt{G}##, ##\eta^*\sqrt{G})## for an arbitrary gain ##G>1##. How do I proceed from here to get <n|##\rho_{out}##|n>? Do I just take the operator-valued inverse fourier transform, as suggested earlier in the course? If so, I don't know how to do this, so if someone could provide some help in this calculation for a non-coherent state I would appreciate it.

Cheers,

W