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In

Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation Physics Department, Uniuersity of Waikato, Hamilton, ¹tuZealand (Received 29 October 1984) C. W. Gardiner and M. J. Collett

We consider a quantized electromagnetic field that will interact with a quantum system.

This field thus have annihilation & creation operator associated to the photons of frequency $\omega$.

In this article, they define the following inverse fourier transform:

$$ b_{in}(t) = \frac{1}{\sqrt{2 \pi}} \int e^{-i \omega t} b(\omega) d \omega$$

Where $b(\omega)$ is the operator : "annihilation of photons at frequency $\omega"$

My question is: What does physically this operator $b_{in}(t)$ represents? I see it is the inverse fourier transform of the annihilation operator but what does that physically mean?

Is it like "destruction" of a wavepacket at the time $t$ ? Like if I see the amplitude of the field in function of time, it will create "a hole" in the amplitude at the time $t$ on a timescale $\Delta t$ ?

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