# What this quantum field operator represents $b_{in}(t) = \frac{1}{\sqrt{2 \pi}} \int e^{-i \omega t} b(\omega)$? [duplicate]

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 $$\Delta t$$ ?