Say I was shooting a stream of single photons with a time interval between photons as $\Delta t$. Each time a photon is emitted, it is generated in a mode $\mathbf{k}_i$, where $i$ denotes the photon number in the stream of photons being generated.
For $0\le t< \Delta t$, the Fock space representation would be $\left| 1_{\mathbf{k_1}},0,0,\dots \right>$.
For $\Delta t\le t< 2\Delta t$, the Fock space representation would be $\left|0, 1_{\mathbf{k_2}},0,0,\dots \right>$.
But one can also argue the state should be $\left|1_{\mathbf{k_1}}, 1_{\mathbf{k_2}},0,0,\dots \right>$ to include both photon launching events.
However one can counter-argue by saying $\Delta t$ is so large, we can treat the scenario as being two separate launching events on the system and do not need to include the first photon mode in our equations.
Given this example, how can time be resolved in the Fock space representation? Or, more directly, what is the difference between a two photon state $\left|1_{\mathbf{k_1}}, 1_{\mathbf{k_2}},0,0,\dots \right>$ and two single photon states $\left| 1_{\mathbf{k_1}},0,0,\dots \right>$ and $\left| 0,1_{\mathbf{k_1}},0,\dots \right>$?
Since these states really represent tensor products of independent Hilbert spaces, do any of these distinctions in the above example even matter? Namely, would the math be the same either way?
