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## Main Question or Discussion Point

I saw in a recent review paper- Engineered quantum dot single-photon sources (Rep. Prog. Phys. 75 (2012))- a discussion about how a "timing jitter" problem lead to reduced indistinguishability of single photons, which I find very hard to understand.

According to the paper, for quantum-dot-based single photon sources that use an incoherent pumping (basically, pump the quantum dot to a high excited state, and then it will relax to the first excited state quickly, and decay from this state produces a single photon), a non-infinite relaxation rate from the higher order excited states to the first excited state (from which the single-photon pulse is emitted) leads to a jitter in the arrival time of the single-photon wavepacket, and this will lead to reduction in indistinguishability.

The relevant formula is Eq.(12) of the paper.

According to this formula, a non-infinite relaxation rate will lead to an reduction in the indistinguishability.

Also according to this formula, if relaxation rate is infinite, and if dephasing (another possible source of reduction of indistinguishability) is not present, the indistinguishability can reach 100 percent.

However, I cannot understand this. After all, after the quantum dot reaches its first excited state, it does not emit a photon right away, but will do this at a random time within several lifetimes, which are actually much longer than the relaxation delays. Why this does not create jitters in the arrival times and reduce the indistinguishability?

Two photon emitted by identical decaying atoms should be indistinguishable, whether they are emitted at the same time or not-- This I feel reasonable. But why if there is some random relaxation delay and they are not? (since they are delayed to the random decay times anyway?)

I am sure the paper is correct of course. I must have misunderstood something, but what is it that I have misunderstood?

According to the paper, for quantum-dot-based single photon sources that use an incoherent pumping (basically, pump the quantum dot to a high excited state, and then it will relax to the first excited state quickly, and decay from this state produces a single photon), a non-infinite relaxation rate from the higher order excited states to the first excited state (from which the single-photon pulse is emitted) leads to a jitter in the arrival time of the single-photon wavepacket, and this will lead to reduction in indistinguishability.

The relevant formula is Eq.(12) of the paper.

According to this formula, a non-infinite relaxation rate will lead to an reduction in the indistinguishability.

Also according to this formula, if relaxation rate is infinite, and if dephasing (another possible source of reduction of indistinguishability) is not present, the indistinguishability can reach 100 percent.

However, I cannot understand this. After all, after the quantum dot reaches its first excited state, it does not emit a photon right away, but will do this at a random time within several lifetimes, which are actually much longer than the relaxation delays. Why this does not create jitters in the arrival times and reduce the indistinguishability?

Two photon emitted by identical decaying atoms should be indistinguishable, whether they are emitted at the same time or not-- This I feel reasonable. But why if there is some random relaxation delay and they are not? (since they are delayed to the random decay times anyway?)

I am sure the paper is correct of course. I must have misunderstood something, but what is it that I have misunderstood?

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