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The context of my question is rotational spectroscopy (using microwave radiation), where there is the $J = \pm 1$ selection rule. The way I understand spectroscopy is that the sample is irradiated with a range of frequencies. Is it possible, during the irradiation of the sample (say CO), for the molecule to be excited by 2 levels by 2 successive photons of the appropriate frequencies?

Now this does not affect the locations of the peaks per se, because the relaxation of course has to happen one level at a time. I am specifically wondering about the distribution of peaks, which is supposed to follow the Boltzmann distribution. Let us say, for example, we have a sample at absolute zero, where all the molecules are at the ground state $J = 0$. Is it possible for a molecule to be excited twice (or more), leading to the rotational spectrum showing more than one peak?

Thank you in advance.

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Very technically? Yes.

Realistically? The probability is small enough that even if it does happen, the peaks for the multiple transitions are going to be small enough that we cannot really observe them on the spectrum. The lifetime of a given excited state is so small compared to the analogous time in the ground state that it can basically be considered zero for the situation you're talking about. I'm sure it has happened, but compared to the one at a time transitions, your spectrum isn't really going to show it.

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  • $\begingroup$ I see. I was thinking that the pulse width would be short enough such that this possibility would be very small, so I was wondering more about any theoretical possibilities that would rule this out (e.g. some rule of QM that I don't know about). Thanks for the explanation! $\endgroup$
    – orthocresol
    Commented Jun 1, 2015 at 21:04
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    $\begingroup$ It's certainly a different story for rotational spectroscopy, but excited state absorption can occur quite readily in some materials as one of the phenomena leading to photon upconversion. $\endgroup$
    – Michael DM Dryden
    Commented Jun 1, 2015 at 22:25
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    $\begingroup$ see: en.wikipedia.org/wiki/Hot_band or: en.wikipedia.org/wiki/Two-photon_absorption $\endgroup$
    – ssavec
    Commented Jun 2, 2015 at 5:31
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From memory something like this has been used as a basis for isotope separation using intense $\ce{CO2}$ lasers to fragment molecules. A process of 'ladder climbing' takes place aided by the fact that the electric field of the laser is so intense that it can bring levels into resonance that would otherwise not be so. Hence ladder climbing is possible. Multi-photon effects should also occur.

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Multiple excitations are unlikely to occur incidentally (at least to the extent where you would get an appreciable signal), but I know of research groups that look at multiple excitations as a way of triggering reactions or as a means of studying excited states via pump-probe spectroscopy

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