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Is it true that a spontaneously light-emitting atom changes its lifetime if it is put between two parallel plates that are so near that they attract each other through the Casimir effect?

Thus: does the Casimir effect, and the changes in the vacuum state it induces, influence spontanenous emission?

If so, who measured this effect for the first time? Where can I read about it?

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This is true. The simple explanation is this: For calculating the decay rate of an excited state, you use Fermi's Golden Rule, which involves the matrix element $$|\langle f | V | i \rangle|^2$$ where $f$ and $i$ denote the final and initial state, respectively.

Since the final state contains the electron in its groundstate together with a photon created by this decay, the nature of your cavity determines what the matrix element will be: For example, if your cavity forbids standing waves of the emission frequency, decay is suppressed. The study of these effects goes under the name of Cavity QED

I would not say that this is due to the Casimir effect. Rather, this effect and the Casimir effect are both due to the boundary conditions created by your plates.

I don't exactly know who first studied this. I suggest consulting a review article such as this one.

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I was initially going to comment on Lagerbaer's excellent answer, but it got a bit too long. So to supplement his answer, here is some additional background:

Another point to consider is that Fermi's Golden Rule argument only applies in the perturbative regime of cavity QED. Nowadays many cavity experiments are in the strong coupling regime, where additional effects such as vacuum Rabi splitting/oscillations can be observed. The dynamics are not an exponential decay any more then, such that the notion of a lifetime is replaced by other timescales.

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Presence of something else next to an excited atom influences the lifetime of the excited state. Any such presence is described with some additional interaction energy.

In case of a cavity QED, you can get suppression of radiation rate: $e^{-\gamma_1 t}$ with smaller $\gamma_1$ due to suppression of the corresponding part of the electromagnetic spectrum of the whole system.

In case of a neighboring similar atom in the ground state, you can obtain a decrease of the life-time due to additional independent channel of the excitation deactivation - a resonance transition, for example. So the resulting decay rate will be $e^{-(\gamma_1+\gamma_2) t}$.

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