V. Parigi et al., "Probing Quantum Commutation Rules by Addition and Subtraction of Single Photons to/from a Light Field", Science v.317, p.1890 (2007).
Abstract: The possibility of arbitrarily "adding" and "subtracting" single photons to and from a light field may give access to a complete engineering of quantum states and to fundamental quantum phenomena. We experimentally implemented simple alternated sequences of photon creation and annihilation on a thermal field and used quantum tomography to verify the peculiar character of the resulting light states. In particular, as the final states depend on the order in which the two actions are performed, we directly observed the noncommutativity of the creation and annihilation operators, one of the cardinal concepts of quantum mechanics, at the basis of the quantum behavior of light. These results represent a step toward the full quantum control of a field and may provide new resources for quantum information protocols.
Read also the Perspective on this paper by R. Boyd et al. in the same issue of the journal. In that Perspective, the description of what has been accomplished can be summed up in these 2 paragraphs:
In an intriguing and illustrative report on page 1890 of this issue, Parigi et al. present the results of a laboratory demonstration of what happens in the quantum mechanical operations of photon creation and annihilation, which lacks commutativity. These authors add a single photon to a light beam, which corresponds to the action of the standard quantum mechanical creation operator â. They can also subtract a single photon from the light beam, which corresponds to the annihilation operator a.
Parigi et al. measure the quantum mechanical state of a thermal light field after performing these two operations on it, and they show that the final state depends on the order in which the operations are performed. This result is a striking confirmation of the lack of commutativity of quantum mechanical operators. Moreover, the authors present the strongly counterintuitive result that, under certain conditions, the removal of a photon from a light field can lead to an increase in the mean number of photons in that light field, as predicted earlier.
This is such a clever experiment. And one would think that for people who are still dissing the photon concept, this is almost a smack in the face. One can only hope....