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Science 28 September 2007:
Vol. 317. no. 5846, pp. 1890 - 1893
DOI: 10.1126/science.1146204
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Reports

Probing Quantum Commutation Rules by Addition and Subtraction of Single Photons to/from a Light Field

Valentina Parigi,1 Alessandro Zavatta,2 Myungshik Kim,3 Marco Bellini1,4*

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.

1 European Laboratory for Nonlinear Spectroscopy (LENS), Via Nello Carrara 1, 50019 Sesto Fiorentino, Florence, Italy.
2 Department of Physics, University of Florence, I-50019 Sesto Fiorentino, Florence, Italy.
3 School of Mathematics and Physics, The Queen's University, Belfast, BT7 1NN, UK.
4 Istituto Nazionale di Ottica Applicata (CNR), Largo E. Fermi, 6, I-50125, Florence, Italy.

* To whom correspondence should be addressed. E-mail: bellini{at}inoa.it

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Science. ISSN 0036-8075 (print), 1095-9203 (online)