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Journal of Physics B Atomic Molecular and Optical Physics

Implementation of single-photon creation and annihilation operators: experimental issues in their application to thermal states of light

Valentina Parigi, Alessandro Zavatta, Marco Bellini

Published May 15, 2009• 19 citations
Publisher

Abstract

We have recently realized experimental schemes to implement the action of single-photon creation and annihilation operators onto completely classical and fully incoherent thermal light states (Parigi et al 2007 Science 317 1890). By applying alternated sequences of the creation and annihilation operators we observed that the resulting states depend on the order in which the two quantum operators are applied, thus obtaining the most direct experimental test of non-commutativity. Here we provide an extensive and detailed discussion of the main experimental issues related to the realization of these schemes.

DOI
10.1088/0953-4075/42/11/114005

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We have recently realized experimental schemes to implement the action of single-photon creation and annihilation operators onto completely classical and fully incoherent thermal light states (Parigi et al 2007 Science 317 1890). By applying alternated sequences of the creation and annihilation operators we observed that the resulting states depend on the order in which the two quantum operators are applied, thus obtaining the most direct experimental test of non-commutativity. Here we provide an extensive and detailed discussion of the main experimental issues related to the realization of these schemes.
The recent development of experimental techniques to implement the creation and the annihilation operators in the optical domain has found great interest for quantum information manipulation and processing. Quantum states of light obtained by the application of alternated sequences of the creation and annihilation operators a^†\hat{a}^\daggera^† and a^\hat{a}a^ to a thermal state of light depend on the order in which the two operations are performed. The non-commutativity of the bosonic operators, a^a^†≠a^†a^≠1\hat{a}\hat{a}^\dagger\ne \hat{a}^\dagger\hat{a}\ne 1a^a^†=a^†a^=1, has been experimentally verified in terms of density matrixes and Wigner functions, which are reconstructed by quantum homodyne tomography. Recently, a setup has been proposed to directly and completely prove the bosonic commutation relation where a single-photon interferometer is used to create coherent superpositions of two alternated sequences of operators, such as [a^a^†±a^†a^][\hat{a}\hat{a}^\dagger \pm \hat{a}^\dagger\hat{a}][a^a^†±a^†a^]. Some of the latest experimental results are discussed.
We have realized experimental schemes to implement the action of single photon creation and annihilation operators on single‐mode light fields. In particular, we apply alternated sequences of creation and annihilation operators to completely classical and fully incoherent thermal light states. By verifying that the resulting states depend on the order in which the two quantum operators are applied, we provide the most direct experimental verification of the non‐commutation of bosonic creation and annihilation operators.
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.
We present the experimental realization of a scheme, based on single-photon interference, for implementing superpositions of distinct quantum operations. Its application to a thermal light field (a well-categorized classical entity) illustrates quantum superposition from a new standpoint and provides a direct and quantitative verification of the bosonic commutation relation between creation and annihilation operators. By shifting the focus towards operator superpositions, this result opens interesting alternative perspectives for manipulating quantum states.