Superpositions of bosonic operator sequences by single-photon interference

We propose an experiment to directly prove the commutation relation between bosonic annihilation and creation operators, based on the recent experimental success in single-photon subtraction and addition. We devise a single-photon interferometer to realize coherent superpositions of two sequences of photon addition and subtraction. Depending on the interference outcome, the commutation relation is directly proven or a highly nonclassical state is produced. Experimental imperfections are assessed to show that the realization of the scheme is highly feasible.We propose an experiment to directly prove the commutation relation between bosonic annihilation and creation operators, based on the recent experimental success in single-photon subtraction and addition. We devise a single-photon interferometer to realize coherent superpositions of two sequences of photon addition and subtraction. Depending on the interference outcome, the commutation relation is directly proven or a highly nonclassical state is produced. Experimental imperfections are assessed to show that the realization of the scheme is highly feasible.

arXiv:0901.2708Physical Review LettersDec 31, 200893 citations

A New Light on Single Photon Interferences

Philippe Grangier, G. Roger, Alain Aspect

Annals of the New York Academy of SciencesDec 1, 198630 citations

Experimental Demonstration of the Bosonic Commutation Relation via Superpositions of Quantum Operations on Thermal Light Fields

Alessandro Zavatta, Valentina Parigi, M. S. Kim +2 more

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.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.

arXiv:0909.4450Physical Review LettersOct 2, 2009141 citations

Quantum interference between a single-photon Fock state and a coherent state

A. Windhager, M. Suda, Christoph Pacher +2 more

arXiv:1009.1844Optics CommunicationsDec 23, 201020 citations

Experimental realization of creation and annihilation perators and direct proof of the bosonic commutation relation

Alessandro Zavatta, Valentina Parigi, Marco Bellini

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 $\hat{a}^\dagger$ and $\hat{a}$ to a thermal state of light depend on the order in which the two operations are performed. The non-commutativity of the bosonic operators, $\hat{a}\hat{a}^\dagger\ne \hat{a}^\dagger\hat{a}\ne 1$ , 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 $[\hat{a}\hat{a}^\dagger \pm \hat{a}^\dagger\hat{a}]$ . Some of the latest experimental results are discussed.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 $\hat{a}^\dagger$ and $\hat{a}$ to a thermal state of light depend on the order in which the two operations are performed. The non-commutativity of the bosonic operators, $\hat{a}\hat{a}^\dagger\ne \hat{a}^\dagger\hat{a}\ne 1$, 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 $[\hat{a}\hat{a}^\dagger \pm \hat{a}^\dagger\hat{a}]$. Some of the latest experimental results are discussed.

Jan 1, 20102 citations

\hat{a}^\dagger

and

\hat{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,

\hat{a}\hat{a}^\dagger\ne \hat{a}^\dagger\hat{a}\ne 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

[\hat{a}\hat{a}^\dagger \pm \hat{a}^\dagger\hat{a}]

. Some of the latest experimental results are discussed.