Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Alessandro Zavatta, Valentina Parigi, Marco Bellini

Published Jan 1, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1393/ncb/i2010-10841-3

Related papers

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

Valentina Parigi, Alessandro Zavatta, Marco Bellini

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.

Journal of Physics B Atomic Molecular and Optical Physics•May 15, 2009•19 citations

Scheme for Proving the Bosonic Commutation Relation Using Single-Photon Interference

M. S. Kim, Hyunseok Jeong, Alessandro Zavatta +2 more

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:0901.2708•Physical Review Letters•Dec 31, 2008•93 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.

arXiv:0909.4450•Physical Review Letters•Oct 2, 2009•141 citations

Probing Quantum Rules By The Experimental Implementation Of Single-Photon Creation And Annihilation Operators

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

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.

AIP conference proceedings•Jan 1, 2009•1 citation

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

Valentina Parigi, Alessandro Zavatta, Myungshik Kim +1 more

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.

Science•Sep 27, 2007•462 citations

Probing Quantum Rules with Single-Photon Creation and Annihilation Operators

Alessandro Zavatta, Valentina Parigi, M. S. Kim +1 more

We experimentally apply simple sequences of photon creation and annihilation operators to a light field. By a tomographic analysis of the resulting light states we provide the first direct test of quantum non-commutativity.

International Conference on Quantum Information•Jan 1, 2008•0 citations
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 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.
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 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 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.