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

New Journal of Physics

Subtracting photons from arbitrary light fields: experimental test of coherent state invariance by single-photon annihilation

Alessandro Zavatta, Valentina Parigi, M S Kim, Marco Bellini

Published Dec 9, 2008• 97 citations
Publisher

Abstract

The operator annihilating a single quantum of excitation in a bosonic field is one of the cornerstones for the interpretation and prediction of the behavior of the microscopic quantum world. Here we present a systematic experimental study of the effects of single-photon annihilation on some paradigmatic light states. In particular, by demonstrating the invariance of coherent states by this operation, we provide the first direct verification of their definition as eigenstates of the photon annihilation operator.

DOI
10.1088/1367-2630/10/12/123006

Related papers

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

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.

•Jan 1, 2010•2 citations

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

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

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

Smooth quantum-classical transition in photon subtraction and addition processes

Alexandre V. Dodonov, Salomon Sylvain Mizrahi

Recently Parigi et al. [Science 317, 1890 (2007)] implemented experimentally the photon subtraction and addition processes from and to a light field in a conditional way, when the required operations were produced successfully only upon the positive outcome of a separate measurement. It was verified that for a low-intensity beam (quantum regime) the bosonic annihilation operator $a$ does indeed describe a single photon subtraction, while the creation operator ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$ describes a photon addition. Nonetheless, the exact formal expressions for these operations do not always reduce to these simple identifications, and in this connection here we deduce the general superoperators for multiple photon subtraction and addition processes and analyze the statistics of the resulting states for classical field states having an arbitrary intensity. We obtain closed analytical expressions and verify that for classical fields with high intensity (classical regime) the operators that describe photon subtraction and addition processes deviate significantly from simply $a$ and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$. Complimentarily, we analyze in detail such a smooth quantum-classical transition as a function of beam intensity for both processes.

arXiv:0901.4477•Physical Review A•Feb 18, 2009•12 citations
The operator annihilating a single quantum of excitation in a bosonic field is one of the cornerstones for the interpretation and prediction of the behavior of the microscopic quantum world. Here we present a systematic experimental study of the effects of single-photon annihilation on some paradigmatic light states. In particular, by demonstrating the invariance of coherent states by this operation, we provide the first direct verification of their definition as eigenstates of the photon annihilation operator.
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.
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 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.
Recently Parigi et al. [Science 317, 1890 (2007)] implemented experimentally the photon subtraction and addition processes from and to a light field in a conditional way, when the required operations were produced successfully only upon the positive outcome of a separate measurement. It was verified that for a low-intensity beam (quantum regime) the bosonic annihilation operator aaa does indeed describe a single photon subtraction, while the creation operator ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$ describes a photon addition. Nonetheless, the exact formal expressions for these operations do not always reduce to these simple identifications, and in this connection here we deduce the general superoperators for multiple photon subtraction and addition processes and analyze the statistics of the resulting states for classical field states having an arbitrary intensity. We obtain closed analytical expressions and verify that for classical fields with high intensity (classical regime) the operators that describe photon subtraction and addition processes deviate significantly from simply aaa and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}$. Complimentarily, we analyze in detail such a smooth quantum-classical transition as a function of beam intensity for both processes.