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

arXiv:1008.0845 · Physical Review Letters

Sub-Poissonian Number Differences in Four-Wave Mixing of Matter Waves

Jean-Christophe Jaskula, Marie Bonneau, Guthrie B. Partridge, Valentina Krachmalnicoff, Piotr Deuar, Karen V. Kheruntsyan, Alain Aspect, Denis Boiron, Christoph Ira Westbrook

Published Nov 2, 2010• 79 citations
arXivHTMLPDF

Abstract

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations, whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub-shot-noise interferometry and studies of Einstein-Podolsky-Rosen-type nonlocality tests.

DOI
10.1103/physrevlett.105.190402

Related papers

Atomic four-wave mixing via condensate collisions

A. Perrin, Craig M. Savage, Denis Boiron +3 more

We perform a theoretical analysis of atomic four-wave mixing via a collision of two Bose–Einstein condensates of metastable helium atoms, and compare the results to a recent experiment. We calculate atom–atom pair correlations within the scattering halo produced spontaneously during the collision. We also examine the expected relative number squeezing of atoms on the sphere. The analysis includes first-principles quantum simulations using the positive P -representation method. We develop a unified description of the experimental and simulation results.

arXiv:0712.2145•New Journal of Physics•Apr 30, 2008•43 citations

Atomic four-wave mixing via condensates collisions

A. Perrin, C. M. Savage, Valentina Krachmalnicoff +4 more

We perform first principles quantum simulations of atomic four-wave mixing via a collision of two Bose-Einstein condensates of metastable helium atoms. We analyse the collinear and back-to-back pair correlations of atoms on the s-wave scattering halo. The results provide qualitative and quantitative understanding of the recent experiments at Orsay [A. Perrin et al., arXiv: 0704.3047].

Quantum-Atom Optics Downunder (QAO)•Jan 1, 2007•1 citation

Properties of atomic pairs produced in the collision of Bose-Einstein condensates

Paweł Zin, Tomasz Wasak

During a collision of Bose-Einstein condensates correlated pairs of atoms are emitted. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot-noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within the Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one- and two-particle correlation functions. The obtained formulas, which relate the correlation functions to the condensate wave function, are convenient for numerical calculations. We employ the variational approach for condensate wave functions to obtain analytical expressions for the correlation functions, whose properties we analyze in detail. We also present a useful semiclassical model of the process and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.

arXiv:1703.05516•Physical Review A•Apr 20, 2018•2 citations

Statistics of atomic populations in output coupled wave packets from Bose-Einstein condensates: Four-wave mixing

Kazimierz Rza̧żewski, Marek Trippenbach, Sherwin J. Singer +1 more

The statistics of the atomic population distributions in nonlinear matter-wave processes, such as four-wave mixing of matter waves (or output coupled wave packets produced by Bragg scattering) from Bose-Einstein condensates (BECs), are determined. Fluctuations of the populations of atoms in the four-wave mixing wave packet can be due to (a) fluctuations of the laser fields that produce the separate momentum wave packets of the BEC, (b) quantum fluctuations arising from finite temperature effects, and (c) the quantum-mechanical nature of the mean-field BEC wave function. We focus on the latter source of fluctuations. The distribution of the number of atoms in the four-wave mixing wave packet is binomial and reduces to a Gaussian distribution for strong conversion. We calculate the skewness and kurtosis of the distribution. The differences in the nature of the fluctuations in nonlinear phenomena for atoms (matter waves) and photons are discussed.

Physical Review A•Dec 14, 1999•4 citations

Matter Waves and Quantum Correlations

Mihai Macovei

The Cauchy-Schwarz (CS) inequality-one of the most widely used and important inequalities in mathematics-can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities.Quantum-mechanical correlations can, however, exceed classical bounds.Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo.The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles.

Physics•Jun 25, 2012•1 citation

Violation of the Cauchy-Schwarz Inequality with Matter Waves

Karen V. Kheruntsyan, Jean-Christophe Jaskula, Piotr Deuar +6 more

The Cauchy-Schwarz (CS) inequality-one of the most widely used and important inequalities in mathematics-can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum-mechanical correlations can, however, exceed classical bounds. Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles.

arXiv:1204.0058•Physical Review Letters•Jun 25, 2012•94 citations
We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations, whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub-shot-noise interferometry and studies of Einstein-Podolsky-Rosen-type nonlocality tests.
We perform a theoretical analysis of atomic four-wave mixing via a collision of two Bose–Einstein condensates of metastable helium atoms, and compare the results to a recent experiment. We calculate atom–atom pair correlations within the scattering halo produced spontaneously during the collision. We also examine the expected relative number squeezing of atoms on the sphere. The analysis includes first-principles quantum simulations using the positive P -representation method. We develop a unified description of the experimental and simulation results.
During a collision of Bose-Einstein condensates correlated pairs of atoms are emitted. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot-noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within the Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one- and two-particle correlation functions. The obtained formulas, which relate the correlation functions to the condensate wave function, are convenient for numerical calculations. We employ the variational approach for condensate wave functions to obtain analytical expressions for the correlation functions, whose properties we analyze in detail. We also present a useful semiclassical model of the process and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.
The statistics of the atomic population distributions in nonlinear matter-wave processes, such as four-wave mixing of matter waves (or output coupled wave packets produced by Bragg scattering) from Bose-Einstein condensates (BECs), are determined. Fluctuations of the populations of atoms in the four-wave mixing wave packet can be due to (a) fluctuations of the laser fields that produce the separate momentum wave packets of the BEC, (b) quantum fluctuations arising from finite temperature effects, and (c) the quantum-mechanical nature of the mean-field BEC wave function. We focus on the latter source of fluctuations. The distribution of the number of atoms in the four-wave mixing wave packet is binomial and reduces to a Gaussian distribution for strong conversion. We calculate the skewness and kurtosis of the distribution. The differences in the nature of the fluctuations in nonlinear phenomena for atoms (matter waves) and photons are discussed.
The Cauchy-Schwarz (CS) inequality-one of the most widely used and important inequalities in mathematics-can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities.Quantum-mechanical correlations can, however, exceed classical bounds.Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo.The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles.
The Cauchy-Schwarz (CS) inequality-one of the most widely used and important inequalities in mathematics-can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum-mechanical correlations can, however, exceed classical bounds. Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles.