© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1702.03617 · Physical Review Letters

Solving the Quantum Many-Body Problem via Correlations Measured with a Momentum Microscope

Sean S. Hodgman, R. I. Khakimov, Robert J. Lewis-Swan, Andrew G. Truscott, Karen V. Kheruntsyan

Published Jun 14, 2017• 47 citations

Abstract

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system-the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.

DOI: 10.1103/physrevlett.118.240402

Related papers

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

Many-Body Correlations in Phase-Space Microscopes

Y. Yang, C. Weitenberg, N. R. Cooper

The recently proposed "phase-space microscope" (PSM) extends quantum gas microscopes by allowing joint, single-shot measurements of position and momentum. We show that the $n$-body correlation functions constructed from such phase-space snapshots determine, in principle, all $n$-body observables of a many-body quantum state. This establishes phase-space imaging as a complete probe of strongly correlated matter, beyond what snapshots of position and momentum can provide---a limitation that goes back to a famous question posed by Pauli. Even without the full reconstruction of the density matrices, the PSM provides valuable insight into the quantum states. We demonstrate this power through several applications: witnessing entanglement hidden from both position and momentum, including between spatially separated collective degrees of freedom; resolving pairing structure across the BEC-BCS crossover, including the phase of the pair wavefunction and the reconstruction of its two-body Wigner function; probing inhomogeneous systems and preformed pairs without long-range order, relevant to the pseudogap phase; extracting the interaction energy in a magnetic field; and measurements of the local Chern marker. Furthermore, we discuss phase imprinting in the matter-wave Fourier plane as an alternative method for probing time-reversal-symmetry-broken phases such as chiral $p$-wave superconductors. Together, these results establish the PSM as a versatile new tool for exploring fundamental features of quantum many-body phases in strongly correlated quantum matter.

cond-mat.quant-gasCross-listedarXiv:2611.03112•Nov 3, 2026

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

On solving the quantum many-body problem

Thomas Schweigler, Thomas Gasenzer, Jörg Schmiedmayer +5 more

We experimentally study a pair of tunnel-coupled one-dimensional atomic superfluids, which realize the quantum sine-Gordon/massive Thirring models relevant for a wide variety of disciplines from particle to condensed-matter physics. From measured interference patterns we extract phase correlation functions and analyze if, and under which conditions, the higher-order correlation functions factorize into lower ones. This allows us to characterize the essential features of the model solely from our experimental measurements, detecting the relevant quasiparticles, their interactions and the topologically distinct vacua. Our method provides comprehensive insights into a non-trivial quantum field theory and establishes a general method to analyze quantum many-body systems through experiments.

•May 12, 2015•6 citations

Viewpoint: Matter Waves and Quantum Correlations

Mihai Macovei

Colliding matter waves from a Bose-Einstein condensate violate a relation called the Cauchy-Schwarz inequality, proving that such interactions must be considered quantum mechanically.

•Jun 25, 2012•0 citations

Cauchy-Schwarz inequality and particle entanglement

Tomasz Wasak, Piotr Szańkowski, Paweł Zin +2 more

Recently, violation of the Cauchy-Schwarz inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.

arXiv:1311.3855•Physical Review A•Sep 17, 2014•28 citations

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system-the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.

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 recently proposed "phase-space microscope" (PSM) extends quantum gas microscopes by allowing joint, single-shot measurements of position and momentum. We show that the

n

-body correlation functions constructed from such phase-space snapshots determine, in principle, all

n

-body observables of a many-body quantum state. This establishes phase-space imaging as a complete probe of strongly correlated matter, beyond what snapshots of position and momentum can provide---a limitation that goes back to a famous question posed by Pauli. Even without the full reconstruction of the density matrices, the PSM provides valuable insight into the quantum states. We demonstrate this power through several applications: witnessing entanglement hidden from both position and momentum, including between spatially separated collective degrees of freedom; resolving pairing structure across the BEC-BCS crossover, including the phase of the pair wavefunction and the reconstruction of its two-body Wigner function; probing inhomogeneous systems and preformed pairs without long-range order, relevant to the pseudogap phase; extracting the interaction energy in a magnetic field; and measurements of the local Chern marker. Furthermore, we discuss phase imprinting in the matter-wave Fourier plane as an alternative method for probing time-reversal-symmetry-broken phases such as chiral

p

-wave superconductors. Together, these results establish the PSM as a versatile new tool for exploring fundamental features of quantum many-body phases in strongly correlated quantum matter.

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.

We experimentally study a pair of tunnel-coupled one-dimensional atomic superfluids, which realize the quantum sine-Gordon/massive Thirring models relevant for a wide variety of disciplines from particle to condensed-matter physics. From measured interference patterns we extract phase correlation functions and analyze if, and under which conditions, the higher-order correlation functions factorize into lower ones. This allows us to characterize the essential features of the model solely from our experimental measurements, detecting the relevant quasiparticles, their interactions and the topologically distinct vacua. Our method provides comprehensive insights into a non-trivial quantum field theory and establishes a general method to analyze quantum many-body systems through experiments.

Recently, violation of the Cauchy-Schwarz inequality by the second-order correlation function was reported in a collection of ultracold bosons [Kheruntsyan et al., Phys. Rev. Lett. 108, 260401 (2012)]. We show that the observation of this effect proves the presence of particle entanglement in a many-body system of bosons. Our derivation is based on the analogy between the coherent states of electromagnetic fields and separable states of massive particles. The presented argument applies to any quantum system of identical bosons with either a fixed or a fluctuating number of particles, provided that there is no coherence between different number states.