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

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 manybody momentum microscope. Our measurements allow us to extract a key building block of all higherorder 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 In quantum physics, fully understanding and characterizing complex systems, comprising a large (often macroscopic) number of interacting particles, is an extremely challenging problem. Solutions within the standard framework of (first-quantized) quantum mechanics generally require the knowledge of the full quantum many-body wave function. This necessitates an exponentially large amount of information to be encoded and simulated using the many-body Schrödinger equation. In an equivalent (second-quantized) quantum field theory formulation, the fundamental understanding of quantum many-body systems comes through the description of all physical observables via correlation functions between particle creation and annihilation operators. Here, the exponential complexity of the quantum many-body problem is converted into the need to know all possible multiparticle correlation functions, starting from two-, three-, and increasing to arbitrary N-particle (or higher-order) correlations.From an experimental viewpoint, an operational solution to the quantum many-body problem is therefore equivalent to measuring all multiparticle correlations. In certain cases, however, knowing only a specific set of (few-body or lower-order) correlations is sufficient to allow a solution of the many-body problem to be constructed. This was recently shown for phase correlations between two coupled one-dimensional (1D) Bose gases [1]. Apart from facilitating the description of physical observables, characterizing multiparticle correlations is important for introducing controlled approximations in many-body physics, such as the virial-and related cluster-expansion approaches that rely on truncation of the Bogolyubov-Born-GreenKirkwood-Yvon hierarchy [2,3] Correlations between multiple photons are also routinely used in numerous quantum optics experiments including ghost imaging [15,16], defining criteria for nonclassicality [17,18], analyzing entangled states generated by parametric down conversion [19], and characterizing single photon sources [20].Here, we demonstrate an e...

Entanglement-based 3D magnetic gradiometry with an ultracold atomic scattering halo

“…The scattered mode, in reality, is a superposition of the unoccupied vacuum, a single entangled pair, as well as higher numbers of the pairs [25], analogous to the two-mode squeezed vacuum in quantum optics. Two-body correlations in the scattering halo were experimentally determined [22], and theoretically investigated [25] for applications to quantum metrology, and an agreement between the theory and experiments to higher order correlations was found in [26], although there was no spin degree of freedom in the latter. We note that sensitivity beyond SQL has been demonstrated by directly utilising such number fluctuations in twin Fock states of atomic ensembles [27], but this effect is negligible to the scattering halo which generally operate in the spontaneous regime with average mode occupancy below unity.…”

Correlations of strongly interacting one-dimensional ultracold dipolar few-boson systems in optical lattices

“…Recent experimental progress has propelled the development of a variety of methods for the measurement of spatial and momentum correlation functions thereby providing a detailed probe into the many-body properties of cold atom systems. In particular, time-of-flight measurements yield substantial information on correlation functions up to various orders [95][96][97][98][99][100] complemented by additional techniques such as noise pattern analysis [99], momentum microscopy [100], fluorescence imaging [96]etc.…”

Atomic twin beams and violation of a motional-state Bell inequality from a phase-fluctuating quasicondensate source

“…for k ≈ −k In contrast to the previous result for the CL correlation, the second line of Eq. (22) indicates that this correlation is sensitive to the phase-fluctuations of the source.…”

“…We begin from Eq. (22) in the main text. Adopting the approximation (δφ xx ) 2 −|x − x |/l T , we focus on the unsolved integral which, ignoring prefactors, is:…”

“…This is driven by their potential utility in quantum technologies such as precision atom interferometry [1][2][3][4][5] and quantum simulation [6][7][8], as well as fundamental tests of quantum mechanics such as atomic EPR entanglement [9][10][11], the atomic Hong-Ou-Mandel effect [12][13][14] and demonstrations of a Bell inequality using motional degrees of freedom and massive particles [15][16][17][18][19]. Essential to each of these applications has been the ability to well characterise, both theoretically and experimentally, the nature of these atom-pairs as well as their intrinsic correlations [12,[20][21][22][23][24][25][26][27][28][29][30][31][32][33] Recent experiments involving atom-pairs have relied on protocols which can be reduced to the archetypal process of four-wave mixing: A pair of atoms in a coherent Bose-Einstein condensate (BEC) interact and are scattered into a distinct pair of modes (in terms of either spatial, motional or internal degrees of freedom) outside the condensate. Consequently, the vast majority of theoretical work in the literature pertaining to twin-atom production has focused on this case of scattering from a coherent source [14,19,20,24,25,27].…”