Ideal n-body correlations with massive particles

Abstract

In 1963 Glauber introduced the modern theory of quantum coherence 1 , which extended the concept of first-order (onebody) correlations, describing phase coherence of classical waves, to include higher-order (n-body) quantum correlations characterizing the interference of multiple particles. Whereas the quantum coherence of photons is a mature cornerstone of quantum optics, the quantum coherence properties of massive particles remain largely unexplored. To investigate these properties, here we use a uniquely correlated 2 source of atoms that allows us to observe n-body correlations up to the sixthorder at the ideal theoretical limit (n!). Our measurements constitute a direct demonstration of the validity of one of the most widely used theorems in quantum many-body theory-Wick's theorem 3 -for a thermal ensemble of massive particles. Measurements involving n-body correlations may play an important role in the understanding of thermalization of isolated quantum systems 4 and the thermodynamics of exotic many-body systems, such as Efimov trimers 5 .Glauber's modern theory of optical coherence and the famous Hanbury Brown-Twiss effect 6 were pivotal in the establishment of the field of quantum optics. Importantly, the definition of a coherent state required coherence to all orders, which for example distinguishes a monochromatic but incoherent thermal source of light from a truly coherent source such as a laser. Higher-order correlation functions therefore provide a more rigorous test of coherence.Higher-order correlations, characterized by an n-body correlation function g (n) , are of general interest and have been investigated in many fields of physics including astronomy 6 , particle physics 7 , quantum optics 8 , and quantum atom optics 9 . In particular they have been a fruitful area of research in the field of quantum optics, where they have been used to investigate the properties of laser light, including heralded single photons 10 , and the statistics of parametric down-conversion sources 11 . State-of-the-art quantum optics experiments have measured photon correlation functions up to sixth order for quasi-thermal sources 8 , allowing the possibility of performing full quantum state tomography 12 .Higher-order correlations experiments with massive particles are currently approaching the same level of maturity as with photons. So far, experiments have directly observed correlations up to fourth order with single-atom-sensitive detection techniques for ultracold atomic bosons 9,13,14 , and second-order correlations for an atomic source of fermions 15 demonstrating the uniquely quantum mechanical property of atom-atom antibunching. Alternative, indirect techniques have also been employed to investigate higher-order correlations, including the measurements of twobody (photoassociation 16 ) and three-body 17 loss rates that are sensitive, respectively, to second-and third-order correlation functions. Interestingly, fermionic atom pairs 18 and fermionic antibunching 19 have also been observed in the atomic shot no...

Proposal for a motional-state Bell inequality test with ultracold atoms

“…Similarly, such a scaling emerges through the height of the correlation h: the correlation is typically stronger for four-wave mixing regimes that produce a collisional halo of smaller density or smaller bin occupation (for a fixed bin size), leading to larger values of S. In the four-mode down-conversion model, where the relevant normalized and N = 1.9 × 10 4 (h 27). For a typical time-of-flight expansion time of texp ∼ 300 ms, which maps the atomic momentum distribution into position space density distribution, and which is when the atoms are experimentally detected, these detection bin sizes convert to position space distances of (∆x, ∆y, ∆z) (0.32, 2.5, 2.2) mm (where we have taken λx = 1 for definitiveness), which are several times larger than the three orthogonal resolutions of multichannel plate detectors used in 4 He * experiments [12,40].…”

Experimental characterization of a quantum many-body system via higher-order correlations

“…With the rapid progress in quantum gas experiments [16], measuring higher-order correlation functions [17][18][19][20] is now within reach. To illustrate the power of the above concepts to analyse a non trivial interacting quantum many-body system, we experimentally investigate two tunnel-coupled one-dimensional (1D) bosonic superfluids, realised with quantum degenerate 87 Rb atoms trapped in a double-well (DW) potential with a freely relative DOF DW potential adjustable tunnel-coupling FIG.…”

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

“…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]. Momentum correlations up to sixth order [4] and phase correlations up to eighth [1] and tenth order [5] have so far been measured in ultracold atomic gases. More generally, multiparticle correlation functions have been used to experimentally characterize the fundamental properties of various systems, such as thermal Bose and Fermi gases [6], weakly and strongly interacting 1D Bose gases [7][8][9], tunnel-coupled 1D tubes [1,5], collision halos [10][11][12], and phenomena such as prethermalization [13] and transverse condensation [14].…”