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arXiv:1206.2141 · Physical Review A

Einstein-Podolsky-Rosen correlations from colliding Bose-Einstein condensates

Johannes Kofler, Mandip Singh, Maximilian Ebner, Michael Keller, Mateusz Kotyrba, Anton Zeilinger

Published Sep 18, 2012• 38 citations
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Abstract

We propose an experiment which can demonstrate quantum correlations in a physical scenario as discussed in the seminal work of Einstein, Podolsky, and Rosen. Momentum-entangled massive particles are produced via the four-wave mixing process of two colliding Bose-Einstein condensates. The particles' quantum correlations can be shown in a double--double-slit experiment or via ghost interference.

DOI
10.1103/physreva.86.032115

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We propose an experiment which can demonstrate quantum correlations in a physical scenario as discussed in the seminal work of Einstein, Podolsky, and Rosen. Momentum-entangled massive particles are produced via the four-wave mixing process of two colliding Bose-Einstein condensates. The particles' quantum correlations can be shown in a double--double-slit experiment or via ghost interference.
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In 1935, Einstein, Podolsky, and Rosen (EPR) conceived a gedanken experiment which became a cornerstone of quantum technology and still challenges our understanding of reality and locality today.While the experiment has been realized with small quantum systems, a demonstration of the EPR paradox with massive many-particle systems remains an important challenge, as such systems are particularly closely tied to the concept of local realism in our everyday experience and may serve as probes for new physics at the quantum-to-classical transition.In this work we report an EPR experiment with two spatially separated Bose-Einstein condensates, each containing about 700 rubidium atoms.Entanglement between the condensates results in strong correlations of their collective spins, allowing us to demonstrate the EPR paradox between them.Our results represent the first observation of the EPR paradox with spatially separated, massive many-particle systems.They show that the conflict between quantum mechanics and local realism does not disappear as the system size increases to more than a thousand massive particles.Furthermore, EPR entanglement in conjunction with individual manipulation of the two condensates on the quantum level, as we demonstrate here, constitutes an important resource for quantum metrology and information processing with many-particle systems.
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.
In 1935, Einstein, Podolsky and Rosen (EPR) conceived a Gedankenexperiment which became a cornerstone of quantum technology and still challenges our understanding of reality and locality today. While the experiment has been realized with small quantum systems, a demonstration of the EPR paradox with spatially separated, massive many-particle systems has so far remained elusive. We observe the EPR paradox in an experiment with two spatially separated Bose-Einstein condensates containing about 700 Rubidium atoms each. EPR entanglement in conjunction with individual manipulation of the two condensates on the quantum level, as demonstrated here, constitutes an important resource for quantum metrology and information processing with many-particle systems. Our results show that the conflict between quantum mechanics and local realism does not disappear as the system size is increased to over a thousand massive particles.
We study the generation of nonlocal correlations by atomic interactions in a pair of bimodal Bose-Einstein condensates in state-dependent potentials including spatial dynamics. The wave functions of the four components are described by combining a Fock state expansion with a time-dependent Hartree-Fock ansatz so that both the spatial dynamics and the local and nonlocal quantum correlations are accounted for. We find that despite the spatial dynamics, our protocol generates enough nonlocal entanglement to perform an Einstein-Podolsky-Rosen steering experiment with two spatially separated condensates of a few thousand atoms.
Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrow-band photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrow-band photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrow-band photons is expected to play an essential role in spatially multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyperentangled photons, etc.