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arXiv:1704.00585 · Physical Review A

Einstein-Podolsky-Rosen-entangled Bose-Einstein condensates in state-dependent potentials: A dynamical study

Hadrien Kurkjian, Krzysztof Pawłowski, Alice Sinatra

Published Jul 19, 2017• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.96.013621

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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.
Many-particle entanglement is a fundamental concept of quantum physics that still presents conceptual challenges. Although nonclassical states of atomic ensembles were used to enhance measurement precision in quantum metrology, the notion of entanglement in these systems was debated because the correlations among the indistinguishable atoms were witnessed by collective measurements only. Here, we use high-resolution imaging to directly measure the spin correlations between spatially separated parts of a spin-squeezed Bose-Einstein condensate. We observe entanglement that is strong enough for Einstein-Podolsky-Rosen steering: We can predict measurement outcomes for noncommuting observables in one spatial region on the basis of corresponding measurements in another region with an inferred uncertainty product below the Heisenberg uncertainty bound. This method could be exploited for entanglement-enhanced imaging of electromagnetic field distributions and quantum information tasks.
Spin changing collisions in alkaline Bose-Einstein condensates can be employed to generate highly entangled atomic quantum states. Here, we will report on the generation of two classes of entangled states. Firstly, we demonstrate the generation of two-mode squeezed vacuum states and record their characteristic quadrature correlations by atomic homodyning. We prove that the correlations fulfill Reid’s criterion [1] for continuous-variable Einstein-Podolsky-Rosen entanglement. The homodyne measurements allow for a full tomographic reconstruction, yielding a two-mode squeezed state with a 78% fidelity. The created state can be directly applied to atom interferometry, as is exemplified by an atomic clock measurement beyond the Standard Quantum Limit. Secondly, we demonstrate entanglement between two spatially separated atomic modes. The entangled state is obtained by spatially splitting a Twin Fock state of indistinguishable atoms along a line of zero density. This structure of two separated atomic modes is obtained by utilizing an excited trap mode. The non-classical correlations between these atomic modes are verified by applying a novel entanglement criterion especially sensitive for our case. The method opens a path to exploit the recent success in the creation of many-particle entanglement in ultracold atoms for the field of quantum information, where individually addressable subsystems are required. Finally, we will show how the measurement protocol can be extended to perform a Bell test of quantum nonlocality. [1] M. Reid, Phys. Rev. A 40, 913-923 (1989)
This paper contributes to the proceedings of the Latin-American School of Physics (ELAF-2017) on Quantum Correlations, and is a brief review of quantum entanglement and nonlocality. In such a brief review, only some topics can be covered. The emphasis is on those topics relevant that may be relevant to detecting multi-particle quantum correlations arising in atomic and Bose-Einstein condensate (BEC) experiments. The paper is divided into five sections. In the first section, the historical papers of Einstein-Podolsky-Rosen (EPR), Bell, Schrodinger and Greenberger-Zeilinger-Horne (GHZ) are described in a tutorial fashion. This is followed by an introduction to entanglement and density operators. A discussion of the classes of nonlocality is given in the third section, including the modern interpretation of the correlations of the EPR paradox experiments, known as EPR steering correlations. The fourth section covers the detection and generation of so-called continuous variable entanglement and EPR steering. Various known criteria are derived with the details of the proofs given for tutorial purposes. The final section focuses on the criteria and methods that have been useful to detect quantum correlation in BEC or atomic systems. Recent results relating spin squeezing with quantum correlations, including entanglement and EPR steering, are summarised.
We use the uncertainty relation between the operators associated with the total number of particles and with the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates, and mechanical oscillators. While known entanglement criteria involving the phase observable typically require us to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions to investigate the nonlocal nature of quantum correlations. We present simple examples where our criteria are violated and show their robustness to noise. Apart from being useful for state characterization, they might find application in quantum information protocols, for example, based on number-phase teleportation.