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arXiv:quant-ph/0409149 · International Journal of Quantum Information

POSITION AND MOMENTUM ENTANGLEMENT OF DIPOLE–DIPOLE INTERACTING ATOMS IN OPTICAL LATTICES: THE EINSTEIN–PODOLSKY–ROSEN PARADOX ON A LATTICE

Tomáš Opatrný, MICHAL KOLÁŘ, Gershon Kurizki, Bimalendu Deb

Published Aug 30, 2004• 1 citation
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Abstract

We study a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole–dipole interactions. The Einstein–Podolsky–Rosen (EPR) "paradox"1 with translational variables is then modified by lattice-diffraction effects. This "paradox" can be verified to a high degree of accuracy in this scheme.

DOI
10.1142/s021974990400033x

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We study a possible realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole–dipole interactions. The Einstein–Podolsky–Rosen (EPR) "paradox"1 with translational variables is then modified by lattice-diffraction effects. This "paradox" can be verified to a high degree of accuracy in this scheme.
We propose and investigate a realization of the position- and momentum-correlated Einstein-Podolsky-Rosen (EPR) states [Phys. Rev. 47, 777 (1935)]] that have hitherto eluded detection. The realization involves atom pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipole-dipole interactions. The EPR "paradox" with translational variables is then modified by lattice-diffraction effects and can be verified to a high degree of accuracy in this scheme.
Entanglement of light and matter is an essential resource for effective quantum engineering. In particular, collective states of atomic ensembles are robust against decoherence while preserving the possibility of strong interaction with quantum states of light. While previous approaches to continous-variable quantum interfaces relied on quadratures of light, here we present an approach based on spatial structure of light-atom entanglement. We create and characterize a 12-dimensional entangled state exhibiting quantum correlations between a photon and an atomic ensemble in position and momentum bases. This state allows us to demonstrate the original Einstein-Podolsky-Rosen (EPR) paradox with two different entities, with an unprecedented delay time of 6 μμμs between generation of entanglement and detection of the atomic state.
This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell's theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.
Experiments have reported the entanglement of two spatially separated macroscopic atomic ensembles at room temperature (Krauter et al 2011 Phys. Rev. Lett. 107 080503; Julsgaard et al 2001 Nature 413 400). We show how an Einstein–Podolsky–Rosen (EPR) paradox is realizable with this experiment. Our proposed test involves violation of an inferred Heisenberg uncertainty principle, which is a sufficient condition for an EPR paradox. This is a stronger test of nonlocality than entanglement. Our proposal would enable the first definitive confirmation of quantum EPR paradox correlations between two macroscopic objects at room temperature. This is a necessary intermediate step towards a nonlocal experiment with causal measurement separations. As well as having fundamental significance, the realization of an atomic EPR paradox could provide a resource for novel applications in quantum technology.
Summary form only given. With the rapid development of spatially-resolving single-photon detectors, spatially structured multidimensional entangled states start to play a key role in modern quantum science. In particular, they find extensive applications in emerging fields such as quantum imaging, holography, computation or quantum-enhanced metrology. Moreover, spatially-multiplexed schemes hold a promise to increase the capacity of quantum channels, essential for quantum key distribution. An appealing perspective is to apply these ideas to light-atom interfaces, that are capable of storing and processing continuous-variable (CV) entanglement, critical for novel quantum cryptography, computation and imaging schemes.Here we generate a hybrid bipartite entangled state of a photon and an atomic spin-wave excitation [1], exhibiting Einstein-Podolsky-Rosen (EPR) correlations in real space of continuous position-momentum variables, as in the original EPR proposal [2]. We verify the entanglement by measuring the coincidence patterns corresponding to modulus-squared spatial wavefunctions of the state. By studying temporal evolution and decoherence we find that the EPR entanglement may be stored for several microseconds. Our approach turns out to be by far more robust than the only hitherto performed experiment, based on quadratures of squeezed light and a slow-light medium, where time-delayed EPR correlations were demonstrated [3]. We achieve two orders of magnitude longer delay time using quantum memory setup and significantly stronger violation of EPR inequality [4], with product of variances 3 times below the EPR bound for the full two-dimensional coincidence distribution.