Spatially distributed multipartite entanglement enables Einstein-Podolsky-Rosen steering of atomic clouds (1708.02407v1)

Abstract: A key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. Yet, the robust generation and detection of nonlocal entanglement between spatially separated regions of an ultracold atomic system remains a challenge. Here, we use spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this local entanglement can be spatially distributed by self-similar expansion of the atomic cloud. Spatially resolved spin read-out is used to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen steering between distinct parts of the expanded cloud. Based on the strength of Einstein-Podolsky-Rosen steering we construct a witness, which testifies up to genuine five-partite entanglement.

Analyzing Spatially Distributed Multipartite Entanglement and EPR Steering in Atomic Clouds

This paper examines the generation and characterization of multipartite entanglement using spatially distributed ultracold atomic systems, specifically Bose-Einstein condensates (BECs). By leveraging spin mixing interactions intrinsic to BECs, the paper presents an experimental framework for detecting robust entangled states among spatially separated atomic clouds, and probes the underlying quantum correlations via Einstein-Podolsky-Rosen (EPR) steering protocols.

The authors start with a tightly confined BEC of $^{87}$Rb atoms, in a coherent spin state, and use controlled expansion of the atomic cloud in a potential waveguide to spread the entanglement over multiple spatial regions. A spin mixing mechanism is deployed, leading to the creation of entangled pairs across internal states. This localized entanglement is then disseminated throughout the expanded atomic cloud, revealing nonlocal quantum correlations between different spatial sectors.

Key Findings

1. EPR Steering: The resulting entangled state exhibits strong EPR steering. This quantum correlation, where measurements on one subsystem improve predictions about another beyond local uncertainty limits, is a witness to substantial entanglement between spatial subregions of the atomic cloud. The measured steering product was $S_{\text{A}|\text{B} = 0.62\pm0.12$, demonstrating steering with significant statistical confidence.
2. Multipartite Entanglement: The research constructs a witness for detecting genuine multipartite entanglement. Through spatial subdivision of the atomic signal, the team verifies entanglement involving up to five independent sectors. Specifically, any violation of their derived inequality signalizes multipartite entanglement, indicating more enhanced entanglement resources than previously achievable.
3. Distributed Entanglement: The spatial distribution of separable entanglement through self-similar expansion is underpinning the paper's central theme. This approach uniquely ties particle indistinguishability and bosonic symmetrization with real-world entanglement applications.

Practical and Theoretical Implications

The ability to map indistinguishable-particle entanglement into spatially distinguishable subsystems opens significant avenues for practical applications in quantum information. For instance, creating and controlling complex entangled states within expanded BECs could facilitate advancements in quantum sensing of spatial fields, thereby enhancing resolution through quantum metrology protocols.

Moreover, the demonstrated robustness of this entanglement against spatial partitioning provides a clearer path toward scalable quantum networks. Local controls over entangled subsystems suggest potential adaptability for developing multipartite quantum computation schemes, leveraging cluster-states formed by the BEC.

On a theoretical level, the findings contribute to ongoing discussions about the role of entanglement in dynamics and thermalization processes in quantum many-body systems. Understanding nonlocal correlations in expanded matter-wave systems aids comprehension of entanglement's function in quantum state evolution and decoherence processes.

Anticipated Future Developments

This experimental framework could spur future research into richer entanglement structures, including other continuous variable systems, and extend spatial entanglement studies toward even finer partitions or higher dimensional spaces. Enhanced manipulation of ultracold atomic clouds could eventually lead to novel quantum computing paradigms, benefiting from the inherent adaptability in entanglement production and measurement.

Continued refinement of the apparatus, including finer control over system parameters like spin dynamics and partition resolution, might further elevate our potential to harness multipartite entanglement for various quantum technology platforms. Adapting these findings to different atomic species or interacting Hamiltonians could diversify applications in quantum simulation and encryption methodologies. Overall, the paper presents a robust step into the domain of distributed entaglement systems, opening doors for theoretical exploration and practical quantum developments.