Einstein-Podolsky-Rosen steering between two spatially separated regions in Bose-Einstein condensates

Many-body entanglement is an active field of research due to both its fundamental aspects and its potential applications in quantum communications and in metrology. We study entanglement properties between spatially separated... [ view full abstract ]

Many-body entanglement is an active field of research due to both its fundamental aspects and its potential applications in quantum communications and in metrology. We study entanglement properties between spatially separated spin regions in a ⁸⁷Rb Bose-Einstein condensate (see Figure 1) which violate an EPR steering inequality.

One of the most striking feature of these correlations is revealed when a quantum state is split between two spatially separated regions A and B. As introduced by Schrödinger, upon measurements on the A region, the quantum state in the B regions gets steered. This implies that the information on the measurement result in A is sufficient to accurately predict the result of a measurement in B even in the absence of classical communication channels. This type of predictions are in direct contradiction with local causality which is at the core of the EPR paradox. In a spin framework, one can express a criterion (equation 1) which cannot be violated in any local description of reality. This criterion emphasizes how measurement results in region B are correlated with measurement results in region A. Indeed, violating eq.1 allows one to predict the results of non commuting variables in one region from the knowledge of the measured result in the other region. Furthermore, the product of the inferred results uncertainties is smaller than the Heisenberg relation in the steered region. Although EPR steering has already been demonstrated on optical systems our recent work on massive systems have shown that eq.1 could be violated by spatially separated spins.

On Figure 2 we show that the EPR steering inequality is violated in our system for different relative total number of atoms in region A with respect to the total atom number in both regions. Furthermore, we observe that both regions can be simultaneously steered which is a necessary condition to violate stronger forms of inequalities such as Bell inequalities.

This un-intuitive feature not only provides stringent test to quantum mechanics but it could also be used to measure with increased sensitivity spatially dependent quantities such as electromagnetic field gradients or higher multi-polar moments.