Sensitivity to thermal noise of atomic Einstein-Podolsky-Rosen entanglement

TL;DR

This paper investigates how thermal noise affects the ability to demonstrate EPR entanglement in spinor Bose-Einstein condensates, finding that even minimal thermal populations can destroy the entanglement.

Contribution

It predicts the threshold thermal population level that can be tolerated in experiments demonstrating EPR entanglement with spinor BECs.

Findings

EPR entanglement can be observed with low thermal populations

Thermal populations above approximately 1 atom per mode destroy EPR entanglement

The study provides guidelines for experimental conditions to observe EPR entanglement

Abstract

We examine the prospect of demonstrating Einstein-Podolsky-Rosen (EPR) entanglement for massive particles using spin-changing collisions in a spinor Bose-Einstein condensate. Such a demonstration has recently been attempted by Gross et al. [Nature 480, 219 (2011)] using a condensate of Rb-87 atoms trapped in an optical lattice potential. For the condensate initially prepared in the (F,m_{F})=(2,0) hyperfine state, with no population in the m_{F}=+-1 states, we predict a significant suppression of the product of inferred quadrature variances below the Heisenberg uncertainty limit, implying strong EPR entanglement. However, such EPR entanglement is lost when the collisions are initiated in the presence of a small (currently undetectable) thermal population n_{th} in the m_{F}=+-1 states. For condensates containing 150 to 200 atoms, we predict an upper bound of n_{th}~1 that can be tolerated in this experiment before EPR entanglement is lost.