Continuous Variable EPR Entanglement
In their famous Gedanken-Experiment Einstein, Podolsky and Rosen (EPR) considered a source emitting particles with corrolated momentum and position (a). Due to these correlations a measurement of the position of particle A can be used for a prediction of the position of particle B. In the same way, a mesurement of the momentum of particle A can yield a precise prediction of the momentum of particle B. The combined uncertainties of thes predictions can be lower than the value set by the Heisenberg uncertainty relation which leads to a seeming contradiction to qumatum mechanics.Nowadays, states that can violate this inferred Heisenberg relation are called EPR entangled and are known to be usefull for quantum inforamtion tasks and metrology beyond the standard quantum limit.
Position x = a† + a and momentum p = i (a† - a) in a harmonic oscillator can be described in terms of the creation and inhilation operators a and a†. In the same way position and momentum operators can be defined for the spin states in our spinor condensate (b). These so-called quadratures are equivilent to momentum and position and can be measured by an atomic homodyne measurement. The measurement presented in (c) present a clear violation of the inferred Heisenberg uncertainty and thus show the first demonstration of continuous variable EPR entanglement in an atomic system.