Optical Experiments Illustrating the Significance of the Bell Inequalities

Abstract

Recently the possibility of generating squeezed states of light has provided for an important new tool in studying questions that are of crucial importance for the foundations of quantum mechanics. Squeezed states, being states of the electromagnetic field without a classical analogue, seem particularly suited for studying effects that are typically quantum mechanical. For this reason it is not surprising that they have been applied in tests of the Heisenberg uncertainty relation¹ and of the Bell inequalities (BI)²In the latter experiment, which was performed by Ou and Mandel², the two-photon character of squeezed states generated in parametric downconversion is used in order to obtain a correlated state of the electromagnetic field violating the BI. This was verified in Einstein-Podolsky-Rosen (EPR)-like experiments in which the joint probability P(0 ₁,0 ₂) was measured of one photon being polarized in the direction and the other one in the direction0 ₂In order to test the BI the experiment was repeated for different values of 0_t and 0₂, yielding -1 < P(0₁, 0₂) - P(0₁, 0₂) +(0₁, 0₂)+ (0₁, 0₂) – P(O₁)-P(0 ₂ ) ≤ 0 if the BI are satisfied.