PDF (double-sided) - Physics Department, UCSB - University of ...
PDF (double-sided) - Physics Department, UCSB - University of ... PDF (double-sided) - Physics Department, UCSB - University of ...
10.2.1 Photons The first and most notable experiments to violate the Bell inequality were based on measurements of entangled pairs of polarized photons. The sources used to create the pairs produced a random stream of photon pairs and the measurement was based on coincidence detection of photons received by a detector behind a polarization filter. This setup necessitated the development of modified versions of the Bell inequality, like the CH74 [Clauser and Horne, 1974] inequality. This is due to the fact that the unpredictability of the photon source effectively makes it impossible to ever identify a | 00 〉 measurement and the inefficiencies of the detectors make | 01 〉 or | 10 〉 measurements highly unreliable. Using the CH74 inequality, Aspect et al. showed a violation of the inequality by 9 standard deviations in 1981 [Aspect et al., 1981]. Meanwhile, the experimental setups have become so optimized that more recent experiments are trying to obtain a value of S as close as possible to the quantum mechanical limit of 2 √ 2. For example, in 2005 J.B. Altepeter reported a value of S = 2.7252 ± 0.000585, which corresponds to a violation by 1239 standard deviations [Altepeter et al., 2005]. Unfortunately, due to the non-ideal detector efficiencies, these types of experiments are vulnerable to criticism. They suffer from a flaw called the “Detection Loophole” [Pearle, 1970], which is based on the fact that the photons besides 234
“choosing” between polarizations also have the option to not be detected at all. If two photon pairs are emitted by the source in close succession and in each pair one photon “decides” to remain undetected, the remaining two photons can incorrectly be attributed as belonging to the same pair. 10.2.2 Ions To close the detection loophole, M.A. Rowe et al. re-implemented the experiment using entangled pairs of 9 Be + ions [Rowe et al., 2001]. Since these ions could be sourced predictably, one pair at a time, this allowed the group to use a complete set of measurements of all four possible outcomes. The group obtained a value for S of S = 2.25 ± 0.03, also disproving the existence of local hidden variable theories in favor of quantum mechanics. This experiment was still susceptible to criticism, since the ions remained in relatively close proximity during the entire time of the experiment. Thus, one could postulate an interaction between the ions at the time of measurement that leads to an apparent higher correlation. This flaw is called the “Locality Loophole”. 235
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“choosing” between polarizations also have the option to not be detected at all.<br />
If two photon pairs are emitted by the source in close succession and in each<br />
pair one photon “decides” to remain undetected, the remaining two photons can<br />
incorrectly be attributed as belonging to the same pair.<br />
10.2.2 Ions<br />
To close the detection loophole, M.A. Rowe et al. re-implemented the experiment<br />
using entangled pairs <strong>of</strong> 9 Be + ions [Rowe et al., 2001]. Since these ions<br />
could be sourced predictably, one pair at a time, this allowed the group to use a<br />
complete set <strong>of</strong> measurements <strong>of</strong> all four possible outcomes. The group obtained<br />
a value for S <strong>of</strong> S = 2.25 ± 0.03, also disproving the existence <strong>of</strong> local hidden<br />
variable theories in favor <strong>of</strong> quantum mechanics.<br />
This experiment was still susceptible to criticism, since the ions remained<br />
in relatively close proximity during the entire time <strong>of</strong> the experiment.<br />
Thus,<br />
one could postulate an interaction between the ions at the time <strong>of</strong> measurement<br />
that leads to an apparent higher correlation. This flaw is called the “Locality<br />
Loophole”.<br />
235
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