hing the 50:50 beamsplitter, therefore, they "choose" at random to follow one of the two possible beam paths. 18 17 The sequence of single photons emitted by a light source can be visualized as individual drops falling in a sink from a leaking tap, or individual cars passing on a highway lane: one at time, but at random times. 18 The choice for photons to take one path or the other is dictated by the random fluctuations of the "vacuum field," which enters through the fourth or unused port of the 50:50 beamsplitter. 25.8 Electromagnetic waves, polarization states, photons, and quantum measurements The two choices have exact and equal probabilities of P =0.5. As seen from the figure, the key difference from the previous experiment is that the photon stream is randomly partitioned. Each single-photon detector (SPD) receives one photon at a time, which generates a "ping" count. A ping from detector SPD1 means that the photon has chosen the straight-through path, while a ping from detector SPD2 means that it has chosen the reflection path, as shown. If the straight-through and the reflection paths have strictly equal lengths, there is no possibility of the detectors SPD1, SPD2 generating two pings or counts simultaneously. The two-count histogram is the same as in a coin-flipping experiment (see, for instance, Fig. 1.3). Over a sufficient period of time, the numbers of counts from SPD1 and SPD2 become about equal. This is equivalent to saying that with a sufficiently large number of photons, the light beam has been divided into two beams of equal power, as in the previous experiment with classical light. The second experiment, which is routinely done in the laboratory, rep- resents one of the many physical proofs of the quantum nature of light and its photon granularity. From this point on, we shall assume that we are dealing with single photons, and that the associated E-fields are in any of the four polarization states {1, {n, U} or equivalently {|0), |1)}, {l+), |-)}, respectively. For short, we may say that the ph