quantum mechanics

Introduction



The first indication of the quantum nature of light came in 1900 when Planck dis- covered he could account for the spectral distribution of thermal light by postulating that the energy of a simple harmonic oscillator was quantized. Further evidence was added by Einstein who showed in 1905 that the photoelectric effect could be ex- plained by the hypothesis that the energy of a light beam was distributed in discrete packets later known as photons.
Einstein also contributed to the understanding of the absorption and emission of light from atoms with his development of a phenomenological theory in 1917. This theory was later shown to be a natural consequence of the quantum theory of electromagnetic radiation.
Despite this early connection with the quantum theory, physical optics developed more or less independently of quantum theory. The vast majority of physical-optics experiments can be adequately explained using classical theory of electromagnetism based on Maxwell’s equations. An early attempt to find quantum effects in an op- tical interference experiment by G.I. Taylor in 1909 gave a negative result. Tay- lor’s experiment was an attempt to repeat Young’s famous two slit experiment with one photon incident on the slits. The classical explanation based in the interfer- ence of electric field amplitudes and the quantum explanation based on the inter- ference of probability amplitudes both correctly explain the phenomenon in this experiment. Interference experiments of Young’s type do not distinguish between the predictions of the classical theory and the quantum theory. It is only in higher order interference experiments, involving the interference of intensities, that differ- ences between the predictions of classical and quantum theory appear. In such an experiment the probability amplitudes to detect a photon from two different fields interfere on a detector. Whereas classical theory treats the interference of intensi- ties, in quantum theory the interference is still at the level of probability amplitudes. This is one of the most important differences between the classical and the quantum theory.
The first experiment in intensity interferometry was the famous experiment of
R. Hanbury Brown and R.Q. Twiss. This experiment studied the correlation in the




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photocurrent fluctuations fro two detectors. Later experiments were based on photon counting, and the correlation between photon number was studied.
The Hanbury–Brown and Twiss experiment observed an enhancement in the two- time correlation function of short time delays for a thermal light source, known as photon bunching. This was a consequence of the large intensity fluctuations in the thermal source. Such photon bunching phenomenon may be adequately explained using a classical theory with a fluctuating electric field amplitude. For a perfectly amplitude stabilized light field, such as an ideal laser operating well above thresh- old, there is no photon bunching. A photon counting experiment where the number of photons arriving in an interval of time T are counted, shows that there is still randomness in the arrival time of the photons. The photon number distribution for an ideal laser is Poissonian. For thermal light a super-Poissonian photocount distri- bution results.