In the double-slit experiment of emitting one electron at a time, the results obtained with photons are similar. This picture describes the distribution of electrons arriving at the screen over time.
During the period from 1905 to 19 17, Einstein put forward in his paper that the energy of electromagnetic waves is composed of discontinuous energy photons, such as the tentative view on the generation and transformation of light, the development of our views on the nature and composition of radiation, and the quantum theory of radiation. Since robert millikan completed a series of experiments on photoelectric effect in 19 16, arthur compton observed the scattering of X-rays by free electrons in 1923, and measured the momentum of photons in 1926, and the physical world gradually accepted the fact that electromagnetic waves are also particles. However, if we understand the interference phenomenon from the perspective of photons, we will find the following problems: when two corresponding photons in two coherent beams interfere with each other, four photons need to be generated by these two photons in the case of constructive interference, and these two photons need to cancel each other in the case of destructive interference, which violates the law of conservation of energy.
In order to solve this problem, the Copenhagen interpretation of quantum mechanics holds that photon interference is the superposition of the probability amplitudes of a single photon wave function, and the wave function is a probability wave, and the modulus square of its complex amplitude (probability amplitude) is directly proportional to the probability of the corresponding state (eigenstate). Taking double-slit interference as an example, for each photon, its state is the superposition of quantum states passing through each of the two slits:
Among them, the probability amplitude corresponding to the quantum state passing through slit 1 and slit 2, and the respective probability corresponding to the photon exiting from slit 1 and slit 2 are themselves a complex number.
And the probability that the photodetector detects this photon, statistically speaking, that is, the light intensity detected by the photodetector, is the mode square after the probability amplitude is superimposed:
This expression is very similar to the vector superposition of classical electromagnetic waves-in fact, if the quantum state above is replaced by a specific electromagnetic wave form, that is, the electromagnetic field is used to represent the wave function of photons, the same conclusion as classical interference can be obtained in form. But this equivalence is fundamentally wrong, because in the Copenhagen interpretation, electromagnetic field is an observable measurement, while wave function is an unobservable measurement; From the photon point of view, the double-slit experiment is the interference of the probability wave of a single photon itself, and the probability is also the probability that a single photon appears in a specific quantum state, not the number of photons in a specific quantum state. In this regard, paul dirac explained in the Principles of Quantum Mechanics:
"Not long before the discovery of quantum mechanics, people have learned that the connection between light waves and photons must be statistical. However, they don't clearly understand that the wave function tells us the probability of a photon in a specific position, not the number of photons that may be in that position. The importance of this difference can be clearly seen below. Suppose we divide a beam of photons into two parts with equal intensity. According to the hypothesis that the intensity of the beam is related to the number of possible photons, we will get that the total number of photons generally enters each component separately. Now, if these two components interfere with each other, we must require that the photons in one component can interfere with the photons in the other component. In some cases, these two photons will cancel each other, while in other cases, they will produce four photons. In this way, it will contradict the conservation of energy. The new theory relates the wave function to the probability of a photon, which overcomes this difficulty, because this theory holds that each photon part enters each of the two components. So that each photon only interferes with itself. There will never be interference between two different photons. " -paul dirac's Principles of Quantum Mechanics, fourth edition, chapter 1, section 3.
Although it is theoretically possible for a coherent light source to emit only one photon at a time in double-slit interference, according to the statistical interpretation of wave function, after a long period of accumulation, classical interference fringes will be obtained on the screen; However, under the current technology, it is still very difficult to obtain a single photon state-even if a single-mode laser is used as a coherent light source, multiple photons will still enter the photodetector very close to each other, which is the quantum effect of photons as bosons. A feasible method in practical operation is to generate photon pairs, which can be used as an approximation to generate single photon States. At this time, the frequency and propagation direction of the second photon in the photon pair are related to the first photon, which can be regarded as a single-photon Foucault state. A common method of generating photon pairs is atomic cascade. In the experiment, calcium atoms are excited to 6S0 state, and they will return to the ground state through a second-order radiation process, emitting photon pairs with wavelengths of 55 1.3 nm and 422.7 nm respectively. Another common method is to use parametric down-conversion in nonlinear optics, and use a single ultraviolet photon in the crystal as pump light to generate a signal photon and a idler photon through nonlinear effect. The wavelength of these two photons is about twice that of the pump photon, and the polarization direction is perpendicular to the pump photon. By using birefringent crystal, the phase matching of pump light and down-converted light can be realized, so that the output light intensity can be maximized. Both down-converted photons carry the phase information of the pump light, so they are in an entangled state. Any measurement of signal photons will affect the quantum state of idle photons, and vice versa.