Why is the quantum fluctuation the same as the coherent state?

Coherent state. It is a special quantum state that can be achieved by quantum harmonic oscillators in quantum mechanics [1]. The dynamic properties of quantum harmonic oscillators are very similar to those of harmonic oscillators in classical mechanics.

In 1926, Erwin Schrödinger found the first quantum mechanical solution when solving the Schrödinger equation, which satisfies the corresponding principle, was the coherent state [2]. Quantum harmonic oscillators and coherent states exist in a large number of physical systems. For example, the oscillatory motion of a particle located in a quadratic energy well is a coherent state.

Quantum fluctuations. Temporary changes in the state of the void space allowed by the uncertainty principle. The quantum uncertainty principle allows a small amount of energy to emerge from the total emptiness, provided that the energy disappears again in a short period of time (the smaller the energy involved in the fluctuation, the longer it lasts)".

That's how I used to understand it, I thought of quantum fluctuations as frequencies, and when they fluctuate the same, I imagine them as frequencies. Then they can "interfere" (a bit of an optical influence, but I really find it difficult for me to understand these problems, so I can understand them as easily as I can). They can produce "interference", i.e., coherent states.

You should have studied optics, right? There's a concept of "coherent light" in it. Coherent light refers to two beams of light that are polarized in exactly the same direction and frequency.

When we do the Young's double-slit interference experiment, the reason why we want to ensure that the distance between the two slits and the same light source is to ensure that the two beams of light separated from this light source are coherent light. If we do not take into account the difference in polarization states, then light of the same frequency means that there is a fixed phase difference between two beams of light. You should understand the concept of phase, right?

To put it bluntly, these two light waves have the same ups and downs. This is understood from the macro level of volatility. If we enter the field of microscopic quantum mechanics, it is the so-called quantum fluctuation of the same.

Because quantum mechanics treats all electronic states as "wave functions", except that the wave here is a wave of chance.

1. All of them are a special quantum state that quantum harmonic oscillators can achieve in quantum mechanics.

The dynamic properties of quantum harmonic oscillators are very similar to those of harmonic oscillators in classical mechanics.

Virtual particle pairs of particles and antiparticles are generated in space. Particle pairs are generated by borrowing energy, and then annihilated and returned to energy in a short period of time.

The physical effects of these virtual particles can be measured, for example, the effective charge of the electrons is different from the bare charge. This effect can be observed from the Lamb shift and Casimir effect of quantum electrodynamics.

Quantum fluctuations are very important for the origin of the large-scale structure of the universe, and can explain the problem of why there are superclusters of galaxies and fibrous structures in the universe: according to the theory of cosmic inflation, the universe is uniform at the beginning, and the tiny quantum fluctuations in the uniform universe are amplified to the cosmic scale after the inflation, becoming the seeds of the earliest galaxy structure.

The uncertainty principle allows a small amount of energy to be randomly generated in a completely empty space (pure space), provided that the energy disappears again for a short period of time. The greater the energy generated, the shorter the duration of that energy and vice versa. When we measure energy e and time t, the more accurate the measured energy e, the more uncertain the time t of its existence; Conversely, the more accurate T knows, the more uncertain the energy involved in the fluctuation.

The relationship between them adheres to a certain principle: e t > h 2 (h is Planck's constant). The product of the energy involved in the fluctuation and the time of its existence must always satisfy a value greater than h2.

Look at these, I haven't learned it either, so I'm not looking for it.

The compressed state in quantum information is the least uncertain state, which satisfies the lower bound of Heisenberg's inequality. The anisotropic uncertainty of the compressed state is different, and the directional uncertainty of the compressed state decreases, while the orthogonal direction uncertainty increases. The compressed light should be generated by nonlinear optics, and the number of photons in the compressed state must all appear in pairs.

Vacuum, coherent, and compressive states are all minimally uncertain states, and they all satisfy the lower bound of Heisenberg's inequality, unlike the hot state. Both the vacuum state and the coherent state have equal anisotropic uncertainties, but the average strength of the vacuum state is zero, and the strength of the coherent state is not zero. The anisotropic uncertainty of the compressed state is different, and the directional uncertainty of the compressed state decreases, while the orthogonal direction uncertainty increases.

In quantum optics, the vacuum state is generally an environment without photons. The light produced by the laser is the light that satisfies the coherent state. The compressed light is generated by nonlinear optics, and the photon numbers of the compressed light must all appear in pairs.

All of the above are single quantum states, and entangled states must be at least two quantum states. All states in which quantum entanglement exists are entangled states.

The 1st and 4th dimensions are only diagonal elements, and the eigenstates 1 and 2 can be obtained

It is sufficient to solve the equation in the middle.

In traditional quantum mechanics, the electromagnetic field is an operator that describes electromagnetic interactions, and there is no description of the state of the electromagnetic field, and the wave function of a photon is not written like the wave function of an electron. This is because, in principle, it is not possible to describe the motion of photons in coordinate space. To describe the generation and annihilation of photons, it is necessary to use the quantization method of the field, that is, the method of using the generation and annihilation operators of photons.

The so-called quantum mechanical description of electromagnetic fields or quantum states of electromagnetic fields is not a quantum electrodynamic problem such as the scattering of light and microscopic particles, but a quantum optical problem such as an optical device.

We know that the Hamiltonian operator for harmonic oscillator systems in quantum mechanics is the sum of two terms, one containing the square of the coordinates and the other containing the square of the momentum. Similarly, the total energy of an electromagnetic field is the sum of two terms, one containing the square of the electric field and the other containing the square of the magnetic field. Thus, by properly correlating the components of the electromagnetic field to the coordinates or momentum in the harmonic oscillator, we can obtain the field quantities expressed by the ascending and descending operators of the harmonic oscillator problem, which we interpret as the generation and annihilation operators of photons.

In this way we get the eigenstates of the photon number.

A particle in the stationary state of a harmonic oscillator has the mean value of its coordinates and the mean value of its momentum equal to zero. Correspondingly, the mean electric field and the mean magnetic field of the eigenstates of the photon number are also equal to zero. It can be seen that the photon number eigenstate is a state that is far from the classical electromagnetic field.

Not only that, but generally speaking, according to the uncertainty relation, it is impossible for the coordinates and momentum of particles in any state to take a definite value of zero fluctuations. Correspondingly, it is not possible for the electric and magnetic fields in any state to fluctuate to zero. In addition, quantum mechanics has a similar uncertainty relation to the number of phases and particles.

According to this relation, the phase of the field is completely indeterminate in the eigenstate of the photon number, i.e., the state in which the number of photons is completely determined. From this point of view, it can also be seen that the photon number eigenstate is indeed a state with outstanding non-classical properties. To take for granted the concept of a state with a definite number of photons, that is, the concept of photons, to describe the propagation, interference, and diffraction of light is bound to encounter insurmountable difficulties.

It was in order to be able to properly describe the propagation, interference, and diffraction of light that Glauber proposed the concept of coherent states in 1963. To put it simply, a coherent state is the eigenstate of an annihilation operator. The coherent state is formed by the superposition of the eigenstates of an infinite number of photons, and it is a state in which the number of photons is very uncertain.

And the calculations show that the coherent state is a state in which the fluctuations of the electric field and the magnetic field are quite small, and it is also a state in which the phase of the field is highly determined.

Electromagnetic fields have different quantum states, some of which are suitable for description in photonic language, others not. Even photons in the eigenstate of photon numbers generally cannot describe their motion in coordinate representations. However, when an electromagnetic field interacts with matter, it must appear in the form of photons.

The electric field is a substance because there are two kinds of matter: physical and field.

Matter refers to what has energy. As long as there is energy, it is matter.