# Quantum optics is a reference to a c-number

• Niles
In summary, quantum optics deals with the study and manipulation of light at the quantum level. It involves the use of "c-numbers," or classical values, to represent certain quantities. In this context, it is stated that there is no corresponding Hamiltonian for a c-number, but this may be an approximation as classical fields can also have a well-defined Hamiltonian.
Niles
quantum optics is a reference to a "c-number"

Hi

In my lecture notes on quantum optics is a reference to a "c-number" electric field, and it is stated that, since it is a c-number, there is no corresponding Hamiltonian. As far as I have understood, a c-number is a classical value of some (possibly quantum mechanical) quantity. However, how can this rule out that the c-number has a Hamiltonian? E.g., a classical electric field has a well-defined Hamiltonian given by its energy density.

Niles.

Niles, This would be an approximation, in which the degrees of freedom of the electric field are ignored and the field is treated as a constant external quantity maintained by a classical source.

## 1. What is quantum optics?

Quantum optics is a branch of physics that studies the interactions between light and matter at the quantum level. It combines principles from quantum mechanics and classical optics to understand the behavior of light and its interactions with atoms and molecules.

## 2. What is a c-number in quantum optics?

A c-number, or classical number, is a variable that takes on a continuous range of values. In quantum optics, these values are treated as classical quantities rather than quantum operators, allowing for easier mathematical calculations.

## 3. How is quantum optics related to quantum mechanics?

Quantum optics is a subfield of quantum mechanics that specifically focuses on the behavior of light. It uses quantum mechanical principles, such as wave-particle duality and quantization, to describe the properties and interactions of photons.

## 4. What are some practical applications of quantum optics?

Quantum optics has many practical applications, including in technologies such as lasers, optical communications, and quantum computing. It is also used in research on quantum information and quantum entanglement.

## 5. What are some current areas of research in quantum optics?

Current research in quantum optics includes studying quantum entanglement and its potential applications in quantum communication and computing, developing new techniques for manipulating and controlling light at the quantum level, and exploring the intersection of quantum optics with other fields such as condensed matter physics and quantum chemistry.

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