Fock State: A Picture from Physical Point of View

• KFC
In summary, a Fock state is a state with a definite number of excitations, but an unpredictable phase. It is represented as a line in phase space and is distinct from a coherent state, which is a superposition of different number states.
KFC
I know there were some discussions in the forum about fock state. In text, fock state described as a state with fixed number of particle but unpredictable phase. Instead of talking about the math, could anyone show me a clear picture from physical point of view what is fock state? In the phase space, will fock state always be a circle with one direction squeezed (like ellipse)?

I think that the Fock state would be represented like a line, i.e. $$P(n, \theta) \propto \delta(n)$$
Check for instance this article on the number-phase Wigner function: http://journals.aps.org/pra/abstract/10.1103/PhysRevA.52.3474 , I will try to get a copy.

Also you can try:
- the webpage of Lvovsky's group contains some of their papers on experiments releated to Fock states: http://people.ucalgary.ca/~lvov/Alex-pub.html
- If you have access to some library look for the book Quantum optics in phase space by W. Schleich.

I managed to retrieve a copy of the PhyRevA article <<Moderator note: Deleted content>>.

PS: Can I upload the copy here on forum as attachment?

<<Moderator note: Parts of this message has been deleted.>>

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soarce said:
I managed to retrieve a copy of the PhyRevA article.

PS: Can I upload the copy here on forum as attachement?

No, you are not allowed to do this. APS charges ca \$160 for the right to host an article in this fashion. However, many people here will be able to access the article through university subscriptions so it can still be relevant to give the reference: http://dx.doi.org/10.1103/PhysRevA.52.3474

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dextercioby
KFC said:
I know there were some discussions in the forum about fock state. In text, fock state described as a state with fixed number of particle but unpredictable phase. Instead of talking about the math, could anyone show me a clear picture from physical point of view what is fock state? In the phase space, will fock state always be a circle with one direction squeezed (like ellipse)?
I don't know where you are getting this. A Fock state, also known as a number state, is just a state where the number of excitations is definite. For example a Fock state might something like

"3 photons of momentum ## k_1## and seven of momentum ## k_2##".

Something that is not a Fock state would be superposition of number states, such as

"1 photon with momentum ##k##, prob. amplitude ##a_1##" + "2 photons with momentum ##k##, prob. amplitude ##a_2##". ##a_1\neq 0 ,\,a_2 \neq 0 ##

This would not be a Fock state (although it still is in Fock space).

As for the phase being unpredictable, this can be seen by finding the expectation of the field operators in a Fock state. You will find that it is zero - it doesn't represent a wave with a particular phase, so when you find the average value of the field, it comes out to be zero. For a state more closely represents a classical wave, see a coherent state (which is not a Fock state - it contains all possible number states of one particular momentum in a superposition).

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1. What is a Fock state?

A Fock state is a quantum state in which a specific number of particles are in a specific set of energy levels. It is named after the physicist Vladimir Fock, who first described it.

2. How is a Fock state different from other quantum states?

A Fock state is different from other quantum states because it is a discrete, well-defined state with a specific number of particles and energy levels. Other quantum states can be continuous and have a range of possible values for the number of particles and energy levels.

3. What is the physical significance of a Fock state?

A Fock state has physical significance because it corresponds to the classical notion of a particle occupying a specific energy level. It can be used to describe the behavior of a system of particles in certain situations and is an important concept in quantum mechanics.

4. How is a Fock state represented mathematically?

A Fock state can be represented mathematically as a superposition of energy eigenstates, with each energy eigenstate corresponding to a specific number of particles. It can also be represented using creation and annihilation operators, which describe the creation and destruction of particles in the system.

5. What applications does Fock state have in physics?

Fock states have various applications in physics, such as in quantum optics, quantum computing, and quantum field theory. They can also be used to describe the behavior of certain types of particles, such as photons and phonons. Additionally, Fock states are important in understanding the properties of quantum systems and can help in the development of new technologies.

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