[Quantum Optics] "quantumness"

[microsansfil]

TL;DR Summary

Coherent states would be classic states according to the definition of "quantumness" !

Hi,

In this presentation slide 17 it is mentionned :

Is there any confusion with the fact that coherent states are said to be semi-classical ?

http://lptms.u-psud.fr/ressources/publis/2010/Quantifying quantumness and the quest for Queens of Quantum.pdf

In physics there is a wide consensus that the “least quantum” (or “most classical”) pure states are coherent states. These are states which present the smallest possible amount of quantum fluctuations, as defined by a suitable Heisenberg uncertainty relation, evenly distributed over a pair of non-commuting variables.For example, in quantum optics, coherent states have that property of minimal and equal uncertainty for the field quadratures. Moreover, the dynamics of the latter is identical to that given by the classical equations of motion of the harmonic oscillator, and the property of minimal uncertainty is conserved during the time evolution created by the Hamiltonian of the electromagnetic field. The most classical mixed states possible can be obtained as a statistical mixture of coherent states.

/Patrick

 

[Mentz114]

So what ?
Anyone can find this in any introductory quantum optics book or course from decades ago.
Why announce it as if some great discovery has been made.

 

[microsansfil]

So what ?
Anyone can find this in any introductory quantum optics book or course from decades ago.
Why announce it as if some great discovery has been made.

Where did you read that I announced a great discovery ! ? It's just a question I'm asking.

Do the coherent states that have the property of minimal and equal uncertainty for the field quadratures are classical states and not quantum states?

/Patrick

 

[Cthugha]

Sure, coherent states of the light field are the most classical states you can get.
You can see this easily from the fact that they are eigenstates of the photon annihilation operator, which means that if you subtract a photon from a light field the photon number distribution of the photon-subtracted light field will have the same mean photon number as the light field before photon subtraction.
More formally speaking the correlation function factorizes.

This is the closest thing to the concept of a classical measurement (where measurements are considered non-invasive) that you can get for light fields.

 

[vanhees71]

Coherent states can be defined as describing electromagnetic fields that are produced by a classical charge-current distribution (the cocalled "hemi-classical approximation" to distinguish it from the "semi-classical approximation", where the matter is quantized and the em. field kept classical). In this sense they come closest to classical electromagnetic waves.

 

[microsansfil]

Thank for the answers.

Even if the coherent states of the light field are the most classical states you can get, it seem that you can entangled them together to implement quantum protocol like teleportation. And so behaves like quantum states.

/Patrick

 

[Cthugha]

Sure, but that applies to everything. To use a very exaggerated example: Trains are very classical entities. If you somehow managed to entangle trains, this entangled two-train state would be a quantum state as well.

 

[microsansfil]

Sure, but that applies to everything. To use a very exaggerated example: Trains are very classical entities. If you somehow managed to entangle trains, this entangled two-train state would be a quantum state as well.

Yes, indeed, it is. Polarization of light is classical state. Entangled two-photon with degree of polarization freedom would be a quantum state as well.

What is meant by "A state is considered quantum if it cannot be written as an incoherent mixture of coherent states" ? A coherent state can be written as an incoherent mixture of coherent states !

/Patrick

 

[vanhees71]

A coherent state is a pure state, not a mixture, or what do mean?

 

[microsansfil]

A coherent state is a pure state, not a mixture, or what do mean?

Yes. Why Michael R. Vanner write :

A state is considered quantum if it cannot be written as an incoherent mixture of coherent states.
See e.g. Leonhardt, Measuring the Quantum State of Light(1997)

This implies squeezed states are quantum states and Coherent states are classical states

/Patrick