# Understanding Internal State in Quantum Systems with Cold Atoms

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• KFC
In summary, the conversation discusses the concept of internal states in quantum mechanics and how it relates to describing atoms. Internal states refer to the degrees of freedom other than the center of mass and can include the electronic configuration, spin polarization, and position and momentum of the center of mass. However, internal states alone are not sufficient to fully describe an atom as they do not include properties such as total angular momentum or position of the atom's center of mass. Textbooks and online materials can provide further explanation and examples of internal states. In the simplest example of an electron, its internal state is represented as |↑⟩, while in a hydrogen atom, the internal state is represented as |nml⟩, with the full state including the wave function of

#### KFC

Hi all,
I am reading some introducing materials on quantum information and quantum walk. In some materials, the author mentions to implement the related system with cold atoms and they mention the internal states. I learned the quantum mechanics some times ago but I didn't see any chapter in the text about the internal states. I wonder what is internal state really referring to. Is it other name for eigenstates?

ref: https://books.google.com/books?id=2...=what is internal state of cold atoms&f=false

https://www.cfa.harvard.edu/itamp/bec/zoller/talk.pdf [Broken]

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It is a vague, generic term usually for degrees of freedom other than the centre of mass.

http://www.phys.ens.fr/~dalibard/publi2/New-Physics.pdf
"Two types of degrees of freedom have to be considered for an atom: (i) the internal degrees of freedom, such as the electronic configuration or the spin polarization, in the center of mass reference frame; (ii) the external degrees of freedom, i.e. the position and the momentum of the center of mass."

http://www2.physics.ox.ac.uk/sites/default/files/Brandt2011.pdf
"The internal states ##|n \rangle## are the eigenstates of ##\hat{H}_{el}##"

bhobba, vanhees71 and Demystifier
Thanks. But it is still quite confusing. It looks like that the internal state is not a real quantum state to describe an atom. It is more or less like one parameter (degree of freedom) and using internal state alone is not sufficient to describe the state of atom, is that correct? I am thinking for a picture using in most text to describe the atom ##|nml\rangle##, so can I say using n or m or l alone is the internal state?

I think it is quite confusing on the second reference. There it is said ##|n\rangle## is eigenstates of ##H_{el}##, so does it mean internal state alone some times is sufficient to describe the system? Sorry, the second reference to far beyond my level to understand.

KFC said:
Thanks. But it is still quite confusing. It looks like that the internal state is not a real quantum state to describe an atom. It is more or less like one parameter (degree of freedom) and using internal state alone is not sufficient to describe the state of atom, is that correct?
No, internal state contains all information about the system except that "one" degree of freedom. In the case of an atom, internal state describes almost all the properties of particular electrons and their mutual correlations. The only thing that it does not contain are the few properties of the atom as a whole, like total angular momentum, total linear momentum, or position of the atom's center of mass.

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Thanks for the explanation. I am still looking for concrete example to for further explanation. I am reading some online materials, but all of them simply mention the internal state but no explanation at all. Are there any textbook has clear definition of internal state ?

KFC said:
Thanks for the explanation. I am still looking for concrete example to for further explanation. I am reading some online materials, but all of them simply mention the internal state but no explanation at all. Are there any textbook has clear definition of internal state ?
You can find some explanations here:
http://arxiv.org/abs/1406.3221

KFC said:
Thanks for the explanation. I am still looking for concrete example to for further explanation. I am reading some online materials, but all of them simply mention the internal state but no explanation at all. Are there any textbook has clear definition of internal state ?

In the simplest example of an electron, its complete state is ##|\uparrow \rangle |\Psi \rangle##. It's internal state is ##|\uparrow \rangle##.

KFC said:
Thanks. But it is still quite confusing. It looks like that the internal state is not a real quantum state to describe an atom. It is more or less like one parameter (degree of freedom) and using internal state alone is not sufficient to describe the state of atom, is that correct? I am thinking for a picture using in most text to describe the atom ##|nml\rangle##, so can I say using n or m or l alone is the internal state?

If you have a hydrogen atom with a spinless electron and spinless proton, then ##|nml\rangle## is the internal state (roughly, the motion of the electron around the proton). The full state must include the wave function of the centre of mass (or roughly, the motion of the proton).

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atyy said:
In the simplest example of an electron, its complete state is ##|\uparrow \rangle |\Psi \rangle##. It's internal state is ##|\uparrow \rangle##.
Thanks a lot. It is a good example that I understand. So rigidly, internal state is not sufficient to describe a particle, correct? But in some situation, some internal state may be ignored so the "product" of the rest internal states may be a good approximation to describe a particle?

If you have a hydrogen atom with a spinless electron and spinless proton, then ##|nml\rangle## is the internal state (roughly, the motion of the electron around the proton). The full state must include the wave function of the centre of mass (or roughly, the motion of the proton).
if spin is important, can I say spin state is one of the internal state and ##|nml\rangle## is another internal state, but either one is not sufficient to describe the atom completely, right?

## 1. What are cold atoms and how are they used in understanding internal state in quantum systems?

Cold atoms are atoms that have been cooled to extremely low temperatures, typically close to absolute zero. They are used in understanding internal state in quantum systems because at these low temperatures, their quantum behavior becomes dominant and can be more easily controlled and manipulated.

## 2. What is the significance of understanding internal state in quantum systems?

Understanding internal state in quantum systems is important because it allows us to manipulate and control the behavior of atoms at the quantum level, which has potential applications in quantum computing, precision measurements, and quantum information processing.

## 3. How do scientists study internal state in quantum systems with cold atoms?

Scientists use techniques such as laser cooling and trapping to cool atoms to extremely low temperatures and then use lasers to excite or manipulate the internal states of the atoms. This allows them to observe and study the quantum behavior of the atoms.

## 4. What are some potential applications of understanding internal state in quantum systems?

Some potential applications include quantum computing, where the precise control of internal states could lead to faster and more powerful computers, and quantum sensors, which could have higher sensitivity and accuracy than traditional sensors.

## 5. How does understanding internal state in quantum systems contribute to our overall understanding of quantum mechanics?

Studying internal state in quantum systems allows scientists to observe and manipulate the fundamental building blocks of matter at the quantum level. This can provide insights into the nature of quantum mechanics and help us better understand the behavior of matter and energy on a microscopic scale.