Understanding Atomic Dipoles and Spontaneous Emission

In summary, the interaction between light and atoms in quantum optics is described by a Hamiltonian involving the dipole moment of the atom. This dipole moment is responsible for the asymmetry of the atom, even if it starts from a spherically symmetric state. The emission of a single atom is not isotropic, but when averaged over many atoms, it becomes isotropic due to the factor 3 in the denominator of the Einstein A coefficient formula. It is possible to experimentally orient the atomic dipole, but it is easier with molecules rather than atoms. Dilute gases of atoms can be polarized by shining polarized light on them.
  • #1
McLaren Rulez
292
3
Hi,

In quantum optics, the interaction between light and atoms is described by a Hamiltonian of the form d.E where d is the dipole moment of the atom. The picture given is basically that this is a vector and we take the the dot product with this and the electric field vector (whose direction comes from the polarization direction). I don't understand why the atom has this asymmetry.

1) If the atom is spherically symmetric, how do we get this dipole pointing in one specific direction? Can an experimentalist put an atom with its dipole pointing in a specific way?

2) If we look at spontaneous emission, the rate is given by the Einstein A coefficient which is reproduced using quantum optics. It is
[tex]
\Gamma=\frac{\omega^{2}d^{2}}{3\pi\epsilon_{0} \hbar c^{3}}
[/tex]
Is this sponteanous emission spatially isotropic or is there more radiation in some directions compared to others?

I feel that I may have some misconceptions regarding the whole thing. Please do correct me if I do. Thank you :)
 
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  • #2
1) The point is that d is an operator and, even if you start from a spherically symmetric electronic wavefunction, the operator induces a transition to a state which is not spherically symmetric. E.g. in a hydrogen atom from an s function to a p function.
2) The emission of a single atom will not be isotropic, however the formula for the Einstein A coefficient is averaged over many atoms and the radiation emitted spontaneously by a large ensemble of atoms is isotropic on the mean. This averaging leads to the factor 3 in the denominator.
 
  • #3
Thanks DrDu. So the actual radiation pattern be the same as that due to the dipole antenna, I assume.

Also, is it possible to experimentally orient the atomic dipole in any direction we want? Or is it a random process?

Thank you
 
  • #4
With an atom in a spherically symmetric ground state this is difficult.
You could use e.g. the Stark effect to split the final levels of the transition.
It is much easier with molecules whose molecular axes can be oriented, e.g. in a crystal or polymer matrix.
 
  • #5
DrDu said:
With an atom in a spherically symmetric ground state this is difficult.
Why? If you take a dilute gas of atoms (where collisions are not important) and shine polarized light on it, you will get polarized atoms.
 
  • #6
DrClaude said:
Why? If you take a dilute gas of atoms (where collisions are not important) and shine polarized light on it, you will get polarized atoms.

Admittedly true. I was more referring to spontaneous emission.
 
  • #7
Thank you for the replies! I have a much better idea of the process now.
 

1. What is an atomic dipole?

An atomic dipole refers to the separation of positive and negative charges within an atom, creating a dipole moment. This can occur due to an external electric field or the uneven distribution of electrons within the atom.

2. How does spontaneous emission occur in atoms?

Spontaneous emission is the process in which an excited atom releases energy in the form of a photon, returning to a lower energy state. This occurs randomly and without external stimulation, in accordance with the laws of quantum mechanics.

3. What factors affect the strength of atomic dipoles?

The strength of atomic dipoles can be influenced by several factors, including the size and shape of the atom, the distribution of electrons within the atom, and the strength of any external electric fields.

4. How is spontaneous emission related to the lifetime of excited atoms?

The lifetime of an excited atom is directly linked to the rate of spontaneous emission. The shorter the lifetime, the higher the rate of spontaneous emission, and vice versa.

5. Can atomic dipoles and spontaneous emission be controlled or manipulated?

Yes, atomic dipoles and spontaneous emission can be controlled and manipulated through various methods such as using external electric or magnetic fields, changing the temperature of the atoms, or using specific laser frequencies to excite or de-excite the atoms.

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