# Sideband Cooling: How Does It Bring an Atom From |n+1> to |n>?

• McLaren Rulez

#### McLaren Rulez

Hi,

I refer to this Wikipedia article http://en.wikipedia.org/wiki/Resolved_sideband_cooling

I understand how everything works except for one detail. When the atom is moving towards the laser, the laser frequency is Doppler shifted such that its frequency matches the energy gap $\omega_{0}$. So when it absorbs that photon, it goes from its ground state to excited state. I also understand that the process of absorbing a photon must reduce the atom's momentum by the same amount as the momentum of the incoming photon.

My question is, how do we know that this absorption is able to exactly bring the oscillating atom from $|n+1>$ to $|n>$? The energy gap of the harmonic oscillator has nothing to do with $\omega_{0}$. So how does that work out so nicely?

As always, thank you for all the help.

Because you tune your laser to the frequency w = w0 - v which is the resonance frequency for the transition between |g,n+1> and |e,n>. Without the trap, you wouldn't be able to excite the atom with this laser frequency.

Sorry, I don't see how it works at all. Is the first part of my post correct? The atom moves towards the laser and so the laser beam is Doppler shifted so it can absorb the photon? And so the only time it absorbs photons are when it moves towards the laser. And spontaneous emission is how the atom gets back to ground state.

Now, if this is the case, what does $\nu$ have to do with it? These are the energy gaps for the harmonic potential the atom is in but its not clear to me how it goes from n+1 to n during the process of absorption. Could you explain this?

Thank you.

Sorry, I don't see how it works at all. Is the first part of my post correct? The atom moves towards the laser and so the laser beam is Doppler shifted so it can absorb the photon?
No, that's wrong. Sorry that I didn't state this explicitly in my previous post.

Typically, you start with Doppler cooling, which works like you outlined. The lowest achievable temperature is given by the Doppler limit. If you reach this temperature, you have to use another cooling mechanism, which in your case is sideband cooling.

So you put your particle in a harmonic trap potential. The populations of vibrational states are given by the Boltzmann distribution, which depends on the temperature. Now you tune the cooling laser to a frequency which is resonant to a transition where the final state has a lower vibrational energy (process 1 in the wiki-picture). Spontaneous Emission occurs most likely between states of equal vibrational energy, so there's an effective dissipation of energy.

Does this answer your question or are you troubled with the coupling between particle states and harmonic oscillator states?

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Ah I understand it now! The Doppler shifting has nothing to do with the second stage of the cooling. Thank you kith!