# How are the wavelengths calculated to hold and combine atoms in optical trapping?

I am reading this article of scientists who combined individual atoms using optical tweezers. One optical tweezer used a 700 nm-wavelength light to hold the sodium atom while the other optical tweezer used a 976 nm-wavelength to hold the cesium atom. Even through the 976 nm could hold both atoms, a pulse of light used to join the two atoms together by tuning it to the resonance wavelength of the molecule.

From my understanding after looking at other research, both sodium and cesium are alkali metals and are used because these atoms are suitable for laser cooling. I'm guessing other atoms on the periodic table may not be so easy.

My question is two fold:

1. How do you calculate the wavelength that is needed to hold an individual atom (carbon or hydrogen for example) in an optical trap?

2. How do you find the resonance wavelength to join different atoms together without interfering with the transition wavelengths of the atoms?

Any clarification or equations that can be used to bridge the gap to better help me understand is greatly appreciated.

• You sort of answered your own question: you need to know the energy levels of the electrons both for a single atom and for the binding energy in your case of joining two atoms. Once you are able to "interact" with the electrons to force specific orbital transitions, you're off and running (or to be exact, stopping :-) ) Aug 4, 2021 at 14:53

1. How do you calculate the wavelength that is needed to hold an individual atom (carbon or hydrogen for example) in an optical trap?

To hold atoms in an optical trap, you want to use the light as a trapping potential. This is opposed to the scattering regime, where light is on resonance with the internal atomic transitions, and photons can be absorbed and re-emitted thus providing atoms with momentum kicks - this is what is used in laser cooling.

When light is off-resonance, the scattering effects are negligible and the AC Stark shift dominates. Essentially this gives you a potential that goes as: $$U \propto \frac{I}{\omega - \omega_0} + \frac{I}{\omega+\omega_0},$$ where $$\omega$$ is the frequency of the light and $$\omega_0$$ the frequency of the atomic transition. Usually one writes it as $$U = \alpha I$$ where $$I$$ is the light intensity and $$\alpha$$ is the atomic polarisability, that is frequency and atom dependent. Bottom line, the trapping potential depends on how much light you shine and on how close you are to one of the internal transitions.

1. How do you find the resonance wavelength to join different atoms together without interfering with the transition wavelengths of the atoms?

Usually this is done with photoassociation, that is two colliding atoms absorb a photon and reach a bound molecular state. You need to calculate the energy levels of the free atoms, the energy level of the bound state, and how the interatomic forces change these two levels as they are approaching - the net energy difference is the energy of the photon you have to provide.

You can never really "not interfere" with the transition wavelengths of the atoms. These are always shifted, either by interatomic transitions like above, or even by the presence of light and AC Stark shift discussed in 1. This is especially an issue in atomic clocks, and the only "workaround" is using magic wavelengths the shift is the same for both levels and hence their difference (the transition) remains unchanged.

• Thank you for you answer. This helps in pointing me in the right direction. Do you mind me asking a follow-up on where I can learn this in more detail? I unfortunately did not find this information in any of my optics or intro quantum mechanics books. Aug 12, 2021 at 4:27
• The common bible for optical trapping is Grimm. Don't know about molecules and stuff sorry. Aug 12, 2021 at 4:32