page_title: Magneto-optical trap
section_title: Atomic structure necessary for magneto-optical trapping
hierarchical_section_title: Magneto-optical trap / Atomic structure necessary for magneto-optical trapping
caption_attribution_description: English: A diagram showing the laser needed for the magneto-optical trapping of Rubidium 85 including the cooling cycle and the forbidden transitions which make it a closed optical cycle, and the repumper laser needed to recouple dark states.
context_page_description: A magneto-optical trap is an apparatus that uses laser cooling in order to produce samples of cold, trapped, neutral atoms at temperatures as low as several microkelvins, two or three times the recoil limit.
  By combining the small momentum of a single photon with a velocity and spatially dependent absorption cross section and many absorption-spontaneous emission cycles, atoms with initial velocities of hundreds of metres per second can be slowed to tens of centimetres per second.
  Although charged particles can be trapped using a Penning trap or a Paul trap using a combination of electric and magnetic fields, those traps are ineffective for neutral atoms.
context_section_description: As a thermal atom at room temperature has many thousands of times the momentum of a single photon, the cooling of an atom must involve many absorption-spontaneous emission cycles, with the atom losing up to ħk of momenta each cycle .
  Because of this, if an atom is to be laser cooled, it must possess a specific energy level structure known as a closed optical loop, where following an excitation-spontaneous emission event, the atom is always returned to its original state.
  ⁸⁵Rubidium, for example, has a closed optical loop between the  state and the  state. Once in the excited state, the atom is forbidden from decaying to any of the  states, which would not conserve parity, and is also forbidden from decaying to the  state, which would require an angular momentum change of −2, which cannot be supplied by a single photon.
  Many atoms that do not contain closed optical loops can still be laser cooled, however, by using repump lasers which re-excite the population back into the optical loop after it has decayed to a state outside of the cooling cycle. The magneto-optical trapping of rubidium 85, for example, involves cycling on the closed  transition. On excitation, however, the detuning necessary for cooling gives a small, but non-zero overlap with the  state. If an atom is excited to this state, which occurs roughly every thousand cycles, the atom is then free to decay either the , light coupled upper hyperfine state, or the  "dark" lower hyperfine state. If it falls back to the dark state, the atom stops cycling between ground and excited state, and the cooling and trapping of this atom stops. A repump laser which is resonant with the  transition is used to recycle the population back into the optical loop so that cooling can continue.
caption: The lasers needed for the magneto-optical trapping of rubidium 85: (a) & (b) show the absorption (red detuned to the dotted line) and spontaneous emission cycle, (c) & (d) are forbidden transitions, (e) shows that if the cooling laser excites an atom to the 
    
      
        
          F
          =
          3
        
      
      {\displaystyle F=3}
    
   state, it is allowed to decay to the "dark" lower hyperfine, F=2 state, which would stop the cooling process, if it were not for the repumper laser (f).
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