Stuff that goes on in a MOT
Behavior of atoms in a light field:
Atoms in electric fields undergo energy level shifts and acquire electron dipole moments due to the distortion of its electron cloud. The energy shifts can be regarded as an effective periodic potential through which the atom travels, and the force on the atom is called the dipole force. In addition to the dipole force on the atom, there is also a force due to the momentum exchange upon absorbing photons (although the net momentum is zero from the random emission vectors), called the radiation pressure.
Behavior of atoms in a magnetic field:
A neutral atom can be trapped by manipulation of the Zeeman effect, since the energy of an atomic state is dependent on the magnetic field. By applying an inhomogeneous magnetic field, the atom experiences a time-varying potential. By using Helmholtz coils in the anti-parallel configuration, one can engineer the potential to have a minimum in which the atom can be trapped. The magnetic field causes a split in energy levels, while the radiation pressure is dependent on these energy levels. A MOT works on this principle that radiation pressure is dependent on magnetic field, causing the radiation pressure to be spatially dependent as well. This enables one to trap atoms using 3 pairs of counter-propagating beams, which are then cooled by the Doppler and Sisyphus processes. (can you make a periodic potential with magnetic fields? i.e., a magnetic lattice?)
Initial Cooling - Zeeman Slower:
Principle: want to slow atoms down by applying a light field in the opposite direction, but the Doppler Effect complicates things, since frequency varies in the rest frame of atoms as they slow down. Get rid of the Doppler Effect by applying an inhomogeneous magnetic field that will cause a Zeeman Effect. The field can be tailored so that the Doppler and Zeeman effects cancel. (Why can't we use mag. fields to get rid of Doppler broadening in Sat Spec???). This allows you to use just one frequency of the laser to cool the atoms. Alternatively, one can vary the frequency of the laser in time, a process known as "chirping." (wouldn't we have to chirp faster than the lifetime of the excited state? Why don't we do this instead?)
Doppler Cooling:
Principle: 2 counter-propagating beams detuned from resonance: When an atom absorbs a photon, it loses momentum h(bar)k (its own momentum). When it spontaneously decays, it emits a photon of greater momentum than it originally had: h(bar)k'. Light must be detuned in order to Doppler-shift the atoms up to the resonance frequency, after which they emit light of a higher frequency than that they absorbed. Therefore, the atom loses kinetic energy and slows down. The cooling of atoms involves converting kinetic energy into optical energy, which is carried away by Doppler-shifted photons. The cooling force is velocity-dependent. The slowed atoms collectively form an optical molasses.
However, the atoms can only be cooled to what is known as the "Doppler Limit," which comes from the fact that although the average momentum change from emission is zero (since direction of emission is random) the RMS value is not; it is Nh(bar)k since it is absorbing along one axis, where N=# of absorption cycles. The atom therefore has a finite energy and temperature. The Doppler limit is typically several hundred microkelvin.
Beyond Doppler limit - Sisyphus Cooling:
Principle: Polarization gradients along the x and y axes produce periodic shifts in the energies of the ground state magnetic substates, and pumps transitions between them. These energy shifts form periodic potentials which the atom is continually forced to climb, causing it to lose energy before being pumped into a substate of lower energy. Sisyphus cooling can cool to a limit of a single photon recoil, typically a few microkelvin.
(Unfortunately, a few microkelvin is not enough to make a Bose Einstein Condensate. To cool past the recoil limit, one makes use of evaporative cooling, which involves lowering the depth of the magnetic trap potential. This removes atoms which have energies higher than the average energy, and the remaining atoms are allowed to rethermalize by elastic collisions.)
Optical Molasses:
Stimulated emission and spatial interference between 2 laser beams can be ignored since these are only manifest for large cooling intensities. (Is this why we do not get stimulated emission in Sat Spec? because we only 5% of the laser beam? What is the limit to get stimulated emission?)
Optical molasses cannot be formed in Sat Spec even though there are counter-propagating beams because the laser frequency is on resonance rather than detuned from resonance. Overtuned light does not work for an atom moving away from the light, because atoms will only absorb photons that have momentum in the opposite direction (why?).
Avg. molasses force on the atom is the sum of the forces from the individual counter-propagating laser beams
Optical molasses is not sufficient to trap atoms!! The atoms will drift out of the laser beams from spontaneous emission, since there is no restoring force on the atom to bring it back to center.
Vapor Cell MOT:
A Magneto Optical Trap (MOT) used, to spatially confine the atoms, is a 3D molasses with more features: photon absorption rate is regulated spatially by an inhomogeneous magnetic field and circularly polarized trapping lasers. The magnetic field gradients are formed with anti-Helmholtz coils.
The external magnetic field provides the Zeeman shifts which lift the degeneracy of the three excited state magnetic sublevels.
In a 1D MOT, each beam is oppositely circularly polarized, where the polarization is defined relative to the applied magnetic field. From polarization, get a spatially dependent force. the atom are driven towards z=0, the point where B=0.