Polarization gradient cooling

Shortly after the theory was introduced, experiments were performed that verified the theoretical predictions.

Both configurations can be used for cooling and yield similar results, however, the physical mechanisms involved are very different.

For the lin⊥lin case, the polarization gradient causes periodic light shifts in Zeeman sublevels of the atomic ground state that allows for a Sisyphus effect to occur.

In the σ+-σ− configuration, the rotating polarization creates a motion-induced population imbalance in the Zeeman sublevels of the atomic ground state, resulting in an imbalance in the radiation pressure that opposes the motion of the atom.

Here kb is the Boltzmann constant, T is the temperature of the atoms, and Γ is the inverse of the excited state's radiative lifetime.

Early experiments seemed to be in agreement with this limit, and it was understood to be the main method of laser cooling atoms.

Consider two counterpropagating electromagnetic plane waves with equal amplitude and orthogonal linear polarizations

As an atom moves along z, it will be optically pumped to the state with the largest negative light shift.

, the atom will travel mostly uphill as it moves along z before being pumped back down to the lowest state.

In this velocity range, the atom travels more uphill than downhill and gradually loses kinetic energy, lowering its temperature.

It falls from elliptical polarization that when one vector moves along the propagation axis, the axes of the ellipse rotate accordingly an angle -kz.

This preserves the elliptical polarization of the total electric field regardless of the position along the propagation axis.

The rotating term in the Hamiltonian causes perturbations in the atomic eigenstates such that the Zeeman sublevels become contaminated by each other.

There is a motion induced population imbalance in the Zeeman sublevels in the z basis.

state when the atom is moving to the right (positive velocity) and a higher population in the

Note the similarity to Doppler cooling in the unbalanced radiation pressures due to the atomic motion.

The unbalanced pressure in PG cooling is not due to a Doppler shift but an induced population imbalance.

PG cooling is typically performed using a 3D optical setup with three pairs of perpendicular laser beams with an atomic ensemble in the center.

The laser frequency detuned from a selected transition between the ground and excited states of the atom.

This is done by using a second, "repumping", laser to pump any atoms that fall out back into the ground state of the transition.

The atomic temperature can be measured using the time of flight (ToF) technique.

In this technique, the laser beams are suddenly turned off and the atomic ensemble is allowed to expand.

[1][9] An important theoretical result is that in the regime where PG cooling functions, the temperature only depends on the ratio of

Phillips et al. observed such scaling in their cesium atoms as well as a temperature of 2.5

[10] Recently, PG cooling has been important in research topics such as Bose-Einstein condensates,[11] optical dipole traps,[12] and integrated photonics.

However, such traps typically require large volumes due to necessitating the use of multiple collimated lasers within an atomic vacuum cell.

Thus, there is an active research scene in PICMOTs, or photonic integrated circuit magneto-optical traps.

One proposed avenue through which such small form factors can be achieved is via metasurfaces for devices orders of magnitude smaller.

[14] If this were to be successful, PG cooling could be achieved at a much smaller form factor than currently possible, and deployed in the use of PICMOTs for higher levels of system integration, reduced optical losses, and compact magnetic field generation.

[12] Currently, the efficiency of such an idea is vastly unexplored by literature and thus provides a promising field of interest for further research.

The Sisyphus effect. The ground state light shifts cause the Zeeman sublevels to oscillate with a period of . An atom moves uphill to the right, converting its kinetic energy into potential energy. Near the top of the hill, the atom is excited into an F=3/2 state and decays back into the lowest energy state at the bottom of the hill resulting in an irreversible loss of kinetic energy. As the atom moves through the polarization gradient, this process happens many times.
Clebsch Gordan coefficients for the to transition
A typical set-up for PG cooling. An atomic ensemble is irradiated by three pairs of counterpropagating laser beams with orthogonal polarizations. The repumping laser can be added to any or all of the pairs of beams.