Laser Cooling and Trapping

1. Laser Cooling and Trapping Cooling Atoms With Light

2. Scattering (Radiative) Force

3. Velocity Change • The momentum transfer during absorption will cause the atoms to change velocity • The photon frequency must be approximately equal to the atoms’ resonance frequency 1 2

4. Doppler Shift • The required frequency is dependent on the atoms’ velocity due to Doppler shifts • For atoms heading into the laser beam, the photons are blue-shifted, while for atoms moving with the laser, the photons are red-shifted. • As atoms slow, the Doppler shift and thus the required frequency changes • Only atoms moving toward the laser will be slowed; thus, two counterpropagating beams are needed (in 1D)

5. Dipole Forces • When δ>>γd, spontaneous emission may be less frequent than stimulated emission. The dipole force is the force arising from stimulated emission • The light shift is the Stark shift due to the electromagnetic wave’s electric field • In a standing light wave, the light shift varies sinusoidally. Atoms are excited by one beam and stimulated into emission (thus slowing them) by the other

6. Dipole Forces (cont)

7. Dipole Optical Traps • For a Gaussian beam, the transverse force is • At sufficiently large detuning, atoms will spend little time in the longitudinally repelled state, thus atoms will be trapped both transversely and longitudinally • Trap depth is proportional to the square of the beam’s waist width

8. Optical Traps – Scattering Force • Six counterpropagating lasers can be used to trap atoms • Optical Earnshaw theorem precludes such a trap from being stable so long as the trapping force is proportional to light intensity

9. Optical Molasses

10. Magnetic Trapping/Cooling • Laser cooling can only cool up to a certain limit. Below it, purely magnetic traps are necessary • With a positive magnetic moment, the atom is forced toward higher potentials (high-field seekers); with a negative moment, the atom is forced toward low potentials (low-field seekers)

11. Magnetic Traps – Quadrupole Trap • Field at the center is zero, and will trap low-field seekers • Time varying magnetic fields cause state changes, transforming the atom from a low-field to a high-field seeker, thus causing losses through the zero point of the field. Loss rate is approximately hN/2πml2

12. Magnetic Traps – TOP trap • A rotating uniform field is superimposed on the quadrupole field, changing the location of the zero point faster than the atoms can respond • The field rotates at a frequency ωb, chosen to be smaller than the Larmor frequency

13. Magnetic Traps – Ioffe trap • Another possibility to avoid holes: use a trap with a nonzero minimum • The bars create a local minimum at the center and transverse confinement

14. Magnetic-Optical Trap (MOT) • A MOT uses a combination of lasers and magnetic fields to trap and cool atoms • At z>0, the transition frequency to the m=-1 frequency approaches the laser frequency; atoms moving to the left have a higher probability of absorbing a photon from the beam propagating to the left, moving them to the center • The net force is approximately linear, of the form F=-kz • Many variations

15. Mirror MOT • Two lasers are reflected off a mirror • For an atom in the path of the beam, each of these lasers serves as two counterpropagating lasers • MOT uses four lasers in total

16. Doppler Limit • As the velocity of atoms decrease, so does the cooling rate • At the Doppler temperature, random momentum kicks caused by photon emission counteract further cooling

17. Sisyphus Cooling • For two lasers with perpendicular linear polarization, the magnitude of the electric field potential varies sinusoidally, with maxima and minima having a periodicity of λ/8. • Atoms must traverse an increasing potential until reaching the “hilltop” (where the polarization is circular, with alternating polarization), where they are pumped into the other sublevel • Thus, the atoms keep loosing kinetic energy

18. Limit of laser cooling • All methods involve the absorption and emission of photons by atoms. • At very low temperatures, the “kick” caused to an atom by photon emission is large enough relative to the atom’s velocity to prevent cooling. • The minimal temperature is known as the recoil limit.

19. Evaporative Cooling • Evaporative cooling involves cooling an ensemble of trapped particles by allowing the higher-energy particles to escape from the trap. • Mutual collisions cause the remaining particles to achieve a new, lower mean temperature. • The trap depth is further reduced, allowing the particles at the high-energy end of the new distribution to escape, and the process repeats. • Inelastic collisions may cause the atom to shift to a non-trapped state; thus, the lower cooling limit is dependent on the ration of elastic to inelastic collisions.

20. Evaporative Cooling (cont)

21. Further Reading • Metcalf, H.J, van der Straten, P. (2003) Laser Cooling and Trapping of Neutral Atoms, Journal of the Optical Society of America B, volume 20, 887 • BGU Atom Chip group’s site (http://www.bgu.ac.il/atomchip/) • Nobel Prize site (physics, 1997) (http://nobelprize.org/physics/laureates/1997/index.html) • University of Colorado’s Physics 2000 site (http://www.colorado.edu/physics/2000/bec/lascool1.html)