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Laser Cooling and Trapping Cooling Atoms With Light Scattering (Radiative) Force dp h p ˆ F A dt c 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 h v cm 1 2 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) v D c 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 Dipole Forces (cont) p s0 d 2 2 1s0 D d 2 2 H * 0 2 ls 2 2 2 p s0 2 2 2 ps0 ls 4 8 Fx I x 8Is 2 d Dipole Optical Traps • For a Gaussian beam, the2 r d I0 r w transverse force is F 4 I w 2 e s 0 • 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 0 2 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 P 0 F 0 F nˆ dS F dV 0 S V Optical Molasses 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) F B 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 B 2 4z 2 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 U b 2 2 / b 0 U(t)dt Bb Bg2 4Bb 2 8z 2 .... 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 U A r l P z 2 2 B(, , z) 3A 3z, 0, A1 3A 3 z 2 2 2 2 C 2 2 2i * 2i B A1 3A3 z U Ce C e 2 2A1 2 2 l l C 3A1A 3 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 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 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 TD 2k B 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 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. Tr h m 2 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. Evaporative Cooling (cont) 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/in dex.html) University of Colorado’s Physics 2000 site (http://www.colorado.edu/physics/2000/bec/las cool1.html)