Laser Cooling in Calcium and Magnesium Atomic Beams

Abstract

The extension of the laser cooling technique from Na and Cs to Ca and Mg is of great interest for time and frequenciy metrology [1]. The laser deceleration (cooling) can be achieved by irradiating a thermal Ca or Mg atomic beam with a counterpropagating laser beam in resonance with the ¹S₀-¹P₁ transition at 422 nm and 285 nm, for Ca and Mg respectively. In particular, atoms with an initial velocity v_o are stopped, in a laser field of constant intensity I, after a distance

$$\operatorname{L} (S) = \frac{{\operatorname{v} _0^2M\lambda \tau }}{\operatorname{h} }(1 + \frac{1}{{2S}})$$

(1)

where ti is the radiative lifetime of the upper ¹P₁ level, λ the resonance wavelength, M the atom mass, and S=I/Is the saturation parameter. Only a small fraction of the atoms in the thermal velocity distribution can absorb the laser radiation when a monochromatic single-frequency laser beam is used. It consists of those atoms for which the laser frequency offset is compensated within the natural linewidth by the Doppler effect. As soon the deceleration process starts, the velocity is reduced, the atoms are Doppler shifted out of resonance, and absorption become negligible. The Zeeman tuning of the atomic absorption was used to overcome this difficulty [2]. The Zeeman frequency shift is produced by a magnetic field B(z) of appropriate intensity along the atomic beam axis. This way a continuous beam of cooled atoms can be produced. For a linear Zeeman effect, as in Mg and Ca, and a constant laser intensity, the magnetic field intensity required to keep the atoms in resonance along the beam is

$$\operatorname{B} (z) = \operatorname{B} (0)\sqrt {1 - \frac{z}{{L(S)}}} $$

(2)

In fact the above equation is just giving the minimum value of the field B(z) for any initial value B(0). Other field profiles are allowed but, since the acceleration has a finite value, there is also an upper limit on the field gradient, that must satisfy the boundary condition

$$\frac{{dB}}{{dz}} \leqslant \frac{{\dot v}}{{\mu \lambda \operatorname{v} }}$$

(3)

where μ= 1.4 MHz/gauss for Mg and Ca. If the above constraint is not satisfied, the Zeeman frequency tuning is too fast for the cooling rate and the atoms are shifted out of resonance. Of course a CW , frequency stabilized laser beam of enough power must be available. At 285.2 nm such a CW laser beam was obtained by frequency doubling the radiation at 570.4 nm obtained in a ring Dye laser with Rhodamine 6G dye ; at 422.6 nm the laser beam was obtained by using the Stilben 3 dye pumped with an UV Ar⁺ laser. The deceleration of a Mg atomic beam was recently demonstrated [3], and here we will report the results obtained in the case of a Calcium atomic beam.