Table 5.1: Summary of the double MOT and the push beam parameters. The minimal push intensity is the required intensity in continuous mode to push the MOT cloud away from the MOT system which is operated with the normal intensity. The saturation intensity for isotropic polarized light of the MOT is s0= 13 mW/cm2for the F= 2 → F= 3 transition, for the linearly polarized push light s0= 11 mW/cm2.
Property CC Push Funnel SC
MOT beam MOT
Laser beam 1/e2 (mm) 15 2.0± 0.2 95 17
Maximal intensity (s0) 0.3 70± 10 1/300 0.7
Intensity during pushing (s0) 0.002 - 0
-Push intensity threshold (s0) 0.35 - - 0.81
Field gradient (Gauss/cm) 25 - 8 21
Laser detuning S1/2(F= 2)-P3/2(F= 3) -2Γ 2Γ -2Γ -2Γ
As we are interested in the absolute transfer efﬁciency we brieﬂy discuss the possible systematic errors involved in the determination of the number of trapped atoms. The dominant systematic uncertainty for the transfer efﬁciency measurement is the absolute peak laser intensity at the MOT position. The second dominant effect is the absolute laser frequency. The CC MOT cloud temperature and the capture velocity of the SC MOT depends on the laser detuning. The alignment of the SC MOT was not as stable as the CC MOT, due to the single beam design of the SC MOT. A slight change in optical alignment made the MOT disappear. Vibrating, sharp fringes close to the MOT position were clearly visible. The SC MOT cloud position also shifted several mm as function of the laser detuning, indicating a signiﬁcant intensity inbalance.
The CC MOT operated much more reliable and did not show these problems. An improvement of the SC MOT would therefore improve the transfer measurement stability and systematic studies.
We swapped the Photo Multiplier Tubes (PMTs) of the SC and CC MOT detection systems. The thresholds of the discriminators of the PMTs were the same. The MOT related count rates did not change signiﬁcantly. The laser intensity was stable at the few % level, which is also sufﬁciently stable for our purposes.
5.2 Double MOT transfer using a resonant push beam
We transfer the atoms between the two MOT systems by accelerating the trapped atoms with a pulsed, near resonant laser beam and recapturing them in the second MOT setup. The atoms are captured if they are within the MOT volume and if their velocity is below the capture velocity of the MOT. Due to the temperature of the atom cloud the initial velocity is non-zero. In the push direction the velocity is the product of the number of photons scattered during the pushing phase and the recoil velocity.
In all three directions the initial velocity spread is enlarged due to the heating from
pushing process. Most relevant is the heating in the transverse direction, as it directly affects the transfer efﬁciency.
Experimental observation of pushed atoms
We will now describe two measurements of the pushing process in the CC MOT. To determine the fraction of atoms that is pushed away from the CC MOT, we look at the ﬂuorescence rate just after the push pulse has been applied for two different push times of 10μs and 40 μs. The result of these measurements are shown in ﬁgure 5.4 and ﬁgure 5.5, respectively. When the push beam is switched on we lower the CC MOT beam intensity to avoid that the CC MOT recaptures the pushed atoms. For the trapping beam in the CC MOT of 15 mm diameter and a pushing speed of 7.5 m/s the minimal time in which the MOT beam intensity has to be lowered is 2 ms. When the MOT beam intensity is reduced the ﬂuorescence rate drops to nearly zero. When the MOT beams return back to normal laser intensity two different sequences evolve. For the short push pulse the ﬂuorescence increases in a few ms, then the MOT reaches its saturation ﬂuorescence level with the time constant of the MOT lifetime (drawn curve shows the exponential loading curve). For the long push of 40μs only the standard loading curve can be seen. Thus in the latter case all atoms were removed, while in the former case about 38% was recaptured.
This type of measurement in fact provides a way of measuring the escape velocity.
The escape velocity is directly related to the capture velocity via equation A.5. However, we did not perform such a measurement ourselves, as we realized this during the data analysis process, after the experiments were done. The idea to measure the escape velocity by using a push beam, has been ﬁrst been implemented by Aubin et al..
They determined for a85Rb MOT an escape velocity of about 20 m/s (or a capture velocity of about 28 m/s).
Experimental observation of the recapture process
After the acceleration by the push beam, the atoms ﬂy towards the SC MOT region.
When the atoms enter the SC MOT laser volume, they start to ﬂuoresce. Either the atoms are slowed and trapped, or they leave (slowed) the trapping volume. We make the approximation that only the velocity distribution of the pushed atoms determines the time dependence of the ﬂuorescence rate in the receiving MOT. We assume that the inﬂuence of the slowing process, which happens on the timescale of the order of ms, is either negligible or effectively broadens our observable. With this simple model we extract the mean and width of the velocity distribution of the pushed atoms.
The initial velocity distribution in the MOT cloud is described by a Maxwell-Boltzmann distribution, each of the three components is Gaussian distributed. The scattering of N photons from the push beam results in a ﬁnal velocity along the push beam direction of
v= N vr, (5.1)
5.2 Double MOT transfer using a resonant push beam 125
0 1 2 3 4 5 6 7 8 9 10
/s)6 PMT count rate (10
0 5 10 15 20 25
Time since push beam on (ms)
0 5 10 15 20 25
/s)6PMT count rate (10
0 2 4 6 8 10 12 14
Figure 5.4: A single trace of the PMT count rate signal from the CC MOT for a push pulse duration of 10μs. The inset shows the signal during the ﬁrst 25 ms. About 40% of the atoms are re-trapped by the MOT after being accelerated by the push beam. The ﬂuorescence rate to the number of trapped atoms conversion factor is 45 counts/s/atom.
Table 5.2: Summary of the data in ﬁgure 5.6.
Background count rate 736± 3 · 1031/s
Mean velocity v 8.9± 0.1 m/s
Velocity spreadσ 1.1± 0.1 m/s
Number of trapped atoms SC MOT NSC 1.1± 0.4 · 104 Number of pushed atoms CC MOT NCC 6.0± 2 · 105 Transfer efﬁciencyε = NSC/NCC 1.8± 0.5%
Time since push beam on (ms)
0 5 10 15 20 25
Figure 5.5: See the description of ﬁgure 5.4, the push time is 40μs.
with vr = mλh the recoil velocity, which for Na is 2.95 cm/s. The pushing process increases the initial velocity spread. A random walk ofN steps in three dimensions results in a spatial Gaussian distribution with a standard deviationσ = vr
3 in each of the three dimensions. When the initial velocity spread is v0, after pushing it is
Assuming that the atoms start ﬂuorescing, after being slowed, in the MOT cen-ter ﬁrst, the time dependent ﬂuorescence rate can be obtained by integrating the normalized velocity distribution,
with v the push speed and NSCthe number of atoms captured by the SC MOT.
In ﬁgure 5.6 the ﬂuorescence signal as recorded by the SC MOT detection system is shown for a push time of 17.5μs and a push beam power of 14 mW. Four parameters are ﬁtted to the data: the constant background due to stray light and equation 5.3 with three parameters. The ﬁt results of the latter are summarized in table 5.2.