Dipole trap laser and dynamic modification of its dimensions

The dipole trap is realized with the use of an 100 W IPG Ytterbium fiber Laser GmbH. This laser generates radiation in 1070 nm with a spectral bandwidth of 5 nm and can deliver up to 100 Watts of power in a beam waist of 2 mm. The laser power is controlled with an acousto-optic modulator (AOM), its power is monitored by a logarithmic photodiode and power-locked with the use of a home-made PID controlling system to avoid power fluctuations due to heating in the acousto-optic crystal. Finally, the laser beam is divided in two parts and is recombined in the MOT region to realize the crossed dipole trap. Additionally, the dimensions of the laser beam is controlled with the use of a M-663.465 PI piezoelectric translation stage which displaces one of the two lens of a telescope with a velocity up to 50 mm/s. A schematic representation of the dipole trap set-up is shown in Fig. I.3.8.

The initial waist of 2 mm is converted to a waist of 550 µm after passing a times 1/3.6 telescope realized with a 360 and a 100 mm lens, in order to optimize the AOM performance. For optimum performance of the AOM, the laser waist has to be well within a particular range of values. When a laser beam passes an AOM, a part of the beam is deflected to a small angle vertical to the direction of the incoming RF field. The relative power of the deflecting beam, which is the part of the beam used for the realization of the dipole trap, depends on the RF power and its frequency is the addition of the initial laser frequency and that of the RF. For the time-of- flight temperature measurements of the atoms trapped in the dipole trap, it is essential that the dipole field is cut sufficiently fast. This speed depends on the dimensions of the laser beam on the acousto-optic crystal, if this is too big, the time in which the RF field is diminished is important. On the other hand the dimensions of the beam cannot be too small, because in this case the power density on the acousto-optic crystal will be too large and the poor deflection efficiency would result to an out Fig. I.3.7: Measurement of the atom number in the magnetic trap at various times after the magnetic trap loading with the use of the fluorescence imaging technique. The time before the initial number of atoms is reduced to the 1/e of its initial value equals to 26.9 seconds.

coming beam with a degraded spatial profile.

The laser waist modification is done with the use of the piezoelectric stage on which one of the two lenses of the telescope is mounted. This converging lens can move for 10 cm in a speed of 100 cm/s. The resulting dimensions are calculated and compared to the experimental measurement of the laser waist along the optical path. The distance after the lens in which the waist of the beam finds its minimum value is calculated according to the thin lens formula

1

f = 1

s_i z2R

s_i−f

 1

s_f (3.6)

where f is the lens focal lens distance, sf is the focal distance and si is the is the distance of the previous focalization point of the, which is infinite for a collimated beam.

With these formulas we can predict the waist evolution in the position where the trap is realized. Furthermore, we can compare the result of our calculation measurements of the waist realized with the “razor” method. This simple method consists of placing a power detector in the laser path, and using a razor placed in a micro metric stage to block gradually the beam. The waist of the laser will be the distance between the positions of the razor where the 16.4% and the 84,6%

of the power is detected, a consequence of the Gaussian power distribution of the laser beam.

There exists a more sophisticated method for the determination of the dipole trap dimensions, via the determination of the frequencies of the atomic motion in the trap. Those depend on the traps dimensions as ftrap = (4U0/mw²)^1/2, where U0 is the dipole potential and w the laser’s Fig. I.3.8: Schematic diagram of the dipole trap set-up showing the configuration and the relative distances between the various elements. The logarithmic photodiode is squared since it lies in a different level than the one shown here, and monitors the lasers intensity from the leakage of an intentionally placed mirror, non treated at 1070 nm.

waist. These frequencies are determined with the use of the parametric excitation technique [Sav97]. In this method, after the dipole trap is loaded, the power of the dipole laser is modified in a harmonic fashion, and in a particular frequency. The loss of atoms in the dipole trap is maximized when the frequency of the dipole power modification matches the frequency of the atomic motion in the dipole trap. In Fig. I.3.9 we see the configuration used for the realization of the parametric excitation measurements. The power of the dipole laser is controlled by the RF power inserted in the AOM. Initially, we insert a constant power RF into the AOM so that the dipole trap is loaded.

Then, the RF power is modulated harmonically for approximately half a ms. The number of atoms remaining in the dipole trap is estimated either with the use of the fluorescence or the absorption imaging. The modulation frequency of the RF power is changed and the measurement is repeated for frequencies ranging from some hundreds up to some thousands of Hz. A result of such a measurement is shown in Fig. I.3.10. In this measurement, the dipole laser power was equal to 12 W (6 W in each arm), and the measured frequency corresponds to a waist of 94.9 µm. The presence of a second, less deep resonance is due to the oscillation of the atoms to the vertical direction, and is not used for the measurement of the trap’s dimensions.

The evolution of the waist alone is not sufficient for the calculation of the trap’s dimensions, since this is not realized in the minimum waist, but in the intersection of the two beams, and those positions do not necessarily coincide. Actually, if the traps dimensions are to be modified with a system like the one described here, the minimum waist position will definitely be displaced. This is not necessary a disadvantage, and if properly taken into account, increases the range of possible trap dimensions that can be realized with a given translation stage. One point that has to be stressed is that when the trap loading takes place with a trap that has been realized with the laser beams crossed not in their minimum waist, the minimum waist must be positioned far away from the MOT (or whatever the trap that is used for the loading) so that no atoms are loaded to this minimum that could possibly interact with the trap during the evaporation process. In our experiments, usually the Fig. I.3.9: Configuration used for the parametric excitation measurements. A constant voltage that corresponds to a particular RF output power is combined to a harmonically modulated voltage provided by a function generator and is inserted to the RF driver of the dipole laser’s AOM. The voltage that the RF driver

‘ sees’ during the measure is shown in the inlet down and left.

minimum laser waist lies out of the cell where the trapping takes place, so it is not possible to load any atoms on it. We also note that modification of a laser beams dimensions without displacing the minimum waist position is possible, but requires a complicated motion in more than one optic element and is not considered. The evolution of the laser waist along the laser’s path and versus the piezoelectric stage’s displacement (we refer to it as ‘zoom position’) is shown in Fig. I.3.11.

An important element of the dipole trap compression is its stability during this process.

Small misalignment of the beam out off the axis of the telescope lens motion can result to important displacements of the beam in the trap region. These displacements are actually impossible to be completely eliminated as ‘perfect’ alignment is impossible. These displacements are more important for larger distances between the zoom and the final position of the trap (~2 m in our case). The fact that the trap is realized relatively close the focus of the final lens (L3) helps, since the lens compensates those displacements to a large extent. The alignment becomes more feasible after placing the moving lens in a x-y-z mounting. What can be verified experimentally is that the possible displacements are significantly smaller than the lasers dimensions and the laser beams remain crossed in most of the zoom’s range. This fact is in Fig. I.3.12 where images of the crossed dipole trap are acquired with absorption imaging, a technique which will be explained in the following paragraphs.

Fig. I.3.10: a) Measurement of the dipole trap's dimension with parametric excitation. In this measurement, the dipole laser power was equal to 12 W (6 W in each arm), and the measured frequency of 280 Hz corresponds to a waist of 94.9 µm. The presence of a second, less profound resonance at 940 Hz is due to the oscillation of the atoms to the vertical direction, and is not used for the measurement of the trap’s dimensions. b) Dipole trap geometry. Note that in the x - y plane not both the beams are focused while in the z - x or z – y plane they are, a fact that causes the existence of two different atomic oscillation frequencies, here at 940 and 280 Hz.

Fig. I.3.11: a) Evaluation of the laser waist along the laser path. Zero coincides with the position of the converging (moving) lens L1, while L2 is the diverging lens position L2 and L3 the position of the final lens (see figure 3.5). The stars correspond to measurements made with the ‘razor’ technique. b) Minimum waist dimensions versus zoom position c) minimum zoom position with respect to the position of the MOT and d) waist in the crossed beam position.

Fig. I.3.12: Absorption imaging pictures for several position of the translation stage at a) 25 mm, b) 30 mm c) 35 mm d) 40 mm and e) 45 mm. The size of the atomic cloud or the image contrast is not proportional to the trap’s size since this depends on the number of atoms in the trap. In this point the trap loading is not optimized and it serves only for demonstrating the sufficient laser alignment.