Light generation for laser cooling and trapping of 87 Rb

As was described in section 1.3.10, 87Rb atoms can be trapped and cooled using light forces in a magneto optical trap (MOT). It was seen that many photons need to scatter from an electronic transition in order for a substantial force to be exerted on the atoms, and hence is a prerequisite for cooling and trapping. In the case of 87Rb, the cycling transition is between hyperfine states of the ground and the first excited electronic level, i.e 5 2_S

1/2, F = 2 → 5 2P3/2, F = 3, indicated by the thick arrow in Fig. 2.9 (b). The

selection rules outlined in section 1.3.8 state that ∆F = 0, ±1, and hence spontaneous emission from the excited 52_P

3/2, F = 3 into the 52S1/2, F = 1 is forbidden by this rule.

In reality, the electronic selection rules are not absolute, and in fact about one in every thousand scattering events [92] results in spontaneous emission from the 52P3/2, F = 3

to the 5 2_S

1/2, F = 1 level. To close the cycling transition fully, an extra "repumper"

frequency was therefore required on the 5 2_S

1/2, F = 1 → 5 2P3/2, F = 2 transition,

indicated by the thin arrow in Fig. 2.9 (b). Repumping to the 5 2P3/2, F = 3 level

is not desirable since this transition is not very efficient as per the F selection rules, and also because the 5 2_S

1/2, F = 1 and F = 2 states in this case would couple to one

another coherently via the 52P3/2, F = 3 state, and population would be pumped into

the 52_S

1/2, F = 1 level.

The scheme for producing appropriate light for the magneto-optical trapping of

87_{Rb is presented in Fig. 2.9 (a), and is briefly described here. The cooling laser light}

was provided by a external cavity diode laser (Toptica Photonics, DL100 or DL100

Pro), with output power around 120 mW. The wavelength of the light was determined

780 nm EOM Rb reference cell Interferometer 120 mW 45 mW 15 mW To WM lin. pol. /2 PM fiber EOM Driver 3 2 1 0 2 1 (a) _(b)

Figure 2.9: (a) A photo of a diode laser table showing the important elements for producing fibre coupled light used for laser cooling of 87_{Rb. EOM stands for electro-}

optical modulator, λ/2 is a half wave plate used for rotating the linear polarisation axis of the light from the laser, PM stands for polarisation maintaining, lin. pol. is a linear polariser, and WM stands for wave meter. Also shown are typical powers of the light at various points along the beam path. (b) Energy level structure with cooling (thick arrow) and repumping (thin arrow) transitions for87_{Rb. The frequency of these}

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 Ph ot od io de si gn al (a rb .) Relative frequency (GHz) (a) (b)

Figure 2.10: (a) An interferometer trace showing the modulation of the 87_{Rb carrier}

laser cooling frequency (seen at 0 and 10 GHz) to produce 5 % sidebands at 6.568 GHz for the repumping transition of87_{Rb. The free spectral range of the interferometer was}

10 GHz. (b) A picture of the chamber with labels of the important parts for MOT operation, and superposed laser beam paths. FT stands for "feed through", λ/4 are quarter wave plates for creating circularly polarized light, λ/2 are a half wave plates for adjusting the power ratio in each arm when used in conjunction with a polarizing beam splitter (PBS) cube.

an optical fibre to a wavemeter (Highfinesse, WSU-30 ). The wavelength was stabilized to within ±5 fm by using a proportional-integral-derivative (PID) feedback program implemented in Labview. This program adjusted the wavelength of the light read by the wavemeter by varying the voltage applied to the piezo-electric element determining the fine tuning of the grating angle of the external cavity. The remaining 99% of the laser output was sent through a half-wave plate (λ/2) which rotated the linear polarization axis of the laser output, to a linear polariser to produce a pure horizontal linearly polarized beam.

The repumping transition from 5 2S1/2, F = 1 → 5 2P3/2, F = 2 is shifted by

6.568 GHz from the cooling transition frequency. Rather than use a separate laser for repumping, a portion of the cooling transition light was shifted by 6.568 GHz by an electro-optical (phase) modulator (EOM) (Newport/Spectra Physics, 495010-01-

M). About 5% of the cooling laser light was modulated to the repumping frequency.

The modulation was observed by coupling a portion of the output of the EOM into a scanning Fabry-Perot interferometer. Such an interferometer (ThorLabs, SA201 ) with a free spectral range (FSR) of 10 GHz was used to observe the frequency shift and modulation depth of the light due to the EOM, and a trace of the photodiode signal against frequency is shown in Fig. 2.10 (a). The large peaks are the carrier frequency (i.e the cooling frequency), and the small peaks are the first sidebands (i.e the repumping frequency). Due to the periodic and relative measurements of the

interferometer there are two large peaks (one for each FSR), and two small peaks. The sideband at 6.568 GHz relates to the carrier at 0 GHz, and the sideband at 3.44 GHz relates to the carrier at 10 GHz, such that the first sidebands of each carrier are always 6.568 GHz away. A 40% power loss occurred at the EOM. A portion (≈ 5%) of the remaining light was sent into a Rb vapor cell with a photodiode attached perpendicular to the beam path. Room temperature zero field spectroscopy of87_{Rb was carried out to}

determine the frequency of the cooling transition, and to optimize the EOM frequency shift for the repumping transition frequency. Doppler laser cooling was achieved by red detuning the cooling frequency in the range of 15 - 30 MHz from the maximum of the zero field transition. The remaining light was coupled into a single-mode polarization- maintaining (SMPM) fiber at a typical efficiency of about 35 %, which was directed to the experiment table.

Once collimated onto the experimental table with typical powers of 12 mW, the light was expanded in an adjustable Galilean beam expander between 2 and 10×. The light was then split into three arms by using two polarising beam splitter (PBS) cubes, and the power in each arm adjusted using two half wave plates. The beams were organized around the chamber as shown by Fig. 2.10 (b). Each arm passed through a quarter wave plate (λ/4) just before entry to the chamber to create circular polarisations necessary for MOT operation (see section 1.3.10). The three arms were retro-reflected through λ/4 elements after passing through the chamber, to create the full compliment of six MOT beams. The 1/e2 radius of the MOT beams was chosen as a compromise between the maximisation of the MOT capture volume, and the minimization of ion trap anharmonicities (see sections 1.4 and 2.2). A compromise allowing both stable MOT operation, and only a slight deviation from an ideal harmonic potential for the ions (≈ 6% within 5 mm of the trap axis) was chosen to be r_1/e2 = 2.1 mm.