**4.2 Scanning confocal interferometer**

164 Quantum Optics and Laser Experiments

*<sup>m</sup> <sup>m</sup> <sup>F</sup>*

Extending the absorption equations to te Doppler-free saturation spectroscopy we have

*if*

*dI h n W* 

probe beam with intensity *dI* and the transition probability *W WI <sup>p</sup>* ,

where the population depends on the transition rate *W WI <sup>d</sup>* ,

and 

 *ii iiW W* .

photodiodes.

**4. Experimental details** 

**4.1 The saturated absorption spectrometer** 

Rb cell

43 12

Laser

optical components are given in inches.

1 Thorlabs, Model PTR12114-PTH503

2 Thorlabs, Model DET10

exp 2 2 *B B*

*if if ff ii*

pump beam with intensity *pI* propagating in the opposite direction,

The experiment was installed in a 6x12 feet optical top 1 that was passively damped. The experiment included two tuneable diode lasers, two saturated absorption spectrometers, two scanning interferometers, a complete vacuum system, beam expanders, polarizing optics, infrared camera, optics and mechanics components, a rubidium cells, and

The saturated absorption spectrometer is shown in Fig.8. The laser beam was lifted 15 cm above the optical top level by the mirrors M1 and M2, and directed to the first optical glass beam divider. A small part of the beam was directed to the second optical glass divider, the strongest beam went to the trap. The second beam divider drives the strongest beam to the interferometer and the small beam act as a pump laser in the rubidium cell. The beam reflected off the mirror M3 acts as a test weak beam that was measured by a photodiode 2.

to scanning confocal interferometer

OGD1

Fig. 8. Saturated absorption spectrometer. Pump and probe laser are collinear. PD = photodiode, OGD = optical glass divider, M1, M2, M3 = mirrors. Distance between closest

M1, M2

OGD2 M3 PD

 

 

*k T k T*

1/2 2

*dx* (20)

to beamsplitter and beam

determined by the

detail M1, M2

due to the

(19)

The scanning confocal Fabry-Perot interferometer (Fig.9) is a nice tool to check if the laser is running in single mode operation specially. One of the main features of the Fabry-Perot interferometer is that it can measure with high resolution the spectral content of the laser. A basic Fabry-Perot consists of two identical spherical mirrors with radius *R* separated by a distance *L*. The use of two curved mirrors is convenient as they permit a good match to the Gaussian beam coming from the laser.

Fig. 9. Confocal scanning Fabry-Perot interferometer.

Two parameters defines the properties of a Fabry-Perot, the free spectral range and the *finesse* or resolution. The free spectral range (FSR) is defined by

$$FSR = \frac{c}{4\pi L} \tag{21}$$

where *n* is the index of refraction of the air between the mirrors, *c* the speed of light, *L* the distance between mirrors. Near the centre of the mirrors we have that every time the distance between mirrors is changed by a quarter wavelength ( /4) the same part of the spectrum will be reproduced. The mirrors used in our interferometer 3 have a radius of 75 mm and a *FSR* = 1GHz. The resolution of the interferometer is given by its *finesse* 

$$F^\* = \frac{FSR}{\Delta \nu} = \frac{\pi \sqrt{R}}{1 - R} \tag{22}$$

where is the full with at half maximum of the interference maxima and *R* reflectivity of the mirrors. The *finesse* depends on the mirror reflectivity, the losses due to imperfections on the mirror surfaces or dust, and the alignment of the mirrors. In our interferometer the highest *finesse* reported was larger than *F*\* = 450. A cylindrical piezoelectric transducer (PZT) is attached to one mirror and can move it in small displacements. To displace the mirror a high voltage is applied between the inner and the outer side of the PZT. The interferometer can be used in scanning mode when the laser wavelength is fixed and the piezo transducer is displaced continuously with a ramp function. In this case it is possible to observe the detailed spectra of the laser. Another option is to scan the laser wavelength with a ramp function and the distance between mirrors remains constant. In this case one can observe the laser spectra and change its absolute position in the oscilloscope by applying a

<sup>3</sup> Toptica Photonics, Model FPI100

Cold Atoms Experiments: Influence of Laser Intensity Imbalance on Cloud Formation 167

i h

k

l

o

p

q

r

j

m

n

Fig. 10. Vacuum system a: optical table, b: turbomolecular pump, c: reduction nipple CF 4.5 to 2.75 inch 10, d, j: tee CF 2.75 flange 11 , e: Convectron vacuum sensor, f, p: nipple 12, g, o: manual valve for ultra high vacuum 13 , h: Bayard-Alpert UHV sensor, i: short nipple CF 2.75 flange 14, k: window 15, l: six way cross 16, blank flange for back side 17, m: 8 pins electrical feedthrough, n: bottle with seven horizontal windows and one vertical window, q: ion pump, r: aluminium plate support for ionic pump with dimensions 30x19.5x1 cm mounted

100 cm

cell that uses four optical glass plates with 4 mm wall thickness and dimensions 35 x 50 mm. On the top of the cell we glued a 35 x 35 mm optical glass plate. The cell was glued to the flat side of the flange. The plates were glued with high vacuum Torr seal 18. The second version consisted in an optical glass cell with outer wxlxh wall dimensions 55x55x52.5 mm and 2.5 mm wall thickness 19. The cell was glued on the 4.5 inch side of a zero length reducer from nominal conflate flange 4.5 inch to 2.75 inch. We did not remove the edge of the 4.5 inch side so the cell was installed very tight. This caused that the glass broke after some heat up vacuum procedures. The cell could be repaired several times with the vacuum Torr seal.

in 4 rods of 2 inch diameter, s: L form mount for tubing.

a

f

s

g

b

c

60 cm

d

e

The first two versions of cells are shown in Fig.11.

10 MDC-Vacuum, Model 402013 11 MDC-Vacuum, Model 404002 12 MDC-Vacuum, Model 402002 13 MDC-Vacuum, Model 302001 14 MDC-Vacuum, Model 468008 15 MDC-Vacuum, Model 450020 16 MDC-Vacuum, Model 407002 17 MDC-Vacuum, Model 110008 18 MDC-Vacuum, Model 9530001 19 Hellma Cells, Model 704.003-OG

constant voltage to the PZT. This option is very useful for finding the resonances needed for cooling.
