In Situ Measurement of Vacuum Window Birefringence using ²⁵Mg⁺ Fluorescence

The method presented here, can be used to compensate in a birefringence of vacuum windows, to generate a purely polarized light, inside a vacuum chamber. It can have many applications in proceeding experiments involving cold atoms or ions. The main advantage of this technique is, not atoms or ions are used not only as objects to be started but also, as in-situ detectors of polarization states.

So, we can avoid putting a polarization analyzer into the vacuum system. Demonstrating the procedure will be Wen Hao Yuan, a engineer from our laboratory, Zhi Yu Ma and Peng Hao, two PhD students from our laboratory. To set up the reference directions for the A and B polarizers, place the polarizers into the path of a 280 nanometer fourth harmonic laser beam, and carefully adjust the polarizer holders to keep the back reflection light coincident with the incident light, to keep the laser beam perpendicular to the polarizer surfaces.

Place a power meter behind polarizer A, and rotate the polarizer to maximize the output power. Record the angle of polarizer A by Stepper Motor Rotation Stage and the power behind polarizer A, by power meter. Next, place the power meter behind polarizer B and rotate polarizer B to maximize the output power.

Record the angle of polarizer B, by Stepper Motor Rotation Stage and the power behind polarizer B, by power meter. To set up the reference directions for the azimuthal angles of the wave plates, place a half wave plate into the beam path between the polarizers and rotate the wave plate to maximize the output power. Use the power meter behind polarizer B, to record the rotation angles and the output laser powers.

Place a quarter-wave plate into the beam path between the half wave plate and polarizer B, and rotate the quarter-wave plate to maximize the output power. Use the power meter behind polarizer B, to record the rotation angles and the output laser powers. Then remove polarizer B and the power meter from the beam path.

Use two mirrors to direct the laser beam into the vacuum chamber that houses an ion trap, to interact with magnesium-25 ions. For Doppler cooling of single magnesium-25 ions, first turned a 532 nanometer ablation laser and a 285 nanometer ionization laser. To make sure only one ion is trapped in the ion trap, look at the image of an Electron Multiplied Charged Coupled Device.

Magnesium atoms have three isotopes, so we'll be sure to analyze magnesium-25 isotopes, using proper ionization frequency. Then adjust the HEM holds coil current, to set the magnetic field to 6.5 Gals. To lock the Doppler cooling laser frequency to a wavelength meter, use a frequency counter to skin the frequency of the 280 nanometer laser and the photon multiplier tube, while using a wavelength meter to record the frequency of the laser.

When the resonant frequency at which the fluorescence rate reaches a maximum, use a digital servo control program, to lock the laser frequency to the wavelength meter. To set the intensity of the laser to equal the saturation intensity, adjust the driving power of an acousto-optic modulator, to set the power of the laser. Record the power and the fluorescence counts and use the appropriate equations to fit the curve of the power and the fluorescence counts, to obtain the saturation power.

Then adjust the acousto-optic modulator driving power, to set the laser power to the determined saturation power. Alternatively, adjust the azimuthal angles of the half and quarter-wave plates close, to maximize the fluorescence counts by hand and record the, azimuthal angles of the plates, at their maximum counts. Then use the Stepper Motor Rotation Stages to rotate the plates and record the rotation angles and the corresponding fluorescence counts.

Because magnesium-25 ion has 48 Zeeman levels, analytical solutions cannot be derived from the rate equations. These data can however, be simulated by a numerical program. Here, the relationships between the polarization states and the fluorescence counts under different light intensities are shown, indicating that the polarization state of the light inside the vacuum chamber for this analysis, was greater than 0.999, when the fluorescence counts were maximized.

At this position, the fluctuation of the fluorescence count was less than 2%Here, the relationship of the laser power and the fluorescence counts under different D tuning frequencies, is shown. Plotting the data into curves allows determination of the saturated power value at each frequency. By fixing the azimuthal angle of one wave plate, rotating the other, and recording the angles and the fluorescence counts, differences between the theoretical and experimental results, can be assessed.

In this analysis, the theoretical and experimental data were closely matched, demonstrating the reliability of the method. When putting the polarizers and the wave plates into laser paths, remember that the laser beam must be perpendicular to the surfaces on each polarization element. As birefringence or window is affected by temperature, we can use this simple and the quick method, to compensate some of effects in real time, for your feedback two wave plates.

This method provides measure for obtaining measurements, of birefringence of windows in vacuum based fields, such as optical clocks and experiments.