Frequency Stability of the Iodine Locked Laser

To investigate the laser frequency stability, the beat frequency was utilized to calculate the Allan deviation with 1000 data points, shown in Fig 4-3. The laser frequency had a fractional Allan deviation of 310^-12 at 10 second averaging time, when the laser was stabilized to the a1 component at iodine vapor pressure of 16.5 Pa.

43

Fig. 4-3 Fractional Allan deviation of the measured beat frequency between the laser locked on a₁ component and the OFC.

4.3.3 Absolute Frequency Measurement of the Iodine Hyperfine Transition

The beat frequency between the iodine-stabilized 1070 nm laser and the OFC was measured using a high-frequency counter (Agilent A53150) with a 100 ms gate time and 500 data points were recorded for each beat frequency measurement. Then the average value was used to derive the absolute frequency of the hyperfine transition using Eq. 4.1.

To determine the transition frequency at zero pressure, the pressure shift must be investigated. For pressure shift measurement, the pump and probe powers were fixed at 22.9 mW and 0.39 mW respectively, and the cold finger temperature was changed to control the vapor pressure of the iodine cell. The iodine partial pressure inside the cell can be calculated according to the following formula [86],

3512.830

log( )P 2.013 log( ) 18.37971T T

    , (4.2)

44

where P is the iodine vapor pressure in Pascal and T is the cold finger temperature in Kelvin. The cold finger temperature of the iodine cell was varied from 0.1 ºC (4.2 Pa) to 20.2 ºC (26.9 Pa). All the measured frequencies in the test pressure range were used to determine the zero-pressure absolute frequency and the pressure shift coefficient.

Figure 4-4 shows the frequency measurement versus iodine vapor pressure. The statistical expected zero-pressure absolute frequencies were 560 151 411 260(2) kHz, 560 151 982 649(1) kHz and 560 152 269 813(1) kHz for the a1, a10, and a15

components respectively. The pressure shift coefficients for the a1, a10, and a15

components deduced from the linear relationship of the measured absolute frequencies versus vapor pressures were -5.28 ± 0.08 kHz/Pa, -5.23 ± 0.07 kHz/Pa and -5.12 ± 0.05 kHz/Pa for the a1, a10, and a15 components.

Besides the correction of the pressure shift, another systematic uncertainty come from the servo-loop electronics was found to be around 10 kHz. The DC offset from the lock-in amplifier also enters into an uncertainty of around 2 kHz. Table 4-1 shows the measurement results of the three transition frequencies during one month and the comparisons with the calculated values.

Table 4-1 Selected hyperfine transition frequencies of the P(28) 30-0 line and comparisons to the calculated values (kHz)

Measured^a Calculated^b Measured– Calculated

a1 560 151 411 260 (11) 560 151 405 525 5735 a10 560 151 982 649 (11) 560 151 976 906 5743 a15 560 152 269 813 (11) 560 152 264 072 5741

athe uncertainty is the combined error of statistical error and another systematic uncertainties which come from the servo loop and the DC offset of the lock-in amplifier.

bCalculated from IodineSpec5 [16]

45

Fig. 4-4 Measured absolute frequencies versus iodine vapor pressures for hyperfine components a1, a10, and a15. Each data point represents the mean value of 500 measurements. The standard deviation of the 500 measurements divided by the square root of 500 was assigned as the error bar of each data point.

46

4.3.4 Pressure and Power Broadening of the Iodine Hyperfine Component

To investigate the pressure and power broadening of the a10 component, we adopt the method proposed by Fang et al. [87] to determine the linewidth by measuring the dependence of the peak amplitude of the third-derivative signal on the modulation width. The peak amplitude of the third-derivative signal on the normalized modulation width A can be written as powers were fixed at 22.9 mW and 0.39 mW, and the cold finger temperature of the iodine cell was varied from 0.1 ºC (4.2 Pa) to 20.2 ºC (26.9 Pa). Figure 4-5 shows the variation of the linewidth with iodine vapor pressure. The inset in Fig. 4-5 shows the measured peak amplitude of the third-derivative signal versus the modulation amplitude of the a10 component under different vapor pressure. The pressure broadening coefficient was 125(14) kHz/Pa and the zero-pressure linewidth was 3.72(19) MHz. For the power broadening experiment, shown in Fig. 4-6, the cold finger temperature of the iodine cell was fixed at 0.1 ºC (4.2 Pa), and the pump power was changed from 4.6 to 41.3 mW. The probe power was fixed at 1.7% of the pump power.

The inset in Fig. 4-6 shows the measured peak amplitude of the third-derivative signal versus the modulation amplitude of the a10 component under different pump power.

The relation of linewidth and the pump power is [88], ' (1 1 P P/ _s)

    , (4.4)

where  is the linewidth associated with the limit of weak saturating and probe beams,

47

P is the power in the saturating beam and PS is the saturation power. Through a nonlinear least-squares fit to the data in Fig. 4-6, we obtained = 1.91(4) MHz and PS

= 28.6 mW, corresponding to a saturation intensity of 51.6 mW/cm². However, the saturation intensity was not reliable due to the limited available data points. With a linear fit the measured power broadening slope was 12.6(2) kHz/mW.

Fig. 4-5 Linewidth of a₁₀ versus the iodine vapor pressure. The pump and probe powers were fixed at 22.9 mW and 0.39 mW. The inset shows the measured peak amplitude of the third-derivative signal versus the modulation amplitude under different vapor pressure.

The solid curves in inset depict results of curve fitting.

48

Fig. 4-6 Linewidth of a₁₀ versus pump power. The cold finger temperature of the iodine cell was fixed at 0.1 ºC (4.2 Pa). The inset shows the measured peak amplitude of the third-derivative signal on the modulation amplitude under different pump power. The solid curves in inset depict results of curve fitting.

49

Chapter 5

Frequency Measurement of the 6P

→7S

Transition of Thallium

5.1 Introduction

High precision measurement in atomic system shows very promising in testing new physics beyond the standard model which predicts atomic PNC effects arising from exchange of a Z0 boson between atomic electrons and nucleons. Atomic PNC effects depend intimately on the behavior of the electron wave function near the nucleus. In the atomic PNC measurement an accurate theoretical calculation of atomic structure is needed for such test.

Atomic thallium (Z=81) plays an important role in PNC experiments, since PNC effect grows faster than Z³. The PNC effect had been observed in atomic thallium system using 6P1/2 → 6P3/2 transition in 1995 [3, 4]. The optical rotation measurement of thallium reached 1% of experimental uncertainty. Combining the theoretical calculation, it leads to the weak charge of thallium nucleus, which can be compared with the predication of the standard model. However, the dominating uncertainty is the theoretical calculation, which was as large as 3%. The hyperfine structure is sensitive to the wave functions at small distance from the nucleus. The measured absolute transition energy, HFS and IS of the thallium can provide important information concerning the nuclei to cross-check the theory calculation.

The simplified low-lying energy levels of thallium are shown in Fig. 5-1 with the most precise values of HFS and ISs. HFS measurements with uncertainties <1 kHz for both 6P1/2 and 6P3/2 states have been reported precise HFS using microwave magnetic resonance techniques in the 1950s [32, 33]. The absolute transition frequency and the HFS of the 6P1/2 → 7S1/2 transition have also been reported [9]. However, no precise

50

measurements had been carried out for the 6P3/2 → 7S1/2 transition at 535 nm.

In this work, a precise measurement of the absolute frequencies of hyperfine components of the 535 nm 6P3/2 → 7S1/2 transition for both Tl isotopes was achieved using the single frequency Nd:GdVO4 laser. The results will serve as an experimental constrain for the improvement of theory calculation. A HCL was utilized to provide vapor of the atomic thallium at the metastable 6P_3/2 state. The saturation spectroscopy was employed to resolve all the hyperfine transitions, and their absolute frequencies were measured using a precision wavelength meter.

Fig. 5-1 Energy-level diagram of ²⁰³Tl and ²⁰⁵Tl with the hyperfine splittings and isotope level shifts in the unit of MHz. Energy levels are not to scale. The six lines investigated in this work are labeled A1, A2, A3 and B1, B2, B3. The hyperfine splittings of 6P1/2 and 6P3/2 are taken from [33] and [34], respectively.

The hyperfine splittings of 7S_1/2 are taken from [9]. The level ISs are taken from [35].

51

5.2 Experimental Setup

5.2.1 Description to Laser Setup for Thallium Spectrum

The schematic of our experimental setup for the absolute frequency measurement of the hyperfine components in the 535 nm 6P3/2 → 7S1/2 transition of Tl is shown in Fig. 5-2.

The laser source is the frequency-doubled 1070-nm Nd:GdVO4 laser. The laser used a VBG as the output coupler and the wavelength selector. The frequency of the laser can be tuned coarsely by the VBG temperature via thermal controlling the housing and finely by the PZT voltage. In our experiment, the VBG was heated to ~ 42.5 ℃ to generate the correct wavelength for the 6P3/2 → 7S1/2 transition after frequency

Fig. 5-2 Schematic of the experimental setup. OI: optical isolator, FA:

fiber amplifier, FPI: Fabry-Perot interferometer, PD:

photodiode, PI: PI servo loop, SG: signal generator, Lock-in:

Lock-in amplifier, VA: variable aperture, ABR:

auto-balanced receiver, BS: beam splitter, /4: quarter-wave plate, DM, dichroic mirror, HV DC: high voltage DC power supply for HCL.

52

doubling. By tuning the PZT, the single frequency tuning range without mode-hopping at total output power > 100 mW was about 5 GHz at 1070 nm, which was not wide enough to cover the whole 6P3/2 → 7S1/2 hyperfine transition lines after frequency doubling. Therefore, the whole spectrum of 6P3/2 → 7S1/2 transition was divided into two regions to be separately investigated and the center of each region was set by tuning the VBG temperature. To reduce the laser frequency drift it was locked to a confocal Fabry-Perot interferometer (FPI). The laser frequency was then tuned by scanning the FPI cavity length after it was locked.

The central beam of the VBG laser boosted by a 900-mW Yb-doped fiber was then focused into a 50 mm long MgO:PPLN crystal with a lens (f = 100 mm) for generating 535 nm Laser. The PPLN crystal was temperature-stabilized around 101 ℃ to achieve the quasi-phase matching condition for thallium 6P3/2 → 7S1/2 transition.After passing through the PPLN, the 1070 nm light beam was separated out by two DMs and the second harmonic 535-nm green light was collimated to a beam size of 8.4 mm in diameter. The power of 535 nm light beams after these two DMs was typically 46 mW at 700mW 1070nm fundamental pump power.

5.2.2 See-Through Hollow Cathode Lamp and Optogalvanic Signal

A commercially available see-through HCL was used as the thallium atomic source.

HCL is a metal-vapor discharge lamp specifically developed for atomic absorption spectroscopy and narrow band atomic line filter [89]. Exciting the HCL with a high voltage source, a discharge plasma is generated inside the cathode. HCL produces not only sufficient metal vapor without high temperature oven, but also the atoms at the excited states. When a laser enters the cathode and the atoms inside the discharge plasma resonantly interact with the incident photons, the electrical impedance of the

53

discharge plasma is altered, by which an optogalvanic (OG) signal is obtained.

Optogalvanic effect has been widely used to stabilize laser frequency [90]. In our experiment, a Hamamatsu L2783-81 NE-TL see-through HCL was used as the thallium vapor cell. The cylindrical cathode (19 mm in length and 3 mm in diameter) and the ring anode are sealed with neon buffer gas at a pressure of 14 torr. The HCL was operated at a current of 10.7 mA with a 30 k ballast resistor.

The absorption lines of thallium in the HCL are Doppler broadened by the random thermal motion of the thallium atoms. Saturated absorption spectroscopy was used to eliminate the Doppler-broadening by counter-propagating a strong pump beam over the probe beam. The linear polarized green light passes through a 95:5 (R:T) beam splitter (BS) reaches a precision wavelength meter (HighFinesse, WSU 30) for frequency measurement. The beam reflected by the BS was further reflected by a polarizing beam splitter (PBS) and transformed into circular polarization by a quarter-wave plate (λ/4), and then goes through the HCL acting as the pump beam. The circularly polarized green light was further separated by a 50/50 beam splitter. The beam passing through the BS was retro-reflected by a mirror into the HCL acting as the probe beam. The reflected light was then transformed into linear polarization by going through the λ/4 plate again and passes through the PBS to the signal input of an auto-balanced receiver (ABR, New Focus, 2017 Nirvana). The auto-balanced receiver was used to suppress the intensity noise of the 535 nm light. The counter-propagated pump and probe beams were overlapped within the HCL with powers of 12.5 mW and 2.7 mW, respectively.

The beam reflected by the 50/50 BS was directed into the reference input of the auto-balanced receiver. The optimal power ratio of the signal to the reference beam for noise cancellation was achieved by a variable aperture in front of the reference input.

54

5.2.3 Thallium Absorption Spectrum

To tune the laser wavelength to the thallium transition, the 535 nm green light was first amplitude modulated by a mechanical chopper at 2 kHz. The optogalvanic signal from the HCL was detected with a lock-in amplifier (Standard Research Systems SR830) to obtain the Doppler broadened spectrum of the 6P3/2 → 7S1/2 transition by tuning the laser frequency via scanning the FPI cavity length. To obtain the third-derivative saturated absorption spectrum of the hyperfine transition, the laser cavity length was modulated at 12 kHz and the balanced signal from the auto-balanced receiver was demodulated with a lock-in amplifier at the third harmonics (36 kHz). The time constant was set to 30ms at 12dB/oct. To lock the laser frequency to the center of the hyperfine transition, the demodulated signal was feed through a PI (proportional and integral) servo loop to control the FPI cavity length.

5.2.4 Wavelength Meter Calibration

The absolute transition frequencies were measured using the precision wavelength meter. It is a Fizeau based wavelength meter and a similar wavelength meter has been used to measure the hyperfine splitting in Cs to an accuracy of 0.5 MHz [91, 92]. Our wavelength meter has an absolute accuracy of 30 MHz in 10 h [18] after it is calibrated against a stabilized laser with an accurately known frequency. In our work, a frequency doubled Nd:YAG laser at 532 nm stabilized to the hyperfine component a10 of R(56) 32-0 transition of molecular iodine was utilized to calibrate the wavelength meter. Its absolute frequency has been recommended as an optical frequency standard [14,15].

We find that the drift of the wavelength meter was less than 1 MHz within 10 min after calibration. To check the accuracy of the wavelength meter at 535 nm, the frequency doubled Nd:GdVO4 laser was stabilized to the hyperfine components of the P(28) 30-0

55

transition of molecular iodine at 535 nm, which is less than 10 GHz away from the thallium transitions. The absolute frequencies of the a1, a10, and a15 hyperfine components have been measured using an optical frequency comb (OFC) to an accuracy of 11 kHz, described in Chapter 4. The differences between the absolute frequencies measured by the wavelength meter and the OFC were less than 3 MHz for all three hyperfine components. In addition, the separation of hyperfine components obtained by the wavelength meter was less than 1 MHz deviation from the values obtained by OFC. To avoid the long time drift in the wavelength meter during frequency measurement, the calibration using iodine-stabilized 532 nm laser was carried out every 10 min to assure the accuracy of our measurements was better than 30 MHz.

5.3 Experimental Results and Discussion

5.3.1 Thallium Hyperfine 6P_3/2→7S_1/2 Transition Spectrum

The 6P3/2 → 7S1/2 transition for ²⁰³Tl and ²⁰⁵Tl consists of six hyperfine components as shown in Fig. 5-1. These hyperfine components are labeled as A1, A2, A3 and B1, B2, B3 for ²⁰³Tl and ²⁰⁵Tl, respectively. The output of the lock-in detection of the discharge current modulation, due to the laser intensity modulation by the mechanical chopper, provides the OG spectrum shown in the upper curve of Fig. 5-3. The hyperfine components of 6P3/2 → 7S1/2 transition are not resolved in the OG spectrum due to the Doppler broadening. The Doppler-free saturated absorption spectrum is shown in the lower part of Fig. 5-3. For the strongest component B2, the signal-to-noise ratio (SNR) was 220. The ratio of the signal strength between the observed transitions does not agree with the predicted strength based on the transition rate calculation (shown in the OG spectrum in Fig. 5-3). This discrepancy, which was also observed in the emission

56

profile of the earlier literature [89], was attributed to the high drive current of the HCL.

The SNR of the A1, A2, B1, and B2 components was high enough for laser frequency stabilization and direct frequency measurement using the HighFinesse wavelength meter.

5.3.2 Spectral Linewith of the Thallium Hyperfine Transition

The observed saturated absorption spectrum shown in Fig. 5-3 was acquired using a frequency modulation width that was optimized for the third-derivative signal of the B2 component. For a spectral line with a Lorentzian profile, the third derivative signal

Fig. 5-3 Observed spectrum of hyperfine components of the 6P3/2→7S1/2

transition in atomic thallium at 535 nm. The upper figure is the optogalvanic (OG) spectrum. Vertical lines show the calculated spectral intensity. The lower figure is the third-derivative signal of the saturated absorption spectrum.

57

reaches a maximum while the modulation width is 1.75 × FWHM (full width at half-maximum) and the peak-to-peak frequency interval then equals to 1.65 × FWHM [93]. The peak-to-peak frequency interval was 70 MHz in our experiment, thus the FWHM of the B2 component was 42 MHz. For comparison, the natural linewidth of the B2 component was estimated to be 17 MHz by the lifetime of 7S1/2 state [94].

5.3.3 Frequency Stability of the Frequency Locked Laser

The laser was locked to the zero-crossing points of the third derivative signal. The error signal of the stabilized laser was used to evaluate the stability of the laser frequency.

The 70 MHz peak-to-peak frequency interval of the third-derivative signal of the B2 component was employed to determine the frequency discrimination slope. Figure 5-4 shows the Allan deviation for the frequency doubled Nd:GdVO4 laser stabilized at the B2 component. The frequency stability was 30 kHz at 1 s averaging time and reaches 2 kHz at 10 s.

Fig. 5-4 Allan deviation of the laser locked to B2 component at 535 nm.

58

5.3.4 Absolute Frequency, Hyperfine Splitting and Center of Gravity of the Thallium 6P_3/2→7S_1/2 Hyperfine Transitions

The absolute frequency measurements of the 6P3/2 → 7S1/2 hyperfine transitions were performed using the HighFinesse wavelength meter, while the laser was locked to the zero-crossing points of the third derivative signal. Each measurement of the locked laser frequency was finished in 5 minutes after calibration of the wavelength meter. The accuracy of the wavelength meter was re-checked with the calibration laser after every measurement. The laser was unlocked and relocked between every measurement. More than 5000 data were taken for each individual measurement and more than 20 frequency measurements were taken for each of these four locked laser frequencies.

The standard deviation for each frequency measurement of these four strong components was from 0.8 to 2.6 MHz, which depended on the SNR. The standard error of the mean, as the statistical uncertainty of the central frequency, of each hyperfine transition was from 8 to 18 kHz. Various systematic uncertainties were also studied, including: 0.6 MHz error due to the DC-offset of the third derivative signal and 0.2 MHz uncertainty caused by the electronic noise. However, the final accuracies of frequency measurements, which were dominated by the accuracy of the wavelength meter, were 30 MHz for all of the A1, A2, B1, and B2 components.

The signal amplitude of A3 and B3 components were too small to stabilize the laser for a direct frequency measurement. Alternatively, the frequency intervals A2-A3 and B2-B3 were acquired from the observed spectrum by scanning the laser frequency.

The third derivative spectrum in Fig. 5-3, where the frequency axis was given by

The third derivative spectrum in Fig. 5-3, where the frequency axis was given by