Contrast of Ramsey-CPT Fringes in Quenching and Depolarizing Gases

Molecular nitrogen is often used as a buffer gas in cells with alkali metals due to its known ability to quench resonant fluorescence. It is widely believed that the suppression of spontaneous emission decreases the width of coherent population trapping resonance. However, our recent results have not confirmed this positive action of molecular nitrogen within the typical range of ⁸⁷Rb concentrations and buffer gas pressures. On the opposite, we have observed the negative influence of quenching, the decrease in contrast of the coherent population trapping resonance in ${{\sigma }^{ + }}$–${{\sigma }^{ + }}$ configuration. In this work, we further confirm these results implementing the Ramsey spectroscopy, and compare the characteristics of the central fringe in nitrogen and neon, and show that the latter provides a significantly better contrast-to-width ratio.

INTRODUCTION

All-optical interrogation scheme of the coherent population trapping (CPT) has led to the development of chip-scale atomic clocks [1] that are nowadays used in navigation and communication [2], small satellites known as “CubeSats” [3], undersea sensing [4], etc. Even though these clocks have a small size and low power consumption, there is a need to improve their frequency stability for a wider range of applications [5].

A glass cell containing alkali metal atoms is one of the basic elements of clocks. It is usually filled with buffer gases to decrease the coherence relaxation rate and to narrow reference resonance. Nitrogen is often preferred because it quenches the spontaneous emission, which should lead to the additional broadening of the resonance [1, 6]. On the other hand, it is known that inert gases effectively depolarize the excited state of alkali-metal atoms, while they are almost non-quenching [7]. This effect occurs due to a quick relaxation of the state with nonzero angular momentum upon the collisions and leads to equalization of excited-state sublevel populations [8, 9].

In our recent work [10], we have assumed that quenching can reduce the degree of excited-state depolarization since the cross-sections of these effects are comparable. We performed a numerical calculation of the optical pumping effect in ⁸⁷Rb atoms, accounting for all sublevels of D₁ line. Two extreme cases were considered: (1) there is no depolarization of the excited state, and (2) populations of the excited state sublevels are equal. In the second case, the contrast of the CPT resonance is twice as higher at a significant optical pumping rate. We concluded that nitrogen should provide a smaller contrast than inert gases due to a lower excited state depolarization and verified it experimentally for the ${{\sigma }^{ + }}$–${{\sigma }^{ + }}$ scheme utilized in chip-scale atomic clocks.

Ramsey spectroscopy [11] is currently an attractive approach to develop miniature CPT-based atomic clocks with improved frequency stability [12–14] since the pulsed scheme provides a suppression of the light shift of the microwave transition frequency compared to the continuous interrogation.

In this work, we demonstrate that neon provides a greater contrast-to-width ratio of the central Ramsey fringe than nitrogen and measure the corresponding difference in the short-term frequency stability.

EXPERIMENT

The experimental setup is schematically shown in Fig. 1. A single-mode vertical-cavity surface-emitting laser VCSEL with a wavelength of $\simeq {\kern 1pt} 795$ nm was used. The laser injection current was modulated by the radio-frequency (RF) signal at a frequency close to 3.4 GHz, and the first sidebands of the polychromatic optical field were tuned to transitions ${{F}_{g}} = 2 \to {{F}_{e}}$ = 2, ${{F}_{g}} = 1 \to {{F}_{e}} = 2$ of the ⁸⁷Rb D₁ line. The operating value of the injection current was 1.15 mA, and the RF field power was set so that the intensity of the first spectral sidebands was maximum. An acousto-optic modulator AOM was used to implement the pulsed excitation scheme of the CPT resonance. The first-order diffracted beam passed through the atomic cell and was registered by a photodetector PD. A quarter-wave plate λ/4 was used to form the CPT resonance in the ${{\sigma }^{ + }}$–${{\sigma }^{ + }}$ configuration. The diameter of the laser beam was 3 mm. The frequency of laser radiation was stabilized at the maximum of the absorption contour. For this, the laser injection current was modulated at the frequency of 15 kHz, and the correction signal was applied to the temperature of the laser.

Fig. 1.

(a) Layout of the experimental setup. (b) Diagram of the optical pulse sequence: ${{T}_{p}}$ is the pump pulse duration, ${{T}_{R}}$ is the free evolution time, ${{\tau }_{d}}$ is the detection time, P is the power of laser field during pump pulse. In stability measurement mode the RF field frequency is switched between values ${{\nu }_{1}}$ and ${{\nu }_{2}}$ after detection in each cycle.

The AOM operating signal (80 MHz sine) was modulated by a sequence of rectangular pulses; see Fig. 1b. The field configuration for Ramsey spectroscopy of the CPT resonance differs from the traditional one, containing both optical and microwave pulses [15]. The Ramsey-CPT pulse sequence consists of optical pulses only. The pump pulse must be of sufficient duration and amplitude so that the population distribution over the magnetic sublevels of the ground state and the coherence of the working sublevels reach their steady states. The detection duration must be short enough so that the radiation almost does not disturb the atoms. The pump pulse with duration ${{T}_{p}}$ was followed by a free evolution time ${{T}_{R}}$. The signal of the atomic cell transmission was detected at the beginning of each pump pulse for ${{\tau }_{d}} = 5$ μs. To observe Ramsey fringes (Fig. 2), the frequency of the RF field was linearly scanned near the value corresponding to the frequency of the metrological transition. Data acquisition and pulse sequence control were performed using the NI PCIe-6363 DAQ board and LabVIEW software. The signal from photodetector was used both in the laser frequency stabilization loop and for the detection of the Ramsey-CPT signals.

Fig. 2.

Ramsey fringes observed in a cell with 90 Torr of neon (5-point moving average of raw data). Experimental parameters are P = 30 μW, ${{T}_{p}} = 3$ ms, ${{T}_{R}} = 1.8$ ms, ${{\tau }_{d}}$ = 5 μs. $\Delta \nu$ is the full width at half maximum, $C = A{\text{/}}B$ is the resonance contrast.

We used two cylindrical atomic cells (8 mm diameter, 15 mm length) with ⁸⁷Rb, one filled with nitrogen (N₂) and the other with neon (Ne), both at a pressure of 90 Torr. The cells were studied under the same experimental conditions. The atomic cell was placed in a longitudinal magnetic field of 0.02 G to separate the metrological microwave transition from magneto-sensitive ones at sublevels ${{m}_{{{{F}_{g}}}}} = \pm 1$. The temperature of the atomic cell was maintained at 66°C and its variations during the experiment did not exceed 0.01°C. The cell, the heater, and the solenoid were placed in a three-layer μ-metal magnetic shield providing an over 500-fold suppression of the laboratory magnetic field.

It is known that the width of the central Ramsey fringe is inversely proportional to the free evolution time, and its amplitude exponentially decays with ${{T}_{R}}$. Therefore, the maximum amplitude/width ratio is achieved at a certain value of ${{T}_{R}}$, which is close to the relaxation time of the ground-state coherence. We estimated the latter from the CPT resonance width $\Delta \nu$ registered in the continuous wave mode when extrapolating the optical power to zero, $1{\text{/}}\pi \Delta \nu \simeq 1.8$ ms for   both gases. In further experiment, we used ${{T}_{R}} =$ 1.8 ms in order to obtain the amplitude/width ratio which is close to maximal.

The short-term frequency stability of the atomic clock is often characterized by the ratio of the resonance contrast to its width, Q [16], when limited by the shot noise. We measured the width $\Delta \nu$ and contrast C (Fig. 2) of the central Ramsey fringe and obtained the dependence of Q on optical power for both cells under study; see Fig. 3. The maximum value of Q for N₂ $\simeq {\kern 1pt} 8\%$/kHz is achieved in the range of 30–40 μW. At higher powers, Q decreases due to effective pumping into the non-absorbing state. In the cell with Ne, we obtained a 2.5 times higher value of Q ($\simeq {\kern 1pt} 20\%$/kHz) in the range of 70–100 μW.

Fig. 3.

Contrast-to-width ratio of the central Ramsey fringe versus the optical power in cells with neon and nit-rogen. Experimental parameters are ${{T}_{p}} = 3$ ms, ${{T}_{R}} =$ 1.8 ms, and ${{\tau }_{d}} = 5$ μs.

To confirm the benefits of using Ne in the pulsed ${{\sigma }^{ + }}$–${{\sigma }^{ + }}$ scheme, we carried out measurements of the frequency stability in a way described in [12]. The source of the RF field Agilent 8257C was referenced to a passive hydrogen maser VCH-1007, and the frequency correction signal was recorded. For this, the frequency of the RF field was switched after the detection time in each cycle and the difference of the atomic cell transmission at the RF field frequencies ${{\nu }_{1}}$ and ${{\nu }_{2}}$ was obtained; see Fig. 1b. The frequency difference ${{\nu }_{1}} - {{\nu }_{2}}$ was set close to the half-width of the central fringe to achieve the maximum slope of the correction signal. Thus, the recorded correction signal allows to measure the stability of the Ramsey resonance frequency against the maser.

The measured dependences of the Allan deviation on the averaging time for N₂ and Ne are shown in Fig. 4. The radiation power during the pump pulse was 30 μW for N₂ and 80 μW for Ne. Based on the obtained values of Q, it was expected that the frequency stability up to 100 s in a cell with Ne would be 2.5 times better than in N₂. An approximately 2-fold improvement in the frequency stability was experimentally achieved. However, we registered a higher noise level in Ne compared to N₂ even at the same laser power. Due to the difference in the collisional broadening coefficients [17], the absorption contour of rubidium atoms in a cell with Ne is narrower than in a cell with N₂ under the same conditions. It results in an increased amplitude noise caused by the laser frequency fluctuations, which can be suppressed by using a broadband feedback loop in the laser frequency stabilization system. The pressure 90 Torr is not optimal for the size of the cells used, but is suitable for demonstrating differences between gases. The deterioration of stability after 200 s is caused by a temperature drift, which strongly influences the frequency of the CPT resonance in atomic cells with one buffer gas. Temperature sensitivity can be suppressed by using a mixture of two gases with linear temperature coefficients of opposite signs. Most often, the mixtures Ar–N₂ and Ar–Ne are used, of which the latter has an advantage of a higher contrast-to-width ratio.

Fig. 4.

Allan deviation of the central Ramsey fringe frequency obtained in the studied cells.

CONCLUSIONS

We compared Ramsey CPT resonances registered in the ${{\sigma }^{ + }}$–${{\sigma }^{ + }}$ scheme in two miniature atomic cells filled with two different buffer gases: Ne and N₂. Our results demonstrate that under the same experimental conditions Ne provides a greater contrast-to-width ratio of the central Ramsey fringe. Measurements of Allan deviation showed an improvement in short-term frequency stability of the central Ramsey fringe by a factor of 2 for Ne. This advantage is due to a higher degree of equalization of the populations of the excited state sublevels and thereby the reduced optical pumping into the non-absorbing state. Thus, using a combination of noble buffer gases may be advantageous for improving the frequency stability of miniature Ramsey-CPT atomic clocks.