Pressure effect on hyperfine CPT resonance of ground-state Li atoms in glass hot-vapor cell

Abstract

We report the hyperfine splitting frequency of ground-state lithium atoms. The frequency shift is induced by the collisions to helium and xenon buffer gases. Coherent population-trapping resonance between the hyperfine levels enables the frequency measurements in the range of pressure from 2 to $54\,\hbox {kPa}$ and temperature from 260 to $400\,^{\circ }\hbox {C}$ in borosilicate-glass cells. The buffer-gas density is self-consistently calibrated from the hyperfine splitting in the sealed cells. The resonance frequency and the line width provide an insight into collision-induced spin dynamics, where hyperfine-shift, spin-rotation, and spin-exchange interactions play an important role in atomic lithium vapor and buffer gas.

1 Introduction

Atomic lithium (Li) vapor has been investigated in a few spectroscopic works, but not fully understood due to difficulty of using glass cells [1, 2]. The atom density is too low to measure light absorption at a moderate temperature $\lesssim 200\,^{\circ }\hbox {C}$. By heating, the atoms are believed to attack transparent glasses and crystals. In addition to atom sources such as metal dispenser [3] and light-induced atomic desorption [4], a reliable technique of manufacturing glass Li-vapor cell is necessary for the study of collisional properties of Li atoms to the other atoms and molecules [5], one purpose of this work. It is true that bulk metal breaks the cells when on the walls. On the other hand, the vapor colors the glass, but does not necessarily break it even at high temperature $\sim 400\,^{\circ }\hbox {C}$. We have reported that the borosilicate-glass cells are available at least for hundreds hours with sufficient atom density. In the vapor cell, a ceramic MgO pot is used for protecting bulk metal from contact with the glass walls [6]. Since the ceramics are heat-resisting, the glass cell can be baked with the Li metal to remove impurities at $350\,^{\circ }\hbox {C}$. At the temperature, a negligible amount of metal is evacuated for a few hours of baking. The whole cell can be homogeneously heated, leading to precise measurement of quantities sensitive to temperature and buffer-gas density. Since the vapor cells consist of non-magnetic and non-metallic materials, homogeneous electromagnetic fields are applied to the atomic vapor. Therefore, Li vapor comes to be adapted into precision measurements [7]. In low magnetic fields, the hyperfine-shift interaction during collisions to buffer gas leads to the change of hyperfine splitting (HFS) and the damping of the hyperfine coherence of ground-state atoms [8]. The pressure shift can be an atomic standard of pressure at the range of 1–100 kPa [3]. In higher magnetic fields $\gtrsim 10\,\hbox {mT}$, where the Zeeman splitting becomes comparable to HFS, the same interaction induces the relaxation between the states satisfying the change of magnetic quantum number, $\varDelta m_\mathrm{S} = - \varDelta m_\mathrm{I}$ [5]. Through this relaxation, the nuclear spin can be polarized by optical pumping although the electron spin S and the nuclear spin I are decoupled from each other [9].

In this paper, we report the HFS frequency of ground-state $^7$Li atoms in the buffer gases, helium (He) and xenon (Xe), using sealed glass cells. These buffer gases are adopted based on extremes of character such as light and heavy, a few and many electrons, and with and without nuclear magnetic moment. The pressure broadening of optical transition can be larger than the fine-structure splitting frequency [10], a unique character of the Li atoms. In the wide pressure range, coherent population trapping (CPT) is suitable for measurement of resonance between hyperfine levels. This work is the first application of the CPT resonance to vapor-phase Li atoms. The HFS frequency presents linear dependence on the pressure. The resonance shows narrow linewidth independent of the He-gas pressure, whereas broadening in Xe gas, the first experiment for Li atoms in combination with Xe gas. We will discuss the broadening mechanism of the hyperfine-shift interaction, the spin-rotation interaction, the spin-exchange interaction between the Li valence electron and the Xe nuclei, $^{129}$Xe and $^{131}$Xe, and the effects of formation of van der Waals molecules. By heating, however, the CPT resonance is broadened in He gas. It indicates spin exchange between the electrons of Li atoms in dense atomic vapor.

Fig. 1

a Energy levels of $^7$Li atoms (${I=3/2}$). b A double $\varLambda$ scheme consists of two single $\varLambda$ schemes. Each linearly polarized light is a superposition of two circularly polarized light. Four circularly polarized lights are dark resonant with the hyperfine levels. Gray box schematically shows pressure broadened $D_1$ line. These are not drawn to scale

2 Coherent population-trapping

The energy levels of $^7\hbox {Li}$ atoms are shown in Fig. 1. The HFS frequency of the ground state $\nu _\mathrm{HF}$ is $803.504\,\hbox {MHz}$ in vacuum [1, 11, 12]. The resonant microwave wavelength, ${\lambda _\mu = 0.37\,\hbox {m}}$, is larger than the cell dimension. The atoms are confined within $\lambda _\mu / 8$ at any buffer-gas pressure in this work. Different from heavy alkali metal atoms, Rb and Cs, the frequency $\nu _{\mathrm{HF}}$ is less than the Doppler width of optical transitions ${\delta \nu _{\mathrm{D}} \sim 3\,\hbox {GHz}}$ and the pressure-broadened width $\delta \nu _p$ can be larger than the fine-structure splitting $\nu _{\mathrm{FS}} = 10\,\hbox {GHz}$. Therefore, depopulation optical pumping is not an effective way to create a population imbalance between the hyperfine levels. It is difficult to detect hyperfine resonance using real microwave. On the other hand, the population imbalance is not required for CPT resonance. In addition, pressure broadening of ${\delta \nu _p \sim \nu _{\mathrm{HF}}}$ is desirable for better contrast of the 0-0 hyperfine transition, as described below. The light shift of HFS would happen due to mistuning of laser power and frequency, as often shown in the double-resonance experiment of laser and microwave. Generally, in CPT resonance, it is mostly eliminated because both hyperfine levels are, respectively, resonant with laser beams [13]. It should be noted that one laser beam resonant with one atomic transition is off-resonant to the other transition. Due to smallness of Li HFS, the respective off-resonant lights can induce repulsive light shift. Therefore, a weak light irradiation is preferable to avoid the light shift in Li CPT.

The two laser beams, if the frequency difference equals to $\nu _\mathrm{HF}$, can pump the atoms to a dark state, $|{0 \leftrightarrow 0}\rangle = \alpha |{F=2}, {m_F=0}\rangle +\beta |{F=1}, {m_F=0}\rangle$, where $\alpha$ and $\beta$ depend on polarization, amplitude, and phase of the beams. When the beams are sufficiently stable for pumping time, the complex amplitudes, $\alpha$ and $\beta$, are well defined via common excited states and the light transmission is increased on the CPT resonance. Since the dark state is most populated by a double $\varLambda$ scheme (see Fig. 1) in push–pull optical-pumping [14], ${lin \perp lin}$ [15], ${lin \parallel lin}$ [16], and ${\sigma _{+}-\sigma _{-}}$ [17] configurations, the visibility of the resonance is higher than that of each single $\varLambda$ scheme by circularly polarized beams. The first two configurations are adopted in this work, which establish the CPT resonance more constructively when the pressure broadening is larger than the hyperfine splitting and the fine-structure splitting of the excited states. Since the hyperfine splitting of the excited state is on the order of natural width, the linewidth $\delta \nu _p$ in the buffer-gas pressure of $1\,\hbox {kPa}$ is large enough to satisfy the CPT condition. Therefore, it is possible to measure the frequency $\nu _{\mathrm{HF}}$ in a wide range of buffer-gas pressure. When $\delta \nu _p < \delta \nu _{\mathrm{D}}$, a part of atoms are optically pumped to the dark state. When $\delta \nu _p \sim \delta \nu _{\mathrm{D}}$, the width $\delta \nu _p$ is still smaller than the splitting $\nu _{\mathrm{FS}}$. The $D_1$ transition is isolated from the $D_2$ transition and suitable for the CPT resonance. Therefore, Li atoms are sufficiently pumped to the dark state. When ${\delta \nu _p \gtrsim \nu _{\mathrm{FS}}}$, we are able to detect the CPT signals by tuning the laser frequency to the absorption maximum and by increasing the laser power. Although the Ramsey fringes have been detected for precision measurements [13, 15, 18], the Rabi resonances are used for measurement of the HFS frequency and the resonance width in this work.

3 Experiment

The borosilicate glass Li-vapor cells were manufactured in a similar way to the previous work [6]. At the room temperature, the buffer-gas pressure was measured by a temperature-controlled capacitance manometer, and the cells were sealed off. We used helium and xenon gases of natural abundance, respectively. The number density n was calculated by the equation for an ideal gas. We express the density by ${N = n/n_0}$ in units of amg, where the number density of an ideal gas $n_0=2.69\times 10^{19}\,\hbox {cm}^{-3}$ at a pressure of $1\,\hbox {atm}$ ($101.325\,\hbox {kPa}$) and a temperature $T_0 = 273.15\,\hbox {K}$. The outer diameter of spherical cells was 50 mm. Some degree of distortion and depolarization of the light beam by spherical windows might degrade the visibility of CPT signals. This problem will be resolved in the next design of glass cell.

Fig. 2

Dye laser was tuned to the $^7$Li D lines by a wavemeter and absorption in a hollow-cathode (HC) lamp, and optimized by the CPT signal at each gas pressure. Two laser beams were generated by an acousto-optic modulator (AOM) with two different frequencies and orthogonal linear-polarizations. The beams were irradiated to the glass cell through a polarization-maintain (PM) single-mode optical fiber. The acoustic frequency was modulated to measure the dispersive line shape of the signals by lock-in detection of transmitted laser power. The optical power and the relative phase before the glass cell were stabilized by respective proportional–integral–derivative (PID) controllers. The measurement system was synchronized with a clock locked to the signal of global positioning system (GPS) satellites

The experimental setup is shown in Fig. 2. The optical frequency of a dye laser $\nu _{\mathrm{L}}$ was coarsely tuned to the D lines (671 nm) by a wavemeter and absorption in a hollow-cathode Li lamp. Fine tuning in the pressure width $\delta \nu _p$ and the Doppler width $\delta \nu _{\mathrm{D}}$ was achieved by optimizing the CPT signals. Although the stability of optical frequency $\nu _\mathrm{L}$ remained unchanged from the commercial one $\sim 1\,\hbox {MHz}$, the laser power and pointing noises were reduced in the apparatus. The laser beams of the optical frequency ${\nu _{\mathrm{L}} \pm \nu _\mathrm{S}}$ were generated by an acousto-optic modulator (AOM). The second harmonics of ultrasonic frequency $2 \nu _{\mathrm{S}}$ was phase-locked to the synthesizer (PLL) and modulated typically at the frequency of $\nu _m = 230\,\hbox {Hz}$. The two beams were approximately equal in power because of the same diffraction efficiency. The directions of linear polarization were perpendicular to each other. The optical scheme was the push–pull optical pumping or the ${lin\perp lin}$ configuration, depending on the relative optical phase. To maintain stability of the relative phase, the beams were put into respective single spatial modes of a polarization-maintain (PM) optical fiber. The beam displacement was negligible at the input end of optical fiber when the frequency $\nu _{\mathrm{S}}$ was scanned. From a part of the output beam, the beat signal was generated by a linear-polarizer for interference of two polarized lights. The frequency component at $2 \nu _{\mathrm{S}}$ measured by a fast photo-detector (PD) was phase-sensitively detected (PSD). The phase of beat signal, that is, the relative optical phase was fluctuated by vibration of optical components, air turbulence, and temperature change, and therefore locked to a certain value by feedback to a piezo-mirror. The relative optical phase noise was mostly decreased but the residual noise should contribute to the signal linewidth. To detect small absorption change on the CPT resonance, the power of output beams from the optical fiber was stabilized by feedback to the gain input of the AOM driver. The Allan deviations of phase and power stabilization were, respectively, $0.5\,\hbox {mrad}$ and $2 \times 10^{-6}$ by averaging time of $1\,\hbox {s}$. To avoid competition, three feed-back loops were operated with different frequency responses.

The main part of laser beam irradiated the glass cell along z axis in a two-layer magnetic shielding box. The beam diameter was approximately $2\,\hbox {cm}$ and typical power density was $150\,\upmu \mathrm{W/cm}^2$. A static magnetic field, $B_0 \approx 1\,\upmu$T, was applied parallel to the laser beam. The magnetic field along x and y axes was canceled as much as possible. A non-magnetic E-type thermocouple was located approximately $10\,\hbox {mm}$ of the glass cell. The electric heater was alternately turned on and off in a glass oven. To avoid unwanted magnetic field whether homogeneous and time-varying or not, the light transmission was measured during the turn-off time. The audio-frequency PD output was detected by a lock-in amplifier at the modulation frequency $\nu _{\mathrm{m}}$. The CPT signal of dispersive line shape was measured by scanning the frequency $f = 2 \nu _\mathrm{S}$. For the measurement of linewidth, the modulation frequency and amplitude were set sufficiently low to avoid distortion of the line shape [19].

Fig. 3

Typical CPT signals at various buffer-gas densities and temperatures. The magnetic field was applied at $0.34\,\upmu \mathrm{T}$ for He gas and $1.9\,\mu \mathrm{T}$ for Xe gas, differently, to avoid overlapping of three peaks. Horizontal axis shows the frequency $f = 2\upnu _{\mathrm{S}}$ with the offset of $803\,\hbox {MHz}$ subtracted. a Three resonances ($|{-1 \leftrightarrow -1}\rangle$, $|{0 \leftrightarrow 0}\rangle$, and $|{1 \leftrightarrow 1}\rangle$) were measured in a wide frequency range at the He-gas density $N_{\mathrm{He}}=0.03\,\hbox {amg}$ and the temperature of $330\,^{\circ }\hbox {C}$. The center resonances are shown for b $N_{\mathrm{He}}=0.20\,\hbox {amg}$, $330\,^{\circ }\hbox {C}$, c $N_{\mathrm{He}}=0.49\,\hbox {amg}$, $368\,^{\circ }\hbox {C}$, and d $N_{\mathrm{Xe}}=0.02\,\hbox {amg}$, $360\,^{\circ }\hbox {C}$. The frequency difference $\nu _{\mathrm{pp}}$ was measured to calculate the linewidth

4 Results and discussion

Figure 3 shows typical CPT resonances at the magnetic field of approximately $1\,\upmu \mathrm{T}$. Because of negligible Zeeman shift of the dark state $|{0 \leftrightarrow 0}\rangle$, the resonance peak represented the HFS frequency in the buffer gases. The resonances of the other states $|{\pm 1 \leftrightarrow \pm 1}\rangle$ were Zeeman shifted to both sides by $\pm 2 \textit{g}_{\mathrm{S}} \mu _{\mathrm{B}} B_0/(2I+1)$, where $\textit{g}_\mathrm{S}$ is the electronic g factor and $\mu _{\mathrm{B}}$ is the Bohr magneton. The broadening due to inhomogeneous and fluctuating magnetic field was negligible in the magnetic shielding box. The center peak was larger than the side peaks in our light polarization alignment because the population was distributed to the levels $| F, {m_F=0} \rangle$ by optical pumping and the single $\varLambda$ schemes were, respectively, in part destructive for the states $|{\pm 1 \leftrightarrow \pm 1}\rangle$. The frequency separation of the signals was kept sufficiently larger than the resonance width by adjusting magnetic field $B_0$. Henceforth, we focus simply on the center resonance at different buffer-gas densities and different temperatures. In He gas, the resonance peak was shifted to high frequency side [1] and the resonance width was unchanged by increase of buffer-gas density, as shown in Fig. 3a, b, and c. That is, additional decoherence between the hyperfine levels was not detected by increasing the collision rate. The line shape was expressed by a Gaussian curve, suggesting that statistical processes were more effective than pure damping dynamics. Since the frequency shift was much larger than the width, the shift was not due to the change of statistically weighted line shape but due to collisional phase shift of the HFS frequency. In Xe gas, the peak was shifted to low frequency side, as shown in Fig. 3d, similarly to the HFS frequency shift of the other alkali-metal atoms [5]. The line shape was Lorentzian. The broadened linewidth was much larger than the frequency shift. Assuming that these changes were only due to collision-induced hyperfine-shift interaction, the shift should be proportional to $\langle \phi \rangle$ and the decay rate to $\langle \phi ^2 \rangle$ in binary collisions, where $\phi$ is the phase angle in the hyperfine-shift interaction [5]. Since the decay rate is typically several orders of magnitude smaller than the observed linewidth, the result suggests that the broadening and the shift were, respectively, due to different mechanisms.

Fig. 4

HFS frequency, $\nu _{\mathrm{HF}}(N, T)$, in the buffer gases, He ($\blacktriangle$) at $320\,^{\circ }\hbox {C}$ and Xe ($\blacktriangledown$) at $360\,^{\circ }\hbox {C}$ in this work, He ($\bullet$) at $387\,^{\circ }\hbox {C}$ from the past work [1]. The fitting lines are $(50.39 \pm 0.27) N + 504.105\,\hbox {kHz}$ for He gas ($\blacktriangle$) and $(-46.6 \pm 1.2) N + 504.105\,\hbox {kHz}$ for Xe gas ($\blacktriangledown$)

The atomic collisions are random independent events and mean collision time is much smaller than mean free time. The impulsive interaction in binary collisions induces the HFS frequency shift proportional to the collision rate, $n v \sigma$, where v is the mean relative velocity and $\sigma$ is the collision cross section. In Xe gas, there are additional shifts, linear and nonlinear, which are small and detectable contribution from a three-body formation rate and a two-body breakup rate of van der Waals molecules [20]. Figure 4 shows the HFS frequency in several glass cells. Because of narrow linewidth in He gas, the CPT signals were able to be measured in a wide density range. The frequency shift at a constant temperature was satisfactorily fitted by a linear function of density. Although the temperature dependence is generally complicated, it can be approximated by a linear function [7, 8]. For each cell, the linearity was measured, as shown in Fig. 5 ($\triangledown$, $\circ$, and ▵). However, the density-normalized frequency shifts in different cells were not on a single line. The discrepancy was not from the error of measured frequency $\nu _{\mathrm{HF}}$ in our experiment, but mostly due to the measurement error of the buffer-gas density at the time of glass sealing. Therefore, for each cell, the buffer-gas density was calibrated from the fitting line in Fig. 4 and the measured HFS frequency. By the calibration, the temperature dependence of HFS frequency shift, $\delta \nu _{\mathrm{HF}}(N,T)/N$, lies on a single line, as shown by the marks ($\blacktriangledown$, $\bullet$, and $\blacktriangle$) in Fig. 5. As the result, the HFS frequency shift was obtained as,

$$\begin{aligned} \delta \nu _{\mathrm{HF}}(N, T) = \nu _{\mathrm{HF}}(N, T) - \nu _{\mathrm{HF}}(0, T) = (a T + b) N, \end{aligned}$$

(1)

where $a = 24.27 \pm 0.87 \,\hbox {Hz}/(\hbox {amg}\,\hbox {K})$ and $b = 35.96 \pm 0.53 \,\hbox {kHz}/\hbox {amg}$ by the least-square fitting in He gas. The parameter, $\nu _{\mathrm{HF}}(0, T)$, was fixed at $803\,504.105\,\hbox {kHz}$ consistently to satisfy the fittings in Figs. 4 and 5, and the past work at $387\,^{\circ }\hbox {C}$ ($\bullet$) in Fig. 4. Their measurement was accurate because the density of Rb atoms, which was used for probing the polarization of Li atoms, was sufficiently low and the HFS frequency was insensitive to the spin-exchange interaction with spin-polarized atoms [1].

Fig. 5

Density-normalized temperature dependence of HFS frequency shift, $\delta \nu _{\mathrm{HF}}(N,T)/N$ in unit of $\hbox {kHz} / \hbox {amg}$, for each He-gas density ($\circ$ and ▵). The raw data ($\triangledown$) are far above the vertical range. The fitting line, $(0.02427 \pm 0.00087)\,T + (35.96 \pm 0.53)\,\hbox {kHz}/\hbox {amg}$, is calculated for the He-gas densities ($\blacktriangledown$, $\bullet$, and $\blacktriangle$) calibrated by the fitting line in Fig. 4

For Xe gas, $a = - 121 \pm 24\,\hbox {Hz}/(\hbox {amg}\, \hbox {K})$ and $b = 30 \pm 15\,\hbox {kHz}/\hbox {amg}$ were obtained similarly. When van der Waals molecules, LiXe [21, 22], are formed by three-body collisions, a small nonlinear dependence should be detected by precise scanning of Xe-gas density [23]. The isotope-independent parameter of HFS frequency shift [5],

$$\begin{aligned} \lambda _{\mathrm{C}} = \frac{d}{dN} \left( \frac{\nu _{\mathrm{HF}}(N, T)}{\nu _{\mathrm{HF}}(0, T)} \right) = \frac{aT+b}{\nu _{\mathrm{HF}}(0, T)}, \end{aligned}$$

(2)

is calculated at $660\,\hbox {K}$ as $64.6 \times 10^{-6}\,\hbox {amg}^{-1}$ for He gas and $-62 \times 10^{-6}\,\hbox {amg}^{-1}$ for Xe gas.

The CPT linewidth depends on several factors. For example, the homogeneous width may arise from the hyperfine-shift interaction (Carver-rate damping) [24], the S-damping (spin-rotation) interaction, spin exchange between Li atoms and buffer-gas atoms, atom diffusion, laser-power broadening, and optical phase noise. The collision-induced broadening is enhanced by formation of van der Waals molecules because the interactions last for the lifetime. The inhomogeneous linewidth is likely due to distribution of the HFS frequency in temperature gradient and the residual Doppler effect in the Raman resonance. In our experiments, temperature gradient and Doppler broadening were expected to be negligible. The broadening by laser power and ultrasonic frequency modulation were kept to the minimum. The linewidth was independent of the magnetic field below $3\,\upmu \mathrm{T}$ and the temperature below $350\,^{\circ }\hbox {C}$. Figure 6 shows the linewidth of the CPT signals at several buffer-gas densities. In He gas, the line shape was well described by a Gaussian curve (see Fig. 3). The full width at half maximum (FWHM) is $\sqrt{2 \ln 2\,}\,\nu _{\mathrm{pp}}$, where $\nu _{\mathrm{pp}}$ is the peak-to-peak frequency of the dispersive line shape. The measured width was independent of the He-gas density. It was several orders of magnitude larger than the damping rates estimated from the interactions such as hyperfine-shift and spin-rotation of heavy alkali-metal atoms and He atom [5] and transit-time broadening calculated from the diffusion coefficient [6]. Therefore, a possible reason for the linewidth was the residual and relative optical phase noise.

Fig. 6

Linewidth (FWHM) of the CPT signals measured in He ($\blacktriangle$) below $350\,^{\circ }\hbox {C}$ and Xe ($\blacktriangledown$) gases below $380\,^{\circ }\hbox {C}$, and the fitting lines

As shown in Fig. 7, the additional broadening was observed above $350\,^{\circ }\hbox {C}$ although decoherence due to the hyperfine-shift interaction and optical phase noise should stay constant by heating. The line shape was close to Gaussian at low temperature and came to Lorentzian by heating. At the absorption maximum of $D_1$ line in the He gas of $0.2\,\hbox {amg}$, the light transmission was ${T_{\mathrm{L}}=0.67}$ at $400\,^{\circ }\hbox {C}$ in the case of no CPT resonance. At the temperature, the high atom density ($\gtrsim 1 \times 10^{12}\,\hbox {cm}^{-3}$) should cause the broadening through spin-exchange interaction between the electrons of Li atoms [25, 26]. Here, we make a rough estimation of atomic Li density from the signal magnitude $(\hbox {amplitude}) \times (\hbox {width})/T_{\mathrm{L}}$, where the width shown in Fig. 7 ($\bullet$) and the transmission $T_{\mathrm{L}}$ at each temperature were used. As shown in Fig. 8, the measured signal magnitude were two order of magnitude increased by heating. Additional light absorption by lithium degradation of the cell windows was not observed during the measurement. Since $\delta \nu _p \sim \delta \nu _{\mathrm{D}}$, most of the atoms were resonant with the laser light. As a result, the signal magnitude was proportional to the number density of saturated Li vapor calculated by the reported parameters [27]. That is, in the temperature range, the vapor phase was stable in the borosilicate-glass cell.

Fig. 7

Temperature dependence of the CPT line width in the He gas of $0.2\,\hbox {amg}$. These were calculated by assuming Lorentzian ($\blacktriangledown \,\sqrt{3\,} \nu _{\mathrm{pp}}$) and Gaussian (▵$\sqrt{2 \ln 2\,} \nu _{\mathrm{pp}}$). FWHM ($\bullet$) was directly measured from integral of the dispersive line shape. FWHM was close to $\sqrt{2 \ln 2\,} \nu _{\mathrm{pp}}$ at low temperature and came to $\sqrt{3\,} \nu _{\mathrm{pp}}$ by heating. Solid curve is an eye guide. The inset shows the amplitude-normalized signals measured at $307\,^{\circ }\hbox {C}$ (dashed curve) and $400\,^{\circ }\hbox {C}$ (solid curve). The center of signals is aligned on a horizontal frequency axis

Figure 6 shows the CPT linewidth in Xe gas, where FWHM is equal to $\sqrt{3\,} \nu _{\mathrm{pp}}$ for Lorentzian line shape. The width was increased linearly with respect to the gas density, whereas temperature dependence was not detected over the range from 320 to $390\,^{\circ }\hbox {C}$. Possible mechanisms of broadening are spin exchange between the electron spin of Li atom and the nuclear spin of the atoms, $^{129}$Xe and $^{131}$Xe, and the S-damping (spin-rotation) interaction which is strongly temperature dependent. In addition, formation of van der Waals molecules enhances the interactions as well as hyperfine-shift interaction. Several experiments will be required to distinguish these contributions, those are, similar measurement using gas isotopes with no nuclear magnetic moment ($^{132}$Xe and $^{136}$Xe), precise measurement of nonlinear pressure shift [23], and spin relaxation measurement at high magnetic field [28]. Temporarily, we obtained the decay rate, $\varGamma = 1.5 \times 10^6 N\,\hbox {s}^{-1}$, of the dark state.

Fig. 8

Temperature dependence of the signal magnitude ($\bullet$) measured at the same laser power in the He gas of 0.2 amg. The signal magnitude (left vertical axis) was scaled to be compared with the atomic Li density (right vertical axis) calculated by [27] (solid curve)

5 Summary

The hyperfine splitting of the ground-state $^7$Li atoms was measured in the buffer gas, He and Xe. For a sufficient period of time, the borosilicate-glass cell gave stable vapor phase for lithium atomic spectroscopy. The CPT resonance permitted the measurement in the wide range of buffer-gas density and temperature. The frequency of hyperfine splitting was linearly increased with respect to the density and the temperature in He gas, consistent with the past work. The CPT linewidth was independent of the collision rate to He gas, where the rate was scanned by changing the He density and the temperature. In Xe gas, the frequency was decreased directly with the gas density and the temperature. The linewidth was proportional to the Xe density and unchanged by temperature. The contributions of the S-damping interaction and the spin-exchange interaction in binary collisions and molecular formation of Li atoms and Xe atoms, however, have not been identified in the present work. When the vapor density was increased by heating, the spin-exchange interaction between the electrons of Li atoms became observed in the CPT resonance width.