## Abstract

We present a study of the saturated-absorption spectroscopy with crossover resonances involving both Cs hyperfine ground-state levels using a dual-frequency laser tuned to the Cs ${D_2}$ line. The crossover resonances are formed by the atomic velocity groups on resonance with both of the dual-frequency laser beams, which are counter-propagated through the vapor cell. A large increase in Doppler-free atomic absorption is observed for certain frequency differences of the dual-frequency laser. This phenomenon is explained by optical pumping and velocity selective optical pumping, imposed by the dual-frequency laser with frequency differences close to but not exactly equal to the level spacing of the two participating ground-state levels. The results obtained in this system are of great interest for laser spectroscopy.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. INTRODUCTION

Saturated-absorption spectroscopy (SAS) is an elegant method widely used in the realization of frequency references for atomic transitions and atomic and molecular physics for high-resolution spectroscopy purposes [1 –6]. This technique overcomes the first-order Doppler effect by using a counter-propagating pump beam to saturate the transition for zero-velocity atoms. However, when the atom has several closely spaced hyperfine transitions overlapping within the Doppler profile, the crossover (CO) resonances between each pair of hyperfine levels are generated [7]. They appear because, for some non-zero-velocity group, the pump drives one transition, while the probe drives the other [8,9]. But, there are no CO resonances involving both ground-state hyperfine levels of alkali metal atom (in particular, Cs) coupled to a single excited level. That is because, in SAS of the Cs D lines, the level spacing between the $F = 3$ and $F = 4$ ground state is 9.192 GHz, while the Doppler width measures only about 400 MHz [10,11].

When an atomic medium is driven by two fields simultaneously, a variety of interesting nonlinear optical phenomena arise, such as coherent population trapping (CPT) [12
–14], electromagnetically induced transparency (EIT) [15
–19], electromagnetically induced absorption (EIA) [20
–22], lasing without inversion [23], the velocity transfer effect [24], etc. In recent years, the atomic coherence resulting from dual-frequency laser fields has attracted the attention of many researchers, because of its significance in various applications, such as the design of highly sensitive magnetometers [25], hyperfine-interval measurement [26], laser frequency stabilization [27], atom interferometry [28], etc. For example, using co-propagating pump–probe beams, the hyperfine spectroscopy with only one CO resonance in contrast to SAS was reported by Singh *et al.* [26] (see also [29]), and they made precise hyperfine-interval measurements by this technique. Apart from the coherence resonances such as CPT, EIT, and EIA, different nonlinear resonances arising from optical pumping and saturation effects due to the pump laser can also be observed in a multi-level system, such as velocity selective optical pumping (VSOP) [30
–33] and velocity selective resonance (VSR) [34,35]. When the pump and probe lasers couple two different ground hyperfine levels and a common set of excited hyperfine levels, distinct velocity groups of one lower level are optically pumped by the pump laser to the other lower level by spontaneous decay via the set of upper levels. Hence, when the weaker probe frequency is tuned across the set of hyperfine transitions, these optically pumped atoms will enhance the probe absorption and produce the VSOP.

In the above techniques, most investigations are based on one laser being tuned to a fixed frequency, while another laser is being scanned. Furthermore, the use of co-propagating dual-frequency laser fields with frequency differences of two ground-state level spacings has also been studied exhaustively. In 2016, Hafiz *et al.* reported the first, to the best of our knowledge, experimental observation of natural-linewidth and strongly enhanced inverted resonance dips through SAS in a Cs vapor cell using a counter-propagating 894 nm dual-frequency laser system with frequency difference of 9.192 GHz, and they showed that the resonance dips are mainly caused by CPT effects [27,36,37]. Besides fundamental interest, this phenomenon has a promising application. The laser frequency stabilization demonstrated by this technique is about an order of magnitude better than those obtained using a conventional single-frequency saturated-absorption scheme. Since the first, to the best of our knowledge, experimental research of the application of dual-frequency laser fields in SAS scheme for the ${D_1}$ transition of Cs was reported, the spectral properties of driven atomic media with the ${D_2}$ transition by a dual-frequency laser have not yet been studied in detail.

In this work, motivated by the observation of CPT resonances in a SAS regime using a dual-frequency laser system [27,36], we provide an experimental study of SAS in a Cs vapor cell using an 852 nm dual-frequency laser system with frequency difference close to but not exactly equal to the level spacing of the two participating ground-state levels. Single-frequency radiation is modulated by an electro-optic modulator (EOM), so that two first-order optical sidebands induce the saturated-absorption process. Using two pairs of counter-propagating beams with two different frequencies, the usual SAS signals with several inverted CO resonances [11] involving both Cs hyperfine ground-state levels are generated due to four closely spaced hyperfine levels within the Doppler profile. The CO resonances corresponding to enhanced absorption are caused by optical pumping and VSOP.

## 2. EXPERIMENTAL SETUP

The scheme of the experimental setup is presented in Fig. 1(a). The laser source is a home-built single-frequency external cavity diode laser (ECDL) tuned on the Cs ${D_2}$ line at 852 nm. An optical isolator is used to prevent optical feedback. The beam from the ECDL is reflected by high-reflection mirrors (M1 and M2) and then coupled into a pigtailed Mach–Zehnder intensity EOM (iXBlue Photonics, NIR-MX800-LN-10) by an optical fiber coupler (FC1). The EOM is driven by a local oscillator (model Agilent E8257D, Agilent Technologies, USA), allowing the generation of two first-order optical sidebands. Because the carrier, as well as second- and third-order optical sidebands (which are rejected at a level of 30 dB), is far off resonance with Cs transitions, they do not contribute to the recorded spectra and can be neglected. Another FC (FC2) is utilized to extract a free-space collimated laser beam from the EOM output. The optical losses of the EOM, FC1, and FC2 are about 80%, 60%, and 60%, respectively. Then, the dual-frequency laser beam counter-propagates through the vapor cell to form saturated-absorption signals. The laser beams partially reflected by the front and back surfaces of a window of silicate glass (SG) and acting as probe laser are sent to a Cs vapor cell, while the transmitted beam is directed to the cell from the opposite side, overlapping with one of the probe beams and acting as a counter-propagating pump beam, thus forming a SAS device. Throughout the experiment, the spectra were recorded with total probe power of 0.04 mW and pump power of 0.15 mW, and both laser fields used for SAS are parallel and linearly polarized in all cases. We denote the dual-frequency pump laser and the probe laser as ${\omega _{{\rm pu}1}}$, ${\omega _{{\rm pr}1}}$, ${\omega _{{\rm pu}2}}$, and ${\omega _{{\rm pr}2}}$. It should be noted that in this paper the frequencies of the pump and probe lasers, as well as the described effects, are presented in the laboratory frame. The pump and probe laser beams are adjusted to spatially overlap almost completely throughout the total length of the cell. The diameter of the dual-frequency laser beam is 1.2 mm. The quartz glass cylindrical vapor cell (length 3 cm, window diameter 1.5 cm) was filled with pure Cs and kept at room temperature (25°C) without a temperature control device and magnetic shielding. The photodetector (PD) is a differential PD, which allows us to eliminate the Doppler background of the SAS.

The relevant transitions of the Cs atom when the laser is tuned to the Doppler-broadened $F = 4 \to F^\prime = 3$, 4, 5 transition acts as ${\omega _{{\rm pu}1}}$, while the laser tuned to the Doppler-broadened $F = 3 \to F^\prime = 2$, 3, 4 transition acts as ${\omega _{{\rm pr}2}}$, as shown in Fig. 1(b). The relevant transitions of the Cs atom when the laser is tuned to the Doppler-broadened $F = 3 \to F^\prime = 2$, 3, 4 transition acts as ${\omega _{{\rm pu}2}}$, while the laser tuned to the Doppler-broadened $F = 4 \to F^\prime = 3$, 4, 5 transition acts as ${\omega _{{\rm pr}1}}$, as shown in Fig. 1(c). The dual-frequency laser fields are scanned by varying the piezoelectric ceramics voltage of the ECDL, covering the hyperfine spectral components of the Cs ${D_2}$ line $F = 4 \to F^\prime = 3,4,5$ and $F = 3 \to F^\prime = 2$, 3, 4 respectively.

## 3. RESULTS AND DISCUSSION

The measured SAS signals by a dual-frequency laser with different modulation frequencies are plotted in Fig. 2. In this figure and all other spectra below, a positive peak means enhanced transmission for the probe beam under the influence of the pump beam with the same frequency, and a negative peak means increased absorption for the probe beam under the influence of the pump beam with the different frequency. The top black line, which is the SAS signal when the EDCL is modulated at about 4.0 GHz, includes the peaks corresponding to hyperfine transitions from Cs $6{S_{1/2}}\;F = 4 \to 6{P_{3/2}}F^\prime = 3,4,5$ (marked by red dotted line) and $6{S_{1/2}}\;F = 3 \to 6{P_{3/2}}F^\prime = 2,3,4$ (marked by blue dotted line). In the middle part of the line, there are some inverted peaks with lower amplitude, which are CO resonances involving both hyperfine ground-state levels. The frequency intervals between the CO dips and usual SAS peaks, as well as the amplitudes of CO resonances, are changing with the modulation frequency. At 9.192 GHz, the amplitudes of all the sub-Doppler features are drastically reduced due to the CPT effect. This observation is in agreement with Ref. [36], where it was shown that the absorption peak was reversed in parallel polarization, but the amplitude of dips is not increased. For crossed polarization only, the regular SAS dips were reversed, while the size of the absorption peak was strongly enhanced. When the frequency difference of the dual-frequency laser is 9.6 GHz, a large increase in CO resonances involving both hyperfine ground-state levels is observed.

The frequency splitting between corresponding excited-state lines of the usual SAS multiplets is defined by the difference between the laser frequency separation and the ground-state splitting. It is known that the usual SAS structure corresponding to ground states $F = 3$ and $F = 4$ overlap when the frequency difference of the dual-frequency laser is 9.192 GHz. If the frequency difference of the dual-frequency laser is larger or smaller than 9.192 GHz, the SAS structures corresponding to ground states $F = 3$ and $F = 4$ will move to opposite sides on the frequency detuning scale. Thus, the positions of the usual SAS multiplets corresponding to ground states $F = 3$ and $F = 4$ are exchanged at the frequency differences of 8 GHz and 10 GHz in Fig. 2.

Figure 3 shows SAS signals in the dual-frequency regime with different frequency differences close to 9.6 GHz. To facilitate the perception of Figs. 2 and 3, we marked inter-ground-state CO resonances by a black dotted line. The location of zero detuning corresponds to the CO resonance, which is located midway between $F = 4 \to F^\prime = 4$ and $F = 3 \to F^\prime = 3$ [abbreviated as (4,3)] in Figs. 2 and 3. It should be noted in the paper that we make a notation ($F^\prime $, $F^\prime $) to simplify the identification of the CO resonance between $F = 4 \to F^\prime $ and $F = 3 \to F^\prime $ mentioned in the text below. The frequency detuning ($x$ axis) in these figures is the absolute optical detuning, which is independent of the modulation frequency. As we record the spectra at different modulation frequencies with fixed initial laser central frequency, the frequencies of the two first-order optical sidebands vary only with the modulation frequency. As is shown in Fig. 3, the SAS dip corresponding to the $F = 3 \to F^\prime = 2$ transition of the top line is located at about ${-} 370\; {\rm MHz}$, while the same dip on the bottom line is located at about ${-} 560\; {\rm MHz}$. Hence, although the CO dip positions on the $x$ axis remain unchanged, the frequency interval between the CO dips and usual SAS dips are changed.

When the frequency difference between the dual-frequency laser matches the energy difference of the lower levels, the CPT condition is fulfilled. However, among the four excited-state hyperfine levels of the ${D_2}$ transition, only two levels couple to both ground-state hyperfine levels simultaneously, whereas for the ${D_1}$ line both of the excited-state levels couple to the ground-state hyperfine levels. The uncoupled states do not contribute to the CPT, rather they provide decay channels for the atoms from the trapped states, reducing the amplitude of the inverted CO resonance dips. Furthermore, the SAS dips observed result from the competition of CPT and optical pumping; thus, the amplitudes of the dips in the experiment will depend not only on respective transition strengths, but also on contributions from optical pumping and CPT. Moreover, the complex multi-level structure must be taken into account. This is a quite difficult task, and we do not discuss it in this paper.

If the frequency difference of the dual-frequency laser is close to 9.6 GHz, for some non-zero velocity groups, when the two laser fields are tuned close to $6{S_{1/2}}\;F = 4 \to \;6{P_{3/2}}\;F^\prime = 3,4,5$ and $6{S_{1/2}}\;F = 3 \to \;6{P_{3/2}}\;F^\prime = 2,3,4$ transitions, the pump laser (${\omega _{{\rm pu}1}}$ or ${\omega _{{\rm pu}2}}$) drives the atoms along the laser beam to one excited state, and they spontaneously decay to the other ground state. Hence, the probe laser with different frequencies from the pump laser (${\omega _{{\rm pr}2}}$ or ${\omega _{{\rm pr}1}}$) drives more atoms in this ground state to another excited state. Consequently, the absorption for the probe beam is increased under the influence of the pump beam with the frequency difference close to the level spacing of the two participating ground-state levels, giving rise to inverted CO resonances involving both hyperfine ground levels, which can be detected by the PD.

In order to analyze the hyperfine transitions and CO resonances in detail, we took the spectra at the modulation frequency of 4.0 GHz as an example to demonstrate the positions of the CO resonances involving both Cs hyperfine ground-state levels. When the modulation frequency is about 4.0 GHz, the frequency difference of the dual-frequency laser is $\Delta \approx 8.0\;{\rm GHz}$. Consequently, as is shown in Fig. 4, the frequency detuning between the peaks of $F = 4 \to F^\prime = 3$ and $F = 3 \to F^\prime = 3$ by the dual-frequency laser is $| {\delta - \Delta} | \approx 1.2\;{\rm GHz}$, where $\Delta$ is the frequency difference between the dual-frequency laser. $\delta$ is the level spacing of the two participating ground-state levels, whose value is 9.192 GHz. There are three distinct CO resonances, which are (4,2), (5,3), and (5,4). Since the experiments are done in a Cs vapor cell with the full Maxwell–Boltzmann distribution of velocities, we have to consider that there will be different velocity classes that absorb from the probe. Taking into account the Doppler effect and the frequency detuning of the CO resonances from the hyperfine transitions, we found that the first velocity class moves at 358 m/s and causes the peak (4,2), the second velocity class moves at 315 m/s and causes the peak (5,3), and the third velocity class moves at 401 m/s and causes the peak (5,4).

Figure 5 provides another picture to demonstrate the positions of the CO resonances involving both Cs hyperfine ground-state levels. When the modulation frequency is about 4.9 GHz, the frequency difference of the dual-frequency laser is $\Delta \approx 9.8\;{\rm GHz}$. Hence, the frequency detuning between the peaks of $F = 4 \to F^\prime = 3$ and $F = 3 \to F^\prime = 3$ by the dual-frequency laser is $| {\delta - \Delta} | \approx 0.6\;{\rm GHz}$. As is shown in Fig. 5, there are three distinct CO resonances, which are (4,2), (3,4), (4,3), and (4,4). Actually, the CO resonance (3,4) overlaps with (4,3), which appears in all cases. The first velocity class moves at 159 m/s and causes the peak (3,3), the second velocity class moves at 173 m/s and causes the peak (3,4), the third velocity class moves at 345 m/s and causes the peak (4,3), and the fourth velocity class moves at 259 m/s and causes the peak (4,4). Nevertheless, there are two weak CO resonances appearing within the original SAS spectra, which are (3,2) and (5,4). Hence, the fifth velocity class moves at 323 m/s and causes the peak (3,2), and the sixth velocity class moves at 366 m/s and causes the peak (5,4).

Since resonant excitation by the pump field followed by spontaneous emission to the lower hyperfine ground state is only possible for the $F = 4 \to F^\prime = 3,4$ [see Fig. 1(b)] and $F = 3 \to F^\prime = 3,4$ [see Fig. 1(c)] transitions, overall there should be eight CO resonances, which are (3,2), (3,3), (4,2), (3,4), (4,3), (4,4), (5,3), and (5,4). However, as is shown in Figs. 4 and 5, some CO resonances disappear in the spectra due to far frequency detuning or overlapping with hyperfine transitions. When bichromatic pump–probe radiations ${\omega _{{\rm pu}1}}$, ${\omega _{{\rm pr}1}}$, ${\omega _{{\rm pu}2}}$, and ${\omega _{{\rm pr}2}}$ with wavevectors ${\vec k_1} = - {\vec k_2}$ and ${\vec k_3} = - {\vec k_4}$ counter-propagate through a Cs vapor cell with a Maxwell–Boltzmann velocity distribution, taking the CO resonance (3,4), for example, only those atoms that move with longitudinal velocity $v$ satisfying the conditions of ${\omega _{{\rm pu}1}} + {\vec k_1} \cdot \vec v = {\omega _{43}}$, ${\omega _{{\rm pr}2}} - {\vec k_2} \cdot \vec v = {\omega _{34}}$, ${\omega _{{\rm pu}2}} + {\vec k_3} \cdot \vec v = {\omega _{34}}$, and ${\omega _{{\rm pr}1}} - {\vec k_4} \cdot \vec v = {\omega _{43}}$, can significantly contribute to the absorption (${\omega _{34}}$ and ${\omega _{43}}$ are the frequencies of $6{S_{1/2}}F = 3 \to 6{P_{3/2}}F^\prime = 4$ and $6{S_{1/2}}F = 4 \to 6{P_{3/2}}F^\prime = 3$ transitions, respectively).

Furthermore, we give a table listing the different velocity classes corresponding to each CO resonance at three selected modulation frequencies. As is seen from Table 1, the addressed velocity classes change with the change of modulation frequency. Since the Doppler width of the Cs ${D_2}$ line is less than 500 MHz [10,11], out of the groups listed in Table 1, only the atoms with velocities less than about 400 m/s can significantly contribute to the absorption.

Moreover, because there are no resonances between hyperfine transitions from two ground states to excited states in the classical SAS of the Cs D lines, it is clear that the observed inverted peaks are not the hyperfine transitions. When they appear, the bichromatic pump frequencies (${\omega _{{\rm pu}1}}$ and ${\omega _{{\rm pu}2}}$) and the bichromatic probe laser frequencies (${\omega _{{\rm pr}1}}$ and ${\omega _{{\rm pr}2}}$) are far off resonance with Cs transitions. Because we measured the spectra at different modulation frequencies with a fixed initial laser center frequency, hence, the two first-order optical sideband frequencies vary only along with the modulation frequency. Thus, the frequency intervals between the CO dips and usual SAS dips are variable data depending solely on the frequency difference of the dual-frequency laser. Consequently, we can control and manipulate the frequency intervals between the CO dips and usual SAS dips, as well as the intensities of CO resonances involving both Cs hyperfine ground-state levels by changing the modulation frequency.

## 4. CONCLUSION

It is known that some techniques can provide formation of narrow resonances far away from atomic resonances, such as atomic transitions shifted by a strong magnetic field in atomic vapor nanocells [38] or SAS with micrometer-thin cells exposed to strong magnetic fields [39]. We also obtained narrow CO resonances far outside the Doppler-overlapped atomic transitions by a dual-frequency laser at some special modulation frequencies. In this paper, we present the observation of CO resonances involving both Cs hyperfine ground-state levels induced by dual-frequency laser with frequency differences close to but not exactly equal to the level spacing of the two participating ground-state levels. For the system studied in this work, with two ground states and four upper-state hyperfine levels, the effect of a counter-propagating strong pump field and weak probe field with special frequency differences on the transmission profile is manifested as enhanced absorption peaks. These CO resonances, the number of which varies with the modulation frequency, are well resolved in the case of the Cs ${D_2}$ transition. It was highlighted that the appearance of high-contrast CO resonances in the middle part of the direct SAS resonances is mainly attributed to the optical pumping processes, and the amplitude of the CO resonances observed for the case of two transitions with two different lower levels is higher than the usual SAS. Unlike the conventional counter-propagating and co-propagating methods of observing hyperfine dips by dual-frequency, the inverted enhanced CO resonances of the Cs ${D_2}$ line due to optical pumping observed in this experiment were not reported in any earlier work. Experimental observations reported in this paper could be of great interest in high-resolution laser spectroscopy.

## Funding

National Natural Science Foundation of China (61771067, 91436210); Equipment Pre-research Key Laboratory Foundation (6142207190106); National High-tech Research and Development Program.

## Disclosures

The authors declare no conflicts of interest.

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