Since the first observation of the magneto-optical trap (MOT) in 1987 [1], MOTs [2–6] have been widely used for laser cooling and trapping of neutral atoms for type-I MOTs, where the excited state has a higher hyperfine level than the ground state. To achieve trapping force from a cycling transition, the upper hyperfine level of the ground state is used to trap alkali atoms, instead of the lower level [7–9].

Several studies have examined type-II MOTs, in which the hyperfine level of the ground state is higher than that of the excited state [10–14]. Investigations have been conducted on cooling mechanisms in sodium atoms in a type-II MOT [12]. Jarvis et al. [13] reported that the performance of a type-II MOT is heavily influenced by the balance between opposing Doppler and sub-Doppler forces, resulting in varied MOT shapes. Compared to type-I MOTs, type-II MOTs are hotter, larger, and weaker, with a much lower density of trapped atoms, which makes them more challenging to implement.

In the type-II case of F_g ≥ F_e, atoms can be optically pumped into a dark state and decoupled from the light. Type-II MOTs typically generate relatively hot low-density clouds, which has led to less interest from researchers. However, in a cold-collision experiment with Na atoms [15] in the lower hyperfine ground state in a type-II trap, fewer inelastic collisions between the ground states were obtained and led to trap loss at low laser intensity. In addition, type-II transitions must be used in cooling and trapping of a molecule with a dark state. The type-II MOT has recaptured considerable attention from researchers for cooling and trapping of molecules [4, 11].

The F_g = 2 → F_e = 1 transition of the D2 line of ⁸⁵Rb atoms can be used for a type-II MOT. However, to the best of our knowledge there has only been one report on the cooling and trapping of ⁸⁵Rb atoms at a lower hyperfine level F_g = 2 [14]. Polarization spectroscopy (PS) [16] was used to lock the trapping-laser frequency. However, the locking-error signal using saturated absorption spectroscopy (SAS) or PS was very weak for the F_g = 2 → F_e = 1 transition of ⁸⁵Rb atoms, because of closely spaced neighboring transition lines and weak transition strength, preventing the observation of distinguishable spectra. In contrast, a strong error signal can be obtained using modulation-transfer spectroscopy (MTS) [17–24]. MTS provides a dispersive error signal for locking the laser frequency without direct modulation of the probe beam, in contrast to SAS, which modulates the probe laser’s frequency. Furthermore, the zero-crossing of the steeper signal offers more accurate discrimination of the corresponding atomic transition. MTS also uses four-wave mixing (FWM) to transfer modulation from the pump to the probe laser beam, and the phase-matching criterion ensures a dispersivelike line-shape with no background. In particular, the MTS signal for the noncycling transition is very weak, whereas the cycling transition’s line shows a strong signal. Thus a strong MTS signal for the F_g = 2 → F_e = 1 transition of ⁸⁵Rb can be observed, owing to its cycling nature. The MTS of the F_g = 2 → F_e = 1 transition of ⁸⁵Rb atoms for such a cycling transition was observed by McCarron et al. [18]; However, the signal was not used for an MOT. Frequency tunability of a laser beam [20, 21, 24, 25] while keeping the laser frequency locked is crucial in precision laser spectroscopy. MTS for the F_g = 2 → F_e = 3 transition in ⁸⁷Rb atom was used to stabilize and tune the frequency of the external-cavity diode laser [20]. Frequency-tunable MTS with an optical-heterodyne-frequency system was also introduced for the F_g = 2 → F_e = 3 transition in ⁸⁷Rb atoms [25]. Singh et al. [26] reported a frequency-tunable Doppler-free dichroic lock (DFDL).

In this study, we explore the tunable characteristics of a MTS system with a dispersivelike tunable reference signal. Frequency scanning is performed with a frequency offset from the resonance frequency using acousto-optic modulators (AOMs), while maintaining laser-frequency stabilization with MTS. The tunability depends on the tuning-frequency resolution and range of the AOM. This setup allows for laser-frequency locking while driving the AOM, without requiring dithering. Tunable MTS (TMTS) generates a dispersive signal with a steep slope and high amplitude across the entire tuning range, which differs from the signal produced by SAS. The MTS used to lock the F_g = 2 → F_e = 1 transition of ⁸⁵Rb provides an enhanced dispersive signal. We implement tunable laser frequencies with detuning of +200 MHz and −200 MHz in the MTS signal. This method is then applied to achieve red detuning of the trap laser from trap resonances for the F_g = 2 → F_e = 1 transition in ⁸⁵Rb, successfully resulting in a type-II MOT.

The experimental setup for the TMTS is illustrated in Fig. 1. A tapered amplifier based on a TA 100 diode-laser system (Toptica AG., Munich, Germany) is used to produce high-power light, generating approximately 390 mW at 780 nm, which is amplified from a seeded diode laser with a power output of tens of milliwatts. In this experiment, the TMTS signal is used to stabilize the laser frequency for the F_g = 2 → F_e = 1 transition in ⁸⁵Rb atoms in a type-II MOT.

Figure 1. Experimental setup for tunable modulation-transfer spectroscopy (TMTS).

To achieve a red detuning of 10 MHz for the trap laser, the frequencies of AOM-1 and AOM-2 in the TMTS are set to −80 MHz and 70 MHz, respectively. TMTS employs a pump-probe configuration in which a pump beam is double-passed through the AOMs for frequency tuning and through an EOM for phase modulation, with a counterpropagating probe beam. For SAS, both the pump and probe beams are resonant with the same velocity group, so the change in laser frequency is double-passed through an AOM. The radio frequency (RF) of the AOM, denoted as δ, can be expressed as follows:

where ω₀ is the frequency of the atomic resonance in which the laser is locked, ω_L denotes the laser frequency, and δ = ω₁ + ω₂, where ω₁ denotes AOM-1’s driving frequency and ω₂ denotes AOM-2’s driving frequency. Offset locking is possible, and the laser scanning frequency is based on ω₁ and ω₂. Detuning can be changed continuously by changing an offset frequency while keeping the trap laser locked. The energy-level diagrams for the experiments with the type-I and type-II MOTs are shown in Fig. 2. A part of the stabilized laser beam, red-detuned by 10 MHz, reaches the tapered amplifier via reflection from an internal optical mirror. The rest of the beam exits one side of the laser system after passing through the mirror, serving as the probe beam for MTS. This probe beam then travels through a rubidium cell and is detected by a fast photodiode. The high-power beam that exits through the tapered amplifier on the other side of the laser system is split into two beams, using a half-wave plate (HWP) and a polarization beam splitter (PBS). The weaker beam is used as the pump beam for the TMTS, while the rest is directed to the MOT setup. To tune the laser frequency, the TMTS setup uses two AOMs. The weak beam reflected from the PBS is first directed through AOM-1 and a quarter-wave plate (QWP). After reflecting off a mirror, it is sent back through AOM-1. The beam then passes through the PBS, AOM-2, and the QWP again before reflecting off a mirror and returning to the QWP and AOM-2. It is then reflected by the PBS and directed towards a custom-built electro-optic modulator (EOM) for MTS. The phase-modulated beam is subsequently directed to a 10-cm-long rubidium vapor cell at room temperature (20 ℃).

Figure 2. Energy-level diagram for experiments with type-I and type-II magneto-optical traps (MOTs).

The output signal from the photodiode is amplified before reaching the phase detector. In the rubidium vapor, a relatively strong pump laser beam is phase-modulated by the EOM, transferring the modulation to a counter-propagating weak probe laser beam. The reference signal from the phase detector is fed into the proportional-integral-derivative (PID) controller housed within the diode-laser controller (Toptica AG.), to stabilize the laser frequency. This setup allows for frequency scanning via offset locking, while keeping the laser frequency stable. In the experiment, the TMTS signal is also used to stabilize the laser frequency for the F_g = 3 → F_e = 4 transition of ⁸⁵Rb atoms in a type-I MOT. To achieve a red detuning of 13 MHz for the trap laser, the frequencies of AOM-1 and AOM-2 in the TMTS setup are set to −80 MHz and 67 MHz respectively. In the MOT experiment, three mutually orthogonal pairs of laser beams and a pair of coils with current flowing in opposite directions are used to cool and trap atoms in a stainless-steel MOT chamber containing rubidium. The background pressure is approximately 1.4 × 10⁻⁸ Torr. A repumping laser is locked to the F_g = 2 → F_e = 3 transition for the type-I MOT, and to the F_g = 3 → F_e = 3 transition for the type-II MOT. The trapping and repumping laser beams contribute to the total beam intensity at the center of the MOT chamber. A constant current of approximately 2.4 A is applied to a rubidium dispenser, which serves as the source of rubidium vapor.

The trapping and repumping laser beams have diameters of about 2 cm. The fluorescence signal, used to measure the number of trapped atoms, is recorded with a calibrated photodetector.

We examine the tuning capability at −200 MHz and +200 MHz. To demonstrate the extended red tuning of the laser frequency, the pump beam passes through AOM-1 and is then reflected back, resulting in a double pass through AOM-1. It then passes through AOM-2, also in a double-pass configuration. The driving frequency for both AOM-1 and AOM-2 is set to 100 MHz with a −1^st-order diffracted beam. According to Eq. (1), this setup red-detunes the pump beam by 200 MHz. The red-detuned beam is then passed through the EOM for phase modulation and sent to the vapor cell. In this nonlinear process, the pump beam transfers the modulation to the probe beam, generating dispersivelike TMTS signals with negligible background. The zero crossings of these signals are accurately centered on the F_g = 3 → F_e = 4 transition of ⁸⁵Rb and the F_g = 2 → F_e = 3 transition of ⁸⁷Rb, as shown in Fig. 3(a). The blue line represents the reference SAS signal with zero detuning. The red and green lines represent detuned SAS and TMTS signals respectively. As shown in Fig. 3(a), the TMTS signal is clearly shifted 200 MHz to the red side. To demonstrate the extended blue tuning of the laser frequency, the pump beam traverses AOM-1 and AOM-2 in a double-pass configuration. The driving frequency for both AOM-1 and AOM-2 is 100 MHz with a +1^st-order diffracted beam. From Eq. (1), the pump beam is blue-detuned at 200 MHz. The blue-detuned beam is sent through an EOM to induce phase modulation, after which it is directed toward the Rb vapor cell. In a nonlinear process, the pump beam facilitates the transfer of modulation to the probe beam, resulting in the generation of dispersivelike TMTS signals for the F_g = 3 → F_e = 4 transition of ⁸⁵Rb and the F_g = 2 → F_e = 3 transition of ⁸⁷Rb, as shown in Fig. 3(b). The blue line represents the reference SAS signal with zero detuning. The red and green lines represent detuned SAS and TMTS signals respectively. The TMTS signal can be observed to be shifted to the blue side by 200 MHz, as shown Fig. 3(b). The lower traces in Figs. 3(a) and 3(b) show the red- and blue-detuned TMTS signals respectively. The TMTS signal in the red detection has a very similar shape to the TMTS signal in the blue detuning. This demonstrates the tunable characteristics of the MTS, which generates a dispersive tunable reference signal. Figure 4 presents the MTS and SAS spectra for the F_g = 2 → F_e = 1 transition of ⁸⁵Rb. The MTS pump and probe powers are 559.5 µW and 130 µW, respectively. The figure shows that, due to several closely spaced hyperfine transitions, the SAS signal for the F_g = 2 → F_e = 1 transition is unresolved, making it unsuitable as an error signal for laser locking in a type-II MOT. However, the MTS signal for the F_g = 2 → F_e = 1 transition is clear and strong compared to other transition lines, as shown in Fig. 4. Figure 5(a) shows the image of a MOT for atoms at the upper hyperfine level of the ground state, forming a spherical shape. In contrast, in type-II MOTs where the cycling transition is F_g < F_e, a ring-shaped MOT is observed, as shown in Fig. 5(b), rather than the spherical cloud of type-I depicted in Fig. 5(a). A ring-shaped MOT can result from misalignment of the laser beams [27, 28]. After creating a type-I MOT, a type-II MOT is achieved by changing only the laser frequencies, without altering the beam paths. Further attempts to adjust the laser beam’s alignment still result in a hollow center.

Figure 3. Comparison of SAS, red-detuned SAS, and TMTS. The detuning is (a) −200 MHz, (b) +200 MHz. The blue, red, and green lines represent the SAS, detuned SAS, and TMTS signals, respectively: SAS, saturated absorption spectroscopy; MTS, modulation-transfer spectroscopy; TMTS, tunable MTS.

Figure 4. Modulation-transfer spectroscopy (MTS) and saturated absorption spectroscopy (SAS) signal for the F_g = 2 → F_e = 1 transition of ⁸⁵Rb.

Figure 5. Magneto-optical trap (MOT) images. Atoms are (a) in the F_g = 3 hyperfine ground state, (b) in the F_g = 2 hyperfine ground state.

Figure 5(b) illustrates a MOT for atoms in the lower hyperfine level of the ground state, using the same trapping parameters as in Fig. 5(a). It is unclear why the type-II MOT forms a ring shape, while the type-I MOT forms a spherical shape. The number of trapped Rb atoms, as measured by fluorescence, is 4.8 × 10⁶. Further studies are underway to investigate the size and shape dependence of MOTs with respect to detuning, to understand the characteristics of type-II MOTs and reinforce preliminary data, with a focus on implementing type-II MOT using TMTS.

The tunable characteristics of MTS, which generates a dispersive, tunable reference signal, were investigated with respect to detuning frequencies. Tunability is based on tuning the frequency resolution and range of the AOM. This setup allows for laser-frequency locking while driving the AOM, without needing to dither it. By integrating TMTS into the MOT system, type-I and type-II MOTs were successfully achieved, enabling the laser cooling and trapping of ⁸⁵Rb atoms. Further detailed studies on these type-II MOTs are currently underway.

This study was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (Grant No. 2020R1A2C1005499 and No. RS-2023-00239275), and research funding from Chosun University (2023).

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The data that support the findings of this study are available from the corresponding author upon reasonable request.