Rare isotopes are very important and useful in many aspects, such as date tracing^[1,2], precision measurement^[3,4], and quantum simulations^[5,6]. In cold atom physics, K40 is an important isotope that is widely used to study the quantum degenerate Fermi gas^[7]. However, the natural abundance of K40 is extremely low, about 0.012%, which is hard to use in the lab. The widely used K source is extracted from nuclear waste with an abundance of about a few percent for K40, which is far away from the natural abundance, and the typical weight is about a few milligrams. It is expensive, and the supply is not stable, so a convenient separation method to achieve such a goal will be very useful. Traditional separation methods, such as the centrifuge and chemical method, are unsuitable for this extremely low abundance isotope. Laser isotope separation has turned out to be a feasible method, which can be used to produce small mount samples with a high enrichment factor such as 100–1000.

Laser isotope separation makes use of the isotope shift, which has typical values of a few hundred MHz to GHz. Although it is small, it can be easily addressed by those narrow linewidth lasers^[8-12]. This idea was extensively explored in the 1980s but only succeeded with small mount samples. In the last decade, an optical magnetic combined method was developed for isotope separation and enrichment^[13]: atoms with different isotopes were first optically pumped to different spin states and then entered a magnetic field regime with a high gradient. Atoms in low-field seeking states can be deflected and then collected, thus achieving isotope separation. The optical pumping efficiency is so high, resulting in high purity of isotopes. Those methods have been demonstrated in both Li^[14,15] and K^[16].

In our prior research, we effectively utilized the magneto-optical method to separate potassium isotopes, achieving a production rate of 1.1 µg/day and enriching K40 to approximately 1% abundance^[16]. While this already presents a significant enhancement of nearly 100 times the natural abundance, it is still 10 times lower than our desired goal. A critical limitation in our previous methodology is the presence of a divergence angle. Despite employing a micro-capillary array in the oven to pre-collimate the atomic beam, a residual divergence angle of about 3° persisted^[17-19]. Because a long magnetic wall (about 2 m) is used to separate the low-field seeking and high-field seeking states, even a small divergence angle still results in a large spreading of atoms and thus loss. Although implementing a collimation hole could potentially reduce the divergence angle, it would also curtail the production rate.

The advancements in laser cooling techniques offer a promising solution by enabling the reduction of divergence angles through two-dimensional (2D) transverse cooling. Laser cooling easily achieves a transverse temperature lower than millikelvin^[20-24], corresponding to a divergence angle of a few milliradians. This enhancement can lead to a one-order-of-magnitude improvement in separation efficiency.

It is noteworthy that while 2D transverse cooling has been widely used in cold atom physics, its application in the laser isotope separation remains unexplored. An essential consideration is its impact on production rates. In our scenario, the pivotal step is optical pumping, known for its high efficiency, requiring only a minimal number of photons to induce spin flips and separation^[13,15,16]. Conversely, 2D transverse cooling necessitates several hundred to a thousand photons for beam collimation, which may reduce the production rate significantly. However, in our specific context, the natural abundance of K40 is approximately 600 times lower than that of K41, and 8000 times lower than that of K39. Therefore, it is the photon count associated with K39 that limits the production rate, not K40, even with 2D transverse cooling. Our approach holds particular promise for rare isotopes with exceptionally low abundance.

Figure 1(a) illustrates the experimental setup. The atomic beams are collimated using a micro-capillary array, consisting of 400 needles with an inner diameter of 0.3 mm and a length of 10 mm^[17]. Post-oven, atoms undergo 2D transverse cooling (along x and y) facilitated by a laser operating at the D2 transition at 767 nm. This laser comprises two frequencies: a transition from F=9/2 to F′=11/2 and another from F=7/2 to F′=9/2. These frequencies are well-separated from the transitions of K39 and K41, with a minimum detuning of 369 and 264 MHz, respectively. Importantly, our experimental observations indicate that the addition of 2D lasers has minimal influence on the signals of K39 and K41.

Subsequently, the atoms are optically pumped to high-field seeking states for K39 and K41 and low-field seeking states for K40 using narrow linewidth lasers (L1 and L2). These lasers are stabilized by dichroic-atomic-vapor laser locking (DAVLL) with a linewidth of 500 kHz. The polarized potassium atoms then enter the 1.5-m-long Halbach array with a maximum magnetic gradient of 2.5 T/cm near the magnet surface. In this configuration, only low-field seeking atoms are deflected, enabling the deflection and collection of K40. For more details, please refer to our previous work^[16].

Figure 1(b) shows an enlarged view of the 2D region where the particles are collimated. In the transverse cooling regime, the laser beam has an elliptical size of 15mm×7.5mm, undergoing more than 10 reflections by mirrors with a total transmission rate of 0.9 in each cycle, resulting in an effective cooling regime of 14.5 cm. The two mirrors are positioned at an angle of approximately 0.05°. Initially, the incidence beam has an angle of about 2°, gradually becoming nearly perpendicular to the mirrors. Such a small angle allows light to bounce back and forth between the two flat mirrors and spread the light spot as far as possible over the entire 2D area. On the other hand, because the incident angle of 2D light is gradually decreasing, it can match the velocity direction of atoms over a long distance and also match the velocity direction of different atoms. This configuration was widely used in the early study of the laser cooling of atoms^[24-26] and more recently of the laser cooling of molecules.

Laser cooling typically reduces the transverse temperature to a few microkelvins, implying a divergence angle of just a few milliradians. Since the 2D transverse cooling is exclusively applied for K40, resulting in highly collimated K40 atoms, while K39 and K41 atoms remain unaffected, this leads to a further enhancement in isotope enrichment. Figure 1(c) displays typical data of K40 fluorescence captured in the detection area. The upper panel depicts data without 2D transverse cooling, whereas the lower panel incorporates 2D transverse cooling. An enhancement of approximately 20 times is observed with the application of 2D transverse cooling.

To study the enhancement effect with 2D transverse cooling, we applied a numerical simulation based on multi-level rate equations^[27,28], which we briefly summarize here. The populated fraction in each sublevel for a multi-level system is calculated as {dNldt=Γ∑url,uNu+∑u,pRl,u,p(Nu−Nl)dNudt=−ΓNu+∑l,pRl,u,p(Nl−Nu),(1)where Nl and Nu are the populated fractions for the lth sublevel in the ground state and the uth sublevel in the excited state, respectively, Γ is the spontaneous decay rate of the excited state, rl,u is CG factor, Rl,u,p=Γ2rl,usp1+(2Δp/Γ)2(2)is the excitation rate for l→u transition from the pth laser beam, sp is the saturation factor, and Δp is the detuning.

Numerically, we simulate numerous potassium atoms with random positions, random velocity, and two random angles, allowing us to determine velocities in all three directions. The initial position is confined within a size of 6mm×6mm set by the furnace. One angle spans from 0 to 2π, while the other is more restricted, as discussed below. The cooling force is computed following our previously described methodology. Atomic trajectories are then calculated accordingly with the geometry constraint of our experimental setup.

Figure 2(a) displays typical trajectories of particles after their exit from the source. We define the divergence angle as the deviation angle of particle velocity from the main axial direction. Due to the mechanical limitations of the vacuum chamber, the actual divergence angle is capped at 0.38°. Only atoms with divergence angles smaller than this value are eventually counted. Finally, we analyze the distribution and count the number of atoms at the detection regime. By calculating the ratio of the number of K40 atoms with and without 2D transverse cooling, we derive the enhancement of K40.

Figures 2(b) and 2(c) display the dependence of K40 enhancement on the laser detuning and intensity of the 2D laser. Maximum enhancement is observed in Fig. 2(b) when the detuning is around 5 MHz with a total intensity of 280mW/cm2 and an oven temperature of 600 K. Despite the usual requirement for red-detuned lasers in laser cooling, we need to use a blue-detuned laser in our experiment due to the small angle between our laser and the atomic beam as shown in Fig. 1(b). According to the fitting function y=A×I/(I+Is), we obtain that the enhancement of potassium reaches saturation at around 100mW/cm2 when the detuning is 5 MHz and the oven temperature is 600 K, as shown in Fig. 2(c). Notably, the saturation intensity of potassium is Isat=1.75mW/cm2, and the simulated saturation intensity is 30 times that value. We suspect that the reason for this discrepancy may be due to the initial collimation of particles by the laser. A relatively high intensity helps collimate particles faster, and more likely they will enter the detection region.

Figure 2(d) shows the divergence angle of the atomic beam leaving the 2D region with and without 2D transverse cooling. When 2D transverse cooling is switched on (red line), the divergence angle is reduced significantly, which increases the K40 atoms by one order of magnitude.

Figure 3 illustrates the flux rate of K40 at the detection area at varying temperatures with a total intensity of 260mW/cm2. A notable enhancement occurs when the detuning is within 5–8 MHz, as shown in Fig. 3(a). The slight offset detuning is attributed to the small angle between the laser and the atomic beams^[25]. Center frequencies exhibit a slight shift with increasing the oven temperature, influenced by the varying forward velocities connected with the temperatures. Figure 3(b) displays the intensity dependence of the K40 signal, which starts to saturate around 150mW/cm2, reaching a flux rate of 2.8×1010/s at 300°C.

Figure 4(a) explores the temperature dependence of the enriched abundance of K40 and the gain from 2D transverse cooling under saturated intensity and optimal detuning. Abundance was calculated by measuring the signal intensity of K40 divided by the signal intensity of K40 plus the signal intensity of K39 and the signal intensity of K41 when all lights were turned on. With the increase in temperature, the abundance reaches more than 20% at 240°C, and then gradually decreases to 12% at 300°C. The gain, defined as the signal ratio with and without 2D transverse cooling, increases the K40 production rate by 17 to 22 times across the temperature range from 220°C to 300°C. This aligns closely, albeit slightly higher, with theoretic prediction, reinforcing the significance of the divergence angle in the final production rate. At higher temperatures, the gain exhibits a slight reduction. Two potential reasons are considered: first, the optimized conditions for 2D transverse cooling at lower temperatures may not be ideal at higher temperatures due to increased forward atom velocities; second, higher temperatures result in elevated K atom density, leading to increased scattering and a potential decrease in optical pumping efficiency. Figure 4(b) shows the suppression ratio for both K39 and K41. The suppression ratio, indicating the atomic output with and without optical pumping, remains nearly constant for K41, while for K39, it decreases with rising temperature. The decrease is attributed to reduced optical pumping efficiency due to scattering light from 2D transverse cooling and optical pumping regimes. Given the high natural abundance of K39, the decrease in the suppression ratio correlates with a decline in the abundance of enriched K40, as shown in Fig. 4(a).

Collimation of the atomic beam is crucial for our laser isotope separation method, and we have found that 2D transverse cooling effectively addresses this issue. The magnetic isotope separate stage has some phase space (position-velocity) acceptance region. Typically, we regulate the total velocity by adjusting the temperature. However, the average speed v¯ proportional to T1/2 changes minimally in the experiment’s temperature range (220°C–300°C), varying from 508 m/s to 548 m/s. Conversely, the reduction in transverse velocity (divergence angle) with 2D transverse cooling allows more atoms to enter the acceptance region that would otherwise be excluded. Our final experimental results confirm that reducing the divergence angle leads to one order of magnitude improvement. Specifically, at a temperature of 300°C, we achieved a potassium production rate of 1.3 µg/day, with approximately 12% of it being K40. This abundance is particularly beneficial for cold atom experiments involving K40. Moving forward, our future plans involve optimizing the needle array and furnace design to further increase the atomic flow rate and production rate for potassium isotopes.

One of the primary limitations we face is the photon number scattered in relation to K39, not K40, due to the extremely low natural abundance of K40. The average forward speed v¯ is approximately 550 m/s when the oven is 300°C. Considering the divergence angle θ of the atomic beam is 2°, the transverse velocity is v⊥=v¯×tanθ=19.2m/s.(3)

The recoil velocity vrec of K40 is 1.3 cm/s. Therefore, the approximate number of photons that need to be scattered in 2D transverse cooling is N=v⊥/vrec≈1500.(4)

The natural abundance of K39 is 8000 times higher than that of K40, given the same intensity of lasers for both K39 and K40, and the final production rate of enriched potassium is still restricted by the photon number scattered by K39.