Acetylene-based frequency stabilization of a laser system for potassium laser cooling

We demonstrate a laser frequency stabilization technique for laser cooling of Potassium atoms, based on saturated absorption spectroscopy in the C-Band optical telecommunication window, using ro-vibrationel transitions of the acetylene molecule (C2H2). We identified and characterized several molecular lines, which allow to address each of the potassium D2 (767 nm) and D1 (770 nm) cooling transitions, thanks to a high-power second harmonic generation (SHG) stage. We successfully used this laser system to cool the 41K isotope of potassium in a 2D-3D Magneto-Optical Traps setup.


Introduction
For laser cooling and trapping experiments, frequency stabilization of the laser system must be ensured, with a stability typically less than the natural linewidth of the transition (a few MHz for alkali atoms). In most cases, this is achieved via sub-Doppler saturated absorption spectroscopy, usually employing the same atomic transition used for laser cooling [1,2]. Semiconductor laser diodes in external cavities [3,4], eventually further amplified with slave diodes or semiconductor 1 arXiv:1909.11631v1 [physics.atom-ph] 25 Sep 2019 tapered amplifiers [5,6,7], are the most common laser sources for laser cooling alkali atoms.
Even though those laser setups have been widely implemented over the last three decades in cold atoms experiments, several drawbacks still remain: limited lifetime of tapered amplifiers or poor quality of spatial mode. This last feature implies significant losses of optical power which is crucial for standard experiments of ultracold and quantum degenerate gases. In some cases, powerful lasers are either too costly (as is the case with Ti:Saphire lasers) or unavailable at the desired wavelengths, and frequency conversion (i.e. second harmonic generation or frequency summation) is necessary [7,8]. This solution allows to take advantage of the optoelectronic devices developed for the telecommunications industry in the 1530-1565 nm band. Powerful fiber lasers/amplifiers are available and can be frequency-doubled to the near-infrared (NIR). For laser cooling experiments, two atomic alkali species are suitable for the use of telecom-domain fiber amplifiers: rubidium and potassium. Solutions relying on telecom technologies and second harmonic generation (SHG) have been successfully tested in the case of rubidium, starting from a laser source at 1560 nm [9,10,11].
For potassium, a similar technique is implemented in our setup using a diode laser in the telecom domain, followed by amplification and SHG in a periodically-poled lithium niobate (PPLN) crystal. This allows us to obtain a high laser power at the desired wavelength, close to the D2 cooling transitions at 766.701 nm [12]. On the other hand, ultracold atom laser systems usually require complex amplitude and frequency light modulation sequences [13]. To allow such arbitrary modulations, two SHG systems are usually developed: a powerful modulated one is dedicated to the atomic laser cooling, while a weaker, unmodulated one is devoted to the frequency locking only [8]. However, this solution is cumbersome and expensive. This is why we chose, in our system, to generate simultaneously the cooling and repumper frequencies using a single telecom amplifier.
Thus, all cooling frequencies are readily present in a single laser beam, at the output of the SHG stage, eliminating subsequent power losses. Furthermore, the cooling and repumper detunings, as well as their respective power ratio can be varied dynamically at will during the different laser cooling phases * . This feature, however, also makes locking onto Potassium saturated absorption, using the SHG output light, quite impractical.
To fully preserve the simplicity and flexibility of the laser system, we chose a different approach to the frequency stabilisation: using a telecom-based locking scheme. In our case, we chose to * The complete details of this amplification stage is out of the scope of this paper, and will be provided in a future work.
use ro-vibrational transitions of the acetylene molecule, which are close to twice the wavelength of the potassium D2 cooling transitions at 766.701 nm [12]. Thus, the frequency stabilisation can be completely decoupled from the power amplification and SHG stages. The performance of the system has been proven, by demonstrating the magneto-optical trap (MOT) of potassium atoms, in 2D+3D MOT system, creating favorable conditions for upcoming cooling stages, paving the way for efficient and reliable potassium Bose-Einstein condensation experiments. In addition, we also tested the same technique for the D1 transition at 770.108 nm, which has a particular interest for achieving sub-Doppler cooling of potassium, folowing the so-called 'gray molasses' technique [13].

Acetylene transitions for potassium laser cooling
The frequency stabilization in our system is realized by using molecular transitions of the (ν 1 + ν 3 ) ro-vibrational band of the 12 C 2 H 2 molecule, the most naturally abundant (97.7599%) isotopologue of acetylene. This molecule contains approximately 50 strong absorption lines in the telecom spectral region, from 1510 nm to 1542 nm [14,15], as shown in Figure 1. The lines form two distinct branches, P and R, and are indexed by an integer quantum number n. The typical frequency interval between consecutive lines ranges from 50, up to 90 GHz. In 12 C 2 H 2 , the intensity of the odd lines is stronger, by typically a factor of three, than the even ones [15].   To determine the transitions of interest for potassium laser cooling, the absorption spectrum of acetylene was recorded using an Optical Spectrum Analyzer (OSA Ando AQ6317B) which contains a reference acetylene cell. As we can see in the Figure  GHz.

Experimental setup
The experimental setup is presented in Figure 2. It is composed of two main parts: the first part is used to stabilize the frequency of a ultra-narrow line (UNL) laser diode on a Doppler-free signal using a acetylene molecular transition in a low-pressure spectroscopy cell. The second part represents an offset phase-lock which is used to 'bridge' the gap between the acetylene and the potassium atomic cooling transition(s), before SHG. In this way, we obtain a simple and compact, mostly fiber-based setup -almost insensitive to vibrations and misalignments.
Our acetylene-based locking setup utilizes a commercial UNL laser diode (OE4023 model from OEwaves, using a whispering gallery mode resonator  Additional SM fiber isolators are placed to further reduce optical feedback, for both the pump and the probe beams.
In the spectroscopy setup, we utilize a 50-cm-long commercial acetylene cell (Precision Glass Blowing, Colorado, USA) with wedged AR coated windows. The acetylene pressure is 50 mTorr (manufacturer specification). Both the probe and the pump are collimated to 1/e 2 diameters of 1.6 mm, using f = 8.18 mm aspheric lenses. They are sent in opposite directions through the cell, and then re-injected, with 90% efficiency, in the opposite optical fibers. Using fibered optical circulators, the probe beam is separated after the cell and directed to a low-noise photodiode 5 for detection, whereas the pump power is sent to a beam trap. The acetylene cell and the two collimating lenses represent the only free-space part of the setup, and are all ruggedly mounted on a rigid cage system; no optical realignment was found necessary, even after several months of operation.
We paid particular attention to avoid optical interferences on the spectroscopy detection scheme.
The fiber-based part of the system has been therefore assembled by fusion splicing. However, residual internal reflections coming from the different fiber components have been found to alter the spectroscopy signal, on a level comparable to the absorption signal (i.e. with a contrast on the 1% level). Two main improvements were made in order to address this issue. First, we found that using SM fiber components, whenever possible, we were able to decrease the amount stray internal reflexions. Second, we used an AOM to shift the frequency of the pump with respect to the probe by f AOM = 110 MHz. The fringes coming from crosstalk between the probe and the high-power pump will thus 'self-average' on the detection photodiode, which allows us to directly observe the saturated absorption signal, in 'single-shot' measurements. To characterize the spectroscopy setup, we temporarily replaced the UNL diode with a dis-tributed feedback (DFB) laser, which provide a wider frequency scan range (via the laser current).

Acetylene saturated absorption spectroscopy and laser locking
This allowed us to observe different spectroscopic lines of interest for the potassium D2 line, shown in Figure 3.a). The Doppler-broadened P(15) line has a width of 440 GHz (FWHM) and an amplitude of 1.1%. In presence of the pump beam, we observe a saturated absorption peak. Due to the relative frequency difference between the pump and the probe beams, its position is shifted by f AOM /2 = 55 MHz with respect to the center of the Doppler profile. Figure 3.b) shows the amplitude of the saturated absorption peak as a function of the pump power. A typical power of 400 mW was chosen for regular operation, to preserve the lifetime of the pump amplifier, which yields a peak amplitude of 0.112%. Additional saturated absorption signals were observed, for the neighboring P(16) and P(17) lines. Using a different DFB laser, centered at 1540 nm, we also observed the P(23) line, with a corresponding 0.032% amplitude of the saturated absorption peak.

Frequency transfer to NIR
As discussed in the section 2, the frequency difference between the P (15) line and 2 × λ D2 transition of the 41 K is ∼ 88 GHz. To bridge this gap, a phase modulator (Photline, model MPZ-LN-10) is implemented after the UNL laser which generate sidebands in the frequency spectrum, up to ∼ 100 GHz (blue peaks in the Figure 5 a)). Using an AC-coupled photodiode, we detect the low-frequency (270 MHz) beatnote between the DFB diode and the lower sixth harmonic of the UNL laser, created by the phase modulator. The photodiode output is demodulated with a RF synthesizer, which generates the phaselock error signal. This signal is sent to a high-bandwidth 7  commercial PID module (Toptica FALC 110), whose output is summed, via a fast bias-T circuit, to the DFB diode current, which phase-locks it to the acetylene-stabilized UNL laser.
After frequency-doubling the DFB laser, we used a separate saturated absorption potassium vapor cell to observe the potassium atomic transitions. This is done by scanning the current of the UNL laser when the two diodes are phase-locked. The offset between acetylene and different potassium transitions can thus be calibrated, by changing the frequency of the phase modulator.  [16]. For this reason, cooling and repumper frequencies are both generated, using fibered AOMs, and mixed together before the fiber amplifier. This way, the output of the SHG crystal readily contains all laser cooling frequencies in the same spatial mode (avoiding the use of free-space AOMs, which typically generate important power losses).
Our cold-atom system consists of a 'standard' 3D MOT fed by a slow beam of atoms, produced using a commercial vapor-cell 2D MOT (developed by the LNE-SYRTE laboratory in Paris, France).
The atomic source for the 2D MOT consists of a potassium ampoule connected to the 2D MOT chamber through a CF16 valve. A temperature gradient helps the potassium to migrate from the source (heated to 80 • C) to the 2D MOT chamber (50 • C). The vapor pressure in the chamber is maintained with a 2l/s ion pump, at ∼ 5×10 −8 mBar. The slow atomic beam is created by six pairs of retro-reflected elliptical beams (three for each transverse direction, with a total interaction region of ∼ 10 mm), together with a 2D magnetic field gradient of 12 G/cm. The 3D MOT is created in a second vacuum chamber, connected to the 2D MOT via a differential pumping stage, pumped by two getter-ion pumps (NexTorr, models D500 and D300). The pressure is on the order of a few 10 −11 mBar, with a MOT lifetime >30 seconds. For the 3D MOT we use three pairs of independent laser beams, with 1/e 2 diameters of 11.5 mm and ∼ 40 mW each. A relatively weak magnetic field gradient (5 G/cm along the axial direction of the coils) is used, to reduce light-assisted collisions processes, which limit the atoms number in potassium MOTs [17]. Using this configuration, we are able to trap up to a few 10 9 atoms of 41 K. Figure 6 shows a loading curve of the MOT as function of the time, with an 1/e loading time of approximately 6 s.

Conclusion
In conclusion, we demonstrated a versatile and robust fiber-based locking scheme of a telecom laser source directly applicable for potassium laser cooling. The laser system was validated by implementing a high-performance potassium MOT. The scheme completely decouples the frequency locking from the amplification and SHG to NIR domain, which greatly widens the experimental possibilities. The scheme, successfully used for cooling 41 K atoms should be easily extended, with minor changes, to the other isotopes of potassium. Further developments will include testing our scheme for the D1 770 mn line of potassium, where sub-Doppler cooling techniques have been demonstrated. The corresponding acetylene line P (23) has been observed, and despite its lower strength (factor three), the signal-to-noise ratio is still good enough to insure a stable locking scheme.
A particularly interesting improvement would consist in developing a fully fiber-based setup, by using acetylene-filled hollow-core optical fibers † . Their implementation would be straightforward in our setup. Thus, interesting perspectives could open towards mobile cold atom setups, with possible metrological applications using Potassium isotopes [18].