Low-temperature, high-density magneto-optical trapping of potassium using the open 4S-5P transition at 405 nm

We report the laser cooling and trapping of neutral potassium on an open transition. Fermionic 40K is captured using a magneto-optical trap (MOT) on the closed 4S-4P transition at 767 nm and then transferred, with unit efficiency, to a MOT on the open 4S-5P transition at 405 nm. Because the 5P state has a smaller line width than the 4P state, the Doppler limit is reduced. We observe temperatures as low as 63(6) microkelvin, the coldest potassium MOT reported to date. The density of trapped atoms also increases, due to reduced temperature and reduced expulsive light forces. We measure a two-body loss coefficient of 2 x 10^-10 cm^3/s, and estimate an upper bound of 8x10^-18 cm^2 for the ionization cross section of the 5P state at 405 nm. The combined temperature and density improvement in the 405 nm MOT is a twenty-fold increase in phase space density over our 767 nm MOT, showing enhanced pre-cooling for quantum gas experiments. A qualitatively similar enhancement is observed in a 405 nm MOT of bosonic 41K.


I. INTRODUCTION
Magneto-optical trapping is a widely applied technique for creating cold, dense samples of neutral atoms. Ultracold gas experiments typically use a MOT for accumulation and pre-cooling, although laser cooling alone has been unable to create a quantum degenerate sample without a subsequent evaporative cooling step. Density in laser cooling is limited by repulsive radiation pressure due to re-absorption [1] and by collisional loss processes [2]. The temperature limit, in the simplest two-level theory, is the Doppler temperature, k B T D = Γ/2, where Γ is the line width of the excited state [3]. Fortuitously, the multi-level structure of ground states can allow for sub-Doppler temperatures [4,5], but these effects are not seen in all atomic species. Particularly, sub-Doppler cooling is non-existent in 6 Li [6] and weak [7] or difficult to observe [8] in 40 K. Since these are the only two stable fermionic alkali isotopes, and thus commonly used for the study of quantum degenerate Fermi gases, new cooling techniques would be beneficial.
Laser cooling on narrower lines can achieve lower temperatures, as has been demonstrated with earth alkaline atoms. In the case of 88 Sr [9], the broad 30 MHz cycling transition ( 1 S 0 → 1 P 1 ) at 461 nm is used to capture atoms, followed by cooling on the narrow 7.5 kHz forbidden transition ( 1 S 0 → 3 P 0 ) at 689 nm. This two-step process combines a large capture rate during the first stage with the low Doppler temperature of the second stage. Alkali atoms do not have forbidden transitions, however higher excited states do have smaller line widths. For example, in potassium, the 5P state has a line width of 1. 19 MHz, roughly five times smaller than the 6.0 MHz line width of the 4P state that has been used in all potassium laser cooling experiments to date. However, the 4S → 5P transition is not a cycling transition, and alternate decay channels could depolarize magnetic sublevels, increase the depumping effect of the cooling laser, and interrupt laser cooling mechanisms.
It has been shown that laser cooling is possible using open transitions, both with metastable helium [10] and with lithium [11]. In the case of He*, a MOT on the 2S → 3P transition at 389 nm was shown to have a lower two-body loss rate β, lower re-absorption rates, and a larger cooling force per recoil, resulting in increased density. No reduction in temperature was seen since the He* 2P and 3P excited states have the same lifetime. In the case of 6 Li, a MOT on the narrower 2S → 3P line did have a reduced temperature, but not an increased density. Unlike lithium and metastable helium, potassium has a D-state decay channel that could perturb laser cooling more significantly (see Fig. 1). In addition to reduced Doppler temperatures, higher-state transitions may provide other advantages: multi-photon decay channels allow for background-free detection, and the smaller transition wavelength reduces the diffraction limit of imaging and manipulation. A specific advantage of the potassium transition at 405 nm is the emergence of inexpensive GaN diode lasers [12] in the 395-410 nm range.
In this paper, we explore cooling and trapping on the "blue" 4S 1/2 → 5P 3/2 transition of 40 K at 405 nm. Atoms are first accumulated in a standard MOT on the "D2" 4S 1/2 → 4P 3/2 transition at 767 nm, for which the capture rate is high. The cloud is then transferred to a blue MOT, where we observe a temperature as low as 63(6) µK and a ten-fold increase in density. Although the capture velocity and beam size of the blue MOT are small, we observe almost perfect transfer between MOTs. We find that loss rates in the blue MOT from two-body loss and photoionization are higher than in the D2 MOT, but these processes play little role on the sub-100-ms timescale that we observe is necessary for equilibration.
Our paper is organized as follows. In Sec. II we discuss the state structure of potassium and calculate the effect of excitation on the 4S 1/2 → 5P 3/2 transition using the steady-state Bloch equations. We estimate the cooling and trapping power with a semiclassical treatment. In Sec. III we describe the critical components of our experimental system, including generation of 405 nm light with diode lasers and the optical configuration of the two-color MOT. Sec. IV presents the primary results of the paper: the capture fraction, lifetime, temperature, and density of a blue potassium MOT. Further laser cooling results, prospects, and conclusions are discussed in Sec. V.
II. 4S 1/2 → 5P 3/2 TRANSITION: THEORY AND BACKGROUND Figure 1 shows a level diagram of potassium including all possible decay paths from the 5P 3/2 state. The line strength of the 4S 1/2 → 5P 3/2 is 2π × 185 kHz, thirty TABLE I. Key excitation properties of the 4S 1/2 → 5P 3/2 transition, with the 4S 1/2 → 4P 3/2 transition shown for comparison. Where relevant, the drive is assumed to be σ + polarized. Saturation intensity is defined as the drive strength at which 25% of the population is the excited state. "Steadystate polarization" is the fraction of atoms in F = 9/2 that are in the mF = +9/2 sublevel, with a drive at Isat. "Depumping probability" is the percent decay from |11/2, 11/2 to the F = 7/2 manifold, through a multi-photon cascade. "Doppler temperature" is the steady-state temperature in the lowintensity limit, and includes open-transition effects for 5P 3/2 . (1)  We calculate excitation properties and cooling rates of the 4S → 5P transition by finding the steady-state solution of the optical Bloch equation (OBE) that includes all relevant levels. Because the transition is not closed, continual excitation requires a repumping beam. As in the experiment, atoms are repumped on the 4S 1/2 , F = 7/2 → 4P 3/2 , F = 9/2 transition, whose strength is chosen here to be powerful enough that it is not the limiting timescale. Table I summarizes key steady-state properties of excitation to the 4P and 5P states. Unlike a cycling transition, polarized optical pumping on the open transition scrambles the m F states. However, the depolarization rate is not quite as bad as Fig. 1 might suggest: 61% of atoms in the F = 9/2 manifold are in the doublypolarized |9/2, 9/2 state. The resonant scattering crosssection is nearly thirty times smaller than the D2 transition due to a narrow line width and smaller wavelength. This could be an advantage for cooling trapped or dense clouds since optical density is reduced. However, for the same reasons, the saturation intensity is an order of magnitude higher, increasing optical power requirements.
Laser cooling and trapping performance of the 4S → 5P transition is estimated by including either Doppler or Zeeman shifts in the OBE calculation. Recoil heating is assumed to arise from momentum diffusion with an energy increase of ( k) 2 /(2M ) per scattering event, where k = ω/c, ω is the transition frequency, c is the speed of light, and M is the mass of 40 K. Heating in the multi-photon decay path is due to the scattering of three photons of various momenta.  Table I. For the 405 nm data there is a 767 nm repump beam on resonance with the 4S 1/2 , F = 7/2 → 4P 3/2 , F = 9/2 transition with 10% of the 405 nm beam intensity. Near zero velocity, the damping rate is γ = 1.8 × 10 4 s −1 for the red and γ = 6.9 × 10 4 s −1 for the blue. Near zero displacement, the spring constant corresponds to an undamped trap frequency ωosc/2π = 730 Hz for the red and ωosc/2π = 650 Hz for the blue.
At comparable scaled detunings and saturations, Fig. 2(a) shows that the blue transition can achieve a higher cooling rate than the D2 transition. However, the maximum force and the capture range are greatly reduced. Figure 2(b) shows that the spring constant is comparable for the two transitions, but that trapping volume is larger for the red MOT. These calculations support the strategy of loading atoms using the 767 nm transition and then transferring later to the 405 nm MOT for additional cooling and compression. We find a steadystate temperature of 24 µK for the blue transition, indeed smaller than the Doppler temperature of the D2 transition. In fact, this steady-state temperature in the lowintensity limit is slightly (∼18%) less than the Γ/2k B expected in the two-level Doppler cooling, because the multi-photon cascade causes slower momentum diffusion than single-photon kicks with the same total energy.
Another difference between laser cooling with blue instead of infrared light is the possibility of photoionization. The ionization energy of potassium is 1049.56782(2) THz [13], so the 5P state can be ionized by the 405 nm MOT light, or by any photon with a wavelength less than 972 nm. By contrast, the 4P state requires photons with a wavelength less than 455 nm, which is not provided by the D2 MOT. The 405 nm trap light may also ionize any state during the radiative cascade, and the 767 nm repump can only ionize the 5P state.

III. LASER AND MOT SETUP
The 4S → 5P transition is placed in a wavelength band for which GaN diode lasers have become readily available, due to recent commercial interest in optical storage media. These sources have been exploited to perform 4S → 5P spectroscopy of natural potassium [12,16,[18][19][20] and enriched 40 K [21], but never laser cooling.
Our 405 nm master is a grating-stabilized diode laser with 10 mW output. Half of this power is injected [22] into a 100-mW diode laser ("slave" laser). At room temperature, and without injection, the slave diode spectrum is nearly 1 nm wide and centered at 407 nm. The poor current and temperature tuning characteristics of the diode, approximately +0.02 nm/mA and +0.05 nm/ • C respectively, necessitate cooling the diode to -20 • C. Without injection the Fabry-Perot spectrum of the slave is featureless, but strong peaks are evident when successfully injected. The output of the slave, typically run at 60 mW, is passed through a single-mode optical fiber before use in the MOT (see Fig. 3).
The remaining 5 mW of master light is used for modulation transfer spectroscopy using a natural-abundance potassium cell heated to 140 • C. The elevated temperature is necessary because the Doppler cross section is two orders of magnitude smaller than the cross section for the D2 transition. We lock to the 4S 1/2 , F = 1 → 5P 3/2 transition in 39 K (with unresolved excited states) that is the closest spectral feature to the 4S 1/2 , F = 9/2 → 5P 3/2 , F = 11/2 transition of 40 K. The additional 0.5 GHz shift is performed with acousto-optic modulators.
The D2 MOT uses retro-reflected beams along three axes, limited by the cell windows to be 4.4 cm diameter in the horizontal axes and 3.8 cm diameter in the vertical axis. A background potassium vapor is created from enriched dispensers (5% 40 K), and collected in the trap using the strong 4S 1/2 → 4P 3/2 transition. During this phase, there are two overlapping 767 nm beams: a trap with 200 mW total power detuned by ∆ = −35 MHz from the F = 9/2 → F ′ = 11/2 transition, and a repump with 150 mW total power detuned by −25 MHz from the F = 7/2 → F ′ = 9/2 transition. After 10 s, the blue MOT is turned on, with up to 30 mW total power. As shown in Fig. 3, the smaller (10-mm diameter) blue beams are mixed with the infrared beams on dichroic mirrors. We use dichroic wave plates to control independently the polarization of the two colors. There is a short time (3 ms) when both MOTs are on before the D2 trap light is turned off (see timing diagram of Fig. 3), while the D2 repump beam is left on at reduced intensity. Blue laser cooling is applied typically for 30 ms.
Laser-cooled atoms are characterized using absorption imaging on the 4S → 4P transition. Temperature is measured in time-of-flight, with a gaussian fit to the density distribution imaged at various free-flight times, 1.5-10 ms after the magnetic field and laser beams have been extinguished. rameters, compression occurs, which is a first indication of cooling (see below for further discussion). Fig. 4(c) shows that cloud sizes in the blue MOT equilibrate with a 1/e relaxation time of 2-4 ms. In a damped oscillator model of atomic motion in a MOT, where γ ≫ ω osc , the atomic position damps with a time γ/ω 2 osc , which is consistent with what we measure -4 ms using the typical force curves of Fig. 2(b). Atomic velocities would damp in a much faster time γ −1 ∼ 15 µs, so after the spatial compression shown in Fig. 4(c), blue laser cooling is complete. Figure 5 shows the capture fraction and gravitational sag as a function of blue trap intensity and D2 repump intensity. In both cases, providing the saturation inten- sity (see Table I) is sufficient for complete transfer into a strong trap. [23] From exponential fits, the transfer efficiency is 90% for 5.5 mW/cm 2 of blue trap intensity and for 0.21 mW/cm 2 of D2 repump intensity. The 26:1 ratio between these follows approximately the ratio of saturation intensities of each transition.
Since the capture rate of a MOT from background vapor is proportional to Γ 4 d 4 for small beam sizes d, one would expect a 10 6 reduction in steady-state number in going from the 767 nm to the 405 nm trap. Accordingly, a measurement of atom number versus time (Fig. 6) shows no sign of saturation after a hundred-fold reduction in number. We can then use such a measurement as a clean measure of loss processes, ignoring additional capture.
We also note that since we are not loading atoms from vapor into the blue MOT, we can choose small beam sizes, and reduce the 405 nm power requirement. In our configuration, the total power required at saturation intensity is roughly 2.5 mW, which our laser system can easily provide.
The loss data in Fig. 6 fits well to two exponential time scales, indicative of two-body losses at high density, and one-body losses (collisions with background atoms plus photoionization) at low density. The loss rate from a MOT is [2] where τ is the one-body lifetime, β is the two-body loss coefficient, and n is the atomic number density. To find τ , we fit the data at long hold times (t > 2 s, N < 5 × 10 6 ) where the atom number is strongly reduced and twobody losses can be neglected. The lifetime versus 405 nm intensity is show as the bottom inset to Fig. 6. The decrease in lifetime versus intensity could be evidence of ionization losses. The line is a fit to a model that includes the intensity dependence of both the ionization rate and the excited state fraction. A separate study of MOT fluorescence versus laser power, comparing D2 and blue MOTs, was used to calibrate excited state fraction versus intensity. Together, we find an ionization cross section of 8 × 10 −18 cm 2 for the 5P 3/2 state at 405 nm. We report this value as an upper bound since the ionizing beams are also the trap beams and we cannot rule out other trap loss processes [24]. There are no measured cross sections for the ionization of the 5P states of potassium, only for the equivalent state, 6P, of rubidium [25][26][27]. These rates may be comparable since the ionization cross section from the potassium 4P states [28,29] is within a factor of three of the 5P cross section for rubidium [30]. Indeed, our upper bound is similar in magnitude to the 2 × 10 −18 cm 2 cross section for the 6P state of rubidium from [27] measured at λ = 350 nm. To measure the two-body loss rate, we assume the MOT density distribution is Gaussian, which is supported by absorption images of the cloud. From the top inset in Fig. 6 we see that the peak density n 0 at short times is roughly constant, so the number decays as We then fit the data at short hold times (t < 300 ms) to an exponential decay and use τ (from our previous measurement) and n 0 to find β. At ∆ = −2 MHz, we find β = 2.0(1) × 10 −10 cm 3 /s for I ≈ 75 mW/cm 2 , and β = 1.4(1) × 10 −10 cm 3 /s for I ≈ 20 mW/cm 2 . These are relatively high two-body loss rates compared to alkali MOTs on the D2 transition, which are typically in the range of 10 −12 to 10 −11 cm 3 /s [2]. Values for 40 K 767 nm MOTs vary from 6 × 10 −13 [31] to 3 × 10 −11 cm 3 /s [32]. Therefore, overall loss rates in the 405 nm MOT are larger than the 767 nm MOT, but for the short timescales (tens of milliseconds) required to decrease temperatures and increase density, these loss rates are still negligible. A primary motivation for cooling on a narrow transition is to achieve a lower asymptotic temperature. Figure 7 shows how the temperature and peak density of the blue MOT change with detuning, at various quadrupole gradients. A minimum temperature of 63(6) µK is seen for a 5 G/cm magnetic quadrupole gradient. Operating the MOT with higher gradients increases both the temperature and density. In all cases, the minimum temperature and maximum density are found near ∆/Γ ≈ −1.
We attribute the increase in density to three factors. First, the temperature in the MOT is lower. Second, expulsive forces due to re-absorption are reduced, because the same spring constant is achieved with a scattering rate that is six times smaller. The open transition may further reduce re-absorption by pumping to the F = 7/2 ground states. Third, the optical density seen by both the incident and the scattered blue photons is reduced by a factor of nearly thirty.
In comparison, our D2 MOT density is typically n 0 = 2 × 10 9 cm −3 and temperature is typically T = 180 µK. Since phase space density scales as n 0 T −3/2 , the combined 75 µK and n 0 = 1.2 × 10 10 cm −3 (achieved with a blue MOT at 7.5 G/cm and -1.5 MHz detuning) realizes a twenty-fold enhancement in phase space density.

V. PROSPECTS AND CONCLUSIONS
Since the lowest observed MOT temperatures occur at low gradients, one might expect continued improvement during an optical molasses phase, in which magnetic fields have been extinguished (see Fig. 3 inset). Figure 8 shows that minimum temperature, roughly 85 µK, is comparable to what is observed in the MOT, although optimized at a lower detuning, ∆/Γ = −0.6(2). These temperatures are still more than three times the Doppler temperature calculated in Sec. II, which may be due to a low cooling rate as compared to the short molasses time available. Indeed we observe that the temperature asymmetry between the vertical and horizontal axes in the MOT persists during the molasses phase, when no gradient asymmetry remains. Even the asymptotic temperature might not be expected to reach the Doppler limit: while the calculation in Sec. II includes multi-level effects, it neglects three-dimensional effects, reabsorption, and heating due the intensity fluctuations. The latter effect has been shown by Chanelière et al. to limit onedimensional Doppler cooling to several times T D in Sr, when Sisyphus and other sub-Doppler mechanisms are absent [33]. In the case of 4S → 5P cooling in 40 K, polarization gradient cooling may be interrupted by the optical pumping and depolarization effects of the three-photon cascade.
We have also observed laser cooling and trapping for bosonic 41 K on the 4S 1/2 → 5P 3/2 transition. A similar order-of-magnitude increase in MOT density was apparent, although further study is warranted. With any isotope of potassium, additional improvements might be possible with more sophisticated timing sequences of detuning and/or intensity of cooling light, which has been fruitful in narrow-line MOTs and in sub-Doppler cooling of bosonic potassium [34].
In sum, we have observed laser cooling and trapping of neutral potassium on the open 4S 1/2 → 5P 3/2 transition. Nearly complete transfer from a D2 MOT is observed, although the blue MOT is ineffective at capturing directly from the vapor. We observe temperatures as low as 63(6) µK along one axis, roughly half of the Doppler limit on the D2 transition. Unlike sub-Doppler cooling observed in 40 K during a molasses phase [7], our approach reduces temperature while the confining MOT quadrupole field is still present. Density is enhanced ten-fold in typical conditions, due to lower temperature and reduced re-absorption effects. Cooling and compression together increase the phase space density by more than an order of magnitude, demonstrating improved pre-cooling for quantum degenerate gas experiments. The reduced wavelength of the 4P 3/2 → 5P 3/2 transition may enable improved imaging or addressing resolution (λ/2 = 202 nm), for instance in the context of strongly correlated lattices where the spacing is typically 500 nm [35].
More generally, since the potassium cascade structure is shared by sodium, rubidium, cesium, and francium, our work along with Ref. [11] suggests that laser cooling and trapping using the nS → (n + 1)P transition will be successful for all alkali atoms.