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

We report the laser cooling and trapping of neutral potassium on an open transition. Fermionic ${}^{40}$K is captured using a magneto-optical trap (MOT) on the closed $4S_{1/2}\to 4P_{3/2}$ transition at 767 nm and then transferred, with high efficiency, to a MOT on the open $4S_{1/2}\to 5P_{3/2}$ transition at 405 nm. Because the $5P_{3/2}$ state has a smaller linewidth than the $4P_{3/2}$ state, the Doppler limit is reduced from 145 μK to 24 μK, and we observe temperatures as low as 63(6) $\mu$K. The density of trapped atoms also increases, due to reduced temperature and reduced expulsive light forces. We measure a two-body loss coefficient of $\beta =1.4\left(1\right)\times {10}^{-10}$ cm${}^3$/s near saturation intensity, and estimate an upper bound of $8\times {10}^{-18}$ 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 precooling for quantum gas experiments. A qualitatively similar enhancement is observed in a 405 nm MOT of bosonic ${}^{41}$K.

Figure 1

Level diagram including all the possible decay channels of the $4S\to 5P$ transition in ${}^{40}$K. Transition probabilities are from [15] and listed as $A=1/\tau$ in units of $\mu {\mathrm{s}}^{-1}$. Except for $4P\to 4S$ (from [16]), the uncertainties in transition probability rates are not shown explicitly. The uncertainties in the $5P\to 4S$ rates are less than $8\%$, but all other rates are estimated to have uncertainties between 25% and 50%. The total measured lifetime from all decay channels is 134(2) ns for $5P_{3/2}$ [17] and 137.6(1.3) ns for $5P_{1/2}$ [18]. Level energies $E$ referenced from the $4S$ state are from [15] and presented in both frequency units (as $E/h$) and wavelength units (in italics, as $hc/E$). Hyperfine splittings $\Delta E$ referenced to the level energies are from [19] for $4S_{1/2}$ and $5P_{3/2}$, from [15] for $4P_{3/2}$, and given in frequency units (as $\Delta E/h$). The solid blue and dashed red arrows indicate the cooling and repump hyperfine transitions, respectively, used for laser cooling.

Figure 2

Blue cooling and trapping. Calculated force (in units of $Mg$, where $g$ is gravitational acceleration) versus (a) velocity (at zero displacement) or (b) position (at zero velocity) for a 10 G/cm MOT at 767 nm (red dashed line) and 405 nm (blue dashed line). Both are calculated for counterpropagating beams at $-\Gamma /2$ detuning from resonance and with intensity per beam of $I_{\mathrm{sat}}/5$ where $I_{\mathrm{sat}}$ is indicated in Table . For the 405 nm data there is a 767 nm repump beam on resonance with the $4S_{1/2},F=7/2\to 4P_{3/2},F^{\prime }=9/2$ transition with 10% of the 405 nm beam intensity. Near zero velocity, the damping rate is $\gamma =1.8\times {10}^4$ s${}^{-1}$ for the red and $\gamma =6.9\times {10}^4$ s${}^{-1}$ for the blue. Near zero displacement, the spring constant corresponds to an undamped trap frequency ${\omega }_{\mathrm{osc}}/\left(2\pi \right)=730$ Hz for the red and ${\omega }_{\mathrm{osc}}/\left(2\pi \right)=650$ Hz for the blue.

Figure 3

The optical configuration of the magneto-optical trap includes 767 nm trapping and repump beams (both shown with red dashed outlines) and a 405 nm trapping beam (shown in solid blue). The two colors are mixed on a dichroic mirror (DM), manipulated with dichroic quarter-wave plates (DWPs), and retroreflected off a broadband mirror (BBM). Each DWP has a quarter-wave retardation at one wavelength and no retardation at the other wavelength. Only one MOT direction has been shown for clarity, but there is an identical beam path in three orthogonal directions. The magnetic quadrupole (QP) coils typically apply 10 G/cm along their strong axis. The potassium (K) cloud is imaged in absorption with a probe beam (not shown). Inset: Timing diagram of laser beam intensities (top three lines) and magnetic field strength. After a 10 s accumulation, the 767 nm trap is extinguished, the 767 nm repump intensity is reduced, and the 405 nm trap is turned on for a variable hold time. The molasses phase is only used in Sec. 5. An absorption image is taken after a variable-length time of flight (TOF).

Figure 4

Trapped cloud measurements. Typical absorption images of (a) a 767 nm MOT with detuning $\Delta =-35$ MHz and intensity $I\approx 16$ mW/cm${}^2$ and (b) a 405 nm MOT, for $\Delta =-1$ MHz, $I\approx 90$ mW/cm${}^2$. In both images, pixel darkness denotes optical density. Images were taken shortly (1.5 ms) after release from the trap, such that clouds are little changed from their in situ distributions. Atom number is ${10}^8$, but the cloud in (b) is clearly compressed. (c) Cooling dynamics are observed in images similar to (b) but with various hold times in a blue MOT; here with $\Delta =-2$ MHz and $I\approx 50$ mW/cm${}^2$. The rms width is shown for both the vertical (open red circles) and horizontal (black squares) directions. Simple exponential fits are shown as solid lines, with a $1/e$ time of 1.8 ms for the vertical width and 4 ms for the horizontal width.

Figure 5

Intensity requirements. A threshold for proper trap function is observed by measuring the capture fraction (black squares, scale on left) and vertical displacement of the cloud from trap center (open red circles, “MOT sag” scale on right) as a function of the six-beam intensity of (a) trap beams and (b) repump beams. Lines are exponential fits to guide the eye. The blue-MOT time was 30 ms for (a) and 20 ms for (b), both at $-2$ MHz detuning. In both sets of data, the trap movement in the direction orthogonal to gravity was less than 100 $\mu$m.

Figure 6

Lifetime. Atom number is shown versus hold time in the blue MOT. The data are fit to exponential decays in different regions as a guide to the eye. Top inset: Peak density for short hold times is approximately constant. Bottom inset: The one-body-lifetime fit at long hold times decreases at higher 405 nm trap intensity.

Figure 7

Performance of a magneto-optical trap at 405 nm. Both (a) temperature and (b) peak density are shown versus detuning from resonance, for several magnetic quadrupole gradients: 5 G/cm (black squares), 7.5 G/cm (red circles), and 10 G/cm (blue triangles). Temperature is shown along a weak axis of the quadrupole; temperatures along the strong axis (along gravity) were 1.82(15) times higher.

Figure 8

Molasses cooling. Blue laser cooling is continued for 10 ms after the magnetic quadrupole field is extinguished, followed by a TOF temperature measurement. The horizontal temperature is shown versus detuning; vertical (along gravity) temperatures are 1.96(11) times higher. In addition to the statistical error bars shown, there is a systematic 0.5 MHz uncertainty in the detuning. The solid line is an OBE calculation, but it is not a quantitative prediction: the approach is constrained to intensities well below saturation (here, $I_{\mathrm{sat}}/50$ per beam), whereas the data were taken with roughly $I_{\mathrm{sat}}/2$ per beam.