# Two-colour laser cooling for ${}^{40}{\text{K }}$-${}^{87}{\text{Rb
}}$quantum gas mixtures

Yann Kiefer, Max Hachmann, Andreas Hemmerich<EMAIL_ADDRESS>Institut für Quantenphysik, Universität Hamburg, 22761 Hamburg, Germany
Zentrum für optische Quantentechnologien, Universität Hamburg, 22761 Hamburg,
Germany
The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany

###### Abstract

We present an efficient cooling scheme for fermionic ${}^{40}{\text{K
}}$atoms, using laser light red and blue detuned with respect to the
$\mathcal{D}2$ and $\mathcal{D}1$ principle flourescence lines, respectively.
The cooling scheme is found to significantly increase the saturation level for
loading of a ${}^{40}{\text{K }}$magneto-optical trap (MOT), resulting in
increased atom numbers or decreased cycle times. While the attainable
${}^{40}{\text{K }}$atom number is approximately doubled if exclusively
${}^{40}{\text{K }}$atoms are cooled, the scheme is particularly powerful for
dual-species MOTs, for example, if ${}^{40}{\text{K }}$and ${}^{87}{\text{Rb
}}$atoms are cooled simultaneously in the same MOT configuration. The typical
atom losses due to light-assisted hetero-nuclear collisions between
${}^{40}{\text{K }}$and ${}^{87}{\text{Rb }}$seem to be reduced giving rise to
a threefold improvement of the ${}^{40}{\text{K }}$atom number as compared to
that in a conventional dual-species MOT, operating merely with $\mathcal{D}2$
light. Our scheme can be a useful extension to most dual-species experiments,
aiming to reach simultaneous degeneracy of both species.

††preprint: APS/123-QED

##  I Introduction

The recent advances in quantum simulation platforms based on ultracold neutral
atoms [1, 2] and molecules [3, 4, 5, 6] have triggered renewed interest in
refined laser cooling techniques enabling rapid cycle times and high fidelity
sample preparation[7, 8]. To study fundamental low-temperature phases of
matter [9, 10], degenerate quantum gases are typically employed, requiring
temperatures on the 100 nK scale, well below the degeneracy temperature
$T_{deg}$, where the behaviour of matter is governed by quantum mechanics. The
usual initial step for preparation of a single-species quantum degenerate gas
is laser-cooling to temperatures below the Doppler temperature $T_{D}$ (on the
order of $100\,\mu$K) in a three-dimensional (3D) magneto-optical trap
(3D-MOT) [11], which combines an optical molasses [12] with a 3D magnetic
quadrupole field. If more than a single atomic species is required, for
example, for the production of ultracold hetero-nuclear molecules, the
simultaneous, spatially overlapped operation of multiple 3D-MOTs is necessary
referred to as a dual-species 3D-MOT. This typically comes with undesirable
density and atom number limitations due to two-body loss processes such as
molecule association via light assisted collisions in presence of photons of
the cooling light [13]. In this article we present a novel cooling scheme in a
dual-species 3D-MOT, which mitigates such losses for the specific case of a
${}^{40}{\text{K }}$-${}^{87}{\text{Rb }}$mixture [14, 15].

A possible way to decrease such losses is the use of the Spontaneous Force
Optical Trap (SPOT) technique discussed in Ref. [16]. This method requires to
place a shadow into the repumping beam blocking the light from irradiating the
atoms in the trap center. As a result since the cooling cycling transition for
alkali atoms is typically not completely closed, the atoms in the trap center
naturally accumulate in a dark state and exit the cooling cycle. Hence, the
overall fluorescence and the rate of light-assisted collisions decrease.
Unfortunately, the SPOT technique is only efficient for rather incompletely
closed cycling transitions as in the case of sodium. Hence, it also does not
apply for many dual-species mixtures of interest. For single-species
scenarios, more recently, laser cooling using multiple atomic transitions was
employed and found favourable for improved 3D-MOT performance in experiments
of alkaline [17] and alkaline earth isotopes [18]. In these works, the
improved performance is linked to shielding effects due to short lived meta-
stable intermediate states.

In the present work, we explore a novel two-colour scheme for cooling a dual-
species ${}^{40}{\text{K }}$-${}^{87}{\text{Rb }}$mixture, where in addition
to the conventional laser radiation, detuned to the red side of the
$\mathcal{D}2$ -transition of ${}^{40}{\text{K }}$at
$767\text{\,}\mathrm{nm}\text{/}$, we include a second spectral component,
detuned to the blue side of the $\mathcal{D}1$ -transition of ${}^{40}{\text{K
}}$at $770\text{\,}\mathrm{nm}\text{/}$. The second species, ${}^{87}{\text{Rb
}}$, is cooled by the conventional single-colour method using red-detuned
light on the $\mathcal{D}2$ -transition of ${}^{87}{\text{Rb }}$at
$780\text{\,}\mathrm{nm}\text{/}$. After introducing the baseline scenario of
a single-colour, single-species ${}^{40}{\text{K }}$3D-MOT, we benchmark the
performance of the two-colour cooling scheme in a single-species
${}^{40}{\text{K }}$3D-MOT in the saturated regime. Here, we find an
approximately twofold improvement of the number of cooled atoms, as compared
to the conventional single-colour laser cooling scheme [19]. Subsequently, by
adding a conventional single-colour 3D-MOT for ${}^{87}{\text{Rb }}$, we
investigate the dual-species (${}^{40}{\text{K }}$-${}^{87}{\text{Rb }}$)
3D-MOT performance when the novel two-colour cooling scheme is applied,
finding an up to threefold improvement of the final potassium atom number,
which we attribute to the suppression of light-assisted hetero-nuclear
collisions.

##  II Experimental setup

### General setup:

The experimental setup consists of a dual-species 3D-MOT formed by the
superposition of single-species MOTs for ${}^{40}{\text{K }}$and
${}^{87}{\text{Rb }}$inside an ultra-high vacuum glass cell. The dual-species
3D-MOT is loaded by cold atomic beams of ${}^{40}{\text{K }}$and
${}^{87}{\text{Rb }}$atoms obtained from two separated source regions, which
connect to the glass cell via differential pumping stages. The preparation of
the cold beams is achieved in so-called $\textrm{2D}^{+}$ \- MOTs, loaded from
dispensers. Essentially, this is a 2D-MOT using a magnetic field with linear
quadrupole geometry and two additional beams along the zero magnetic field
axis, which is referred to by the ”+” sign in the acronym. A detailed
description of this technique is found in Ref. [20].

###  $\textrm{2D}^{+}$ \- MOTs:

The operating parameters of the $\textrm{2D}^{+}$-MOTs can be found in Table 1
(${}^{40}{\text{K }}$) and Table 2 (${}^{87}{\text{Rb }}$) and are not varied
throughout all experiments presented in this paper. The rubidium
$\textrm{2D}^{+}$\- is operated on the $5^{2}S_{1/2}\rightarrow 5^{2}P_{3/2}$
transition ($\mathcal{D}2$). The frequency of the cooling light is tuned to
the red side ($\delta<0$) of the $\ket{F=2}\rightarrow\ket{F^{\prime}=3}$
transition, while the frequency of the repumping light (required to prepare a
closed excitation cycle) is resonant to the
$\ket{F=1}\rightarrow\ket{F^{\prime}=0}$ transition. The potassium
$\textrm{2D}^{+}$-MOT is operated on the $4^{2}S_{1/2}\rightarrow
4^{2}P_{3/2}$ transition ($\mathcal{D}2$), with the cooling light tuned to the
red side of the $\ket{F=9/2}\rightarrow\ket{F^{\prime}=11/2}$ transition and
the repumping light adjusted in resonance with the
$\ket{F=7/2}\rightarrow\ket{F^{\prime}=9/2}$ transition. This is indicated by
the red arrows in Figure 1(a), where the electronic level scheme of
${}^{40}{\text{K }}$is shown. For both species, the circular polarisations of
the cooling and repumping light in the $\textrm{2D}^{+}$-MOTs are orthogonal.
The intensity ratios $I_{cool}/I_{rep}$ of the cooling and the repumping light
in the $\textrm{2D}^{+}$-MOTs are $10$ for ${}^{87}{\text{Rb }}$and $1$ for
${}^{40}{\text{K }}$.

###  ${}^{87}{\text{Rb }}$3D-MOT:

The ${}^{87}{\text{Rb }}$3D-MOT uses the same single-colour cooling scheme as
the ${}^{87}{\text{Rb }}$$\textrm{2D}^{+}$-MOT. Similarly as the parameters of
both $\textrm{2D}^{+}$ \- MOTs, the parameters of the ${}^{87}{\text{Rb
}}$3D-MOT are not varied for all experiments reported here, in order to reduce
complexity.

###  ${}^{40}{\text{K }}$3D-MOT:

To realise the two-colour cooling scheme, the ${}^{40}{\text{K }}$3D-MOT beams
are derived from three tapered amplifiers (TA), divided into six beams of
equal intensity delivered by polarisation maintaining optical fibers. The
cooling and repumping light on the $\mathcal{D}2$-transition is provided by
two separate TAs. The cooling/repumping scheme on the
$\mathcal{D}1$-transition is realised by a single TA, where the phase-coherent
repumping light is imprinted by an electro-acoustic modulator operating at
$f_{HFS,^{40}K}=$1.285\text{\,}\mathrm{GHz}\text{/}$$ [21]. The magnetic
quadrupole field centered around the position of the atoms is realised with a
pair of water-cooled copper coils placed outside the vacuum system.

##  III single-species ${}^{40}{\text{K }}$MOT

Figure 1: In (a), the electronic level scheme of ${}^{40}{\text{K }}$is shown.
The thick red (blue) arrows indicate the $\mathcal{D}2$($\mathcal{D}1$)
cooling transitions. The thin arrows indicate the respective repumping
transitions. The frequencies of the respective transitions are indicated by
their detunings from resonance $\delta_{D2}<0$ and $\delta_{D1}>0$. In (b),
the ${}^{40}{\text{K }}$atom number, after loading during
$t_{load,K}=$3\text{\,}\mathrm{s}\text{/}$$, is plotted against the intensity
$I_{D2}$ of the $\mathcal{D}2$ cooling light and the $\mathcal{D}2$ frequency
detuning $\delta_{D2}$. The solid gray lines indicate two intensities
$I_{D2}=I_{max}$ (upper) and $I_{D2}=0.5\,I_{max}$ (lower). Black dotted lines
are a guide to the eye to indicate the two regimes, see main text. Figure 2:
In (a), the normalised ${}^{40}{\text{K }}$atom number $N_{K}/N_{K,max}$ is
plotted against the $\mathcal{D}1$ cooling light intensity $I_{D1}$ and the
cooling light detuning $\delta_{D1}$. In (b), the ${}^{40}{\text{K }}$atom
number $N_{K}$ after $t_{load}=$3\text{\,}\mathrm{s}\text{/}$$ is plotted
against the $\mathcal{D}2$ cooling light detuning $\delta_{D2}$ and the
$\mathcal{D}1$ intensity $I_{D1}$ for two distinct settings of the
$\mathcal{D}2$ intensity $I_{D2}=0.5I_{D2,max}$(i) and
$I_{D2}=I_{D2,max}$(ii). In (a) and (b), the red rectangle indicates the
parameter settings where maximal ${}^{40}{\text{K }}$atom number is found. In
(c), $N_{K}$ is plotted against the loading time $t_{load,K}$. The light blue
squares show $N_{K}$ for optimal parameters according to Figure 1(b), when
only the $\mathcal{D}2$ -transition is used for cooling. The dark blue
diamonds show $N_{K}$ for cooling on both $\mathcal{D}1$ \- and $\mathcal{D}2$
-transitions for optimal parameters denoted by the black arrow and the red
square in (b).

To assess the performance of the two-colour cooling scheme, for comparison, we
first characterise the operation of a conventional single-colour, single-
species MOT of ${}^{40}{\text{K }}$atoms. In Figure 1(b), we plot the
${}^{40}{\text{K }}$particle number as a function of the $\mathcal{D}2$
cooling light intensity $I_{D2}$ and the $\mathcal{D}2$ cooling light
frequency detuning $\delta_{D2}$ for a loading time of
$t_{load,K}=$3\text{\,}\mathrm{s}\text{/}$$.

In this plot, we identify two different domains, which are clearly separated
for $I_{D2}>$3\text{\,}\mathrm{I_{sat}}\text{/}$$.

The first domain (conventional branch) is found around
$\delta_{D2}<$-4\text{\,}\Gamma$$ and
$I_{D2}>$3\text{\,}\mathrm{I_{sat}}\text{/}$$ (large negative detuning and
large intensity) denoted by the black dotted line, which serves as a guide to
the eye. Here, we find the maximum particle number of
$N_{K}=$2.2\text{\times}{10}^{7}$$ for $\delta_{D2}=$-3.5\text{\,}\Gamma$$ and
$I_{D2}=I_{D2,max}=$7.5\text{\,}\mathrm{I_{sat}}\text{/}$$ (red rectangle in
Figure 1(b)). The second domain (side branch) is found for more resonant
$\mathcal{D}2$ cooling light frequency detuning
$\delta_{D2}\sim$-2\text{\,}\Gamma$$ at almost all settings of the intensity
$I_{D2}$. Here, we find particle numbers up to
$N_{K}=$$1.5\text{\times}{10}^{7}$. Between these two domains we observe a
local minimum of the particle number $N_{K}$. While for the single-colour
scheme, the second domain of the ${}^{40}{\text{K }}$3D-MOT shows slightly
less efficient performance, this domain becomes relevant if the two-colour
operation of the MOT is investigated.

In contrast to conventional laser cooling in a MOT, we additionally employ
blue-detuned light on the $\mathcal{D}1$ -transition of ${}^{40}{\text{K }}$as
indicated by the set of blue arrows in Figure 1(a), similar to the experiments
presented in [22] and reminiscent of VSCPT [23] and gray molasses cooling
[24]. In Figure 2(a), we plot the normalised potassium particle number
$N_{K}/N_{K,max}$ as a function of the $\mathcal{D}1$ detuning $\delta_{D1}$
and the $\mathcal{D}1$ intensity $I_{D1}$. In this experiment we fix the
parameters of the $\mathcal{D}2$ cooling light to
$I_{D2}=$5.76\text{\,}\mathrm{I_{sat}}\text{/}$$ and
$\delta_{D2}=$-1.67\text{\,}\Gamma$$ (optimal values according to Figure 4).
We identify two regimes separated by a local minimum around
$I_{D1}>$3\text{\,}\mathrm{I_{sat}}\text{/}$$ and
$$0.4\text{\,}\Gamma$<\delta_{D1}<$1.0\text{\,}\Gamma$$. Our qualitative
understanding of these domains of optimal performance is limited and subject
of further investigation. The parameter setting for optimal MOT performance of
the $\mathcal{D}1$ frequency detuning $\delta_{D1}=$0.55\text{\,}\Gamma$$ is
indicated by the red rectangle in Figure 2(a) and is kept at this value for
all following investigations.

First, we vary the intensity $I_{D1}$ of the $\mathcal{D}1$ cooling light and
the detuning $\delta_{D2}$ of the $\mathcal{D}2$ cooling light for two
different settings of the intensity $I_{D2}$ of the $\mathcal{D}2$ cooling
light, as can be seen in Figure 2(b). The intensity of the $\mathcal{D}2$
cooling light is set $I_{D2}=0.5\,I_{D2,max}$ in Figure 2(b)i and to
$I_{D2}=I_{D2,max}$ in Figure 2(b)ii according to the solid gray lines in
Figure 1(b). The colour map is set to be identical to the colour map in Figure
1(b), so that the saturated data points correspond to an improved MOT
performance. We observe that with the inclusion of cooling light operating on
the $\mathcal{D}1$ transition of ${}^{40}{\text{K }}$, the optimal setting of
the $\mathcal{D}2$ cooling frequency detuning is at
$\delta_{D2}=$-2\text{\,}\Gamma$$ in contrast to the optimal detuning without
cooling on the $\mathcal{D}1$ transition, which is found to be
$\delta_{D2}=-4.65\,\Gamma$. Additionally, we have varied the ratio of the
intensities $I_{D1}/I_{D2}$. If $I_{D2}=I_{D2,max}$ (see Figure 2(b)ii),
$I_{D1}$ can be set to larger values and still yield reasonable
${}^{40}{\text{K }}$MOT atom numbers. However, we find the best performance
for parameter settings
$I_{D2}=0.5\,I_{D2,max},I_{D1}=$0.33\text{\,}\mathrm{I_{sat}}\text{/}$$ and
$\delta_{D2}=-2\Gamma$ according to the data point indicated with a red
rectangle in Figure 2(b)i. Here, we obtain $N_{K}=$2.51\text{\times}{10}^{7}$$
after $t_{load,K}=$3\text{\,}\mathrm{s}\text{/}$$, a $13\text{\,}\mathrm{\char
37\relax}\text{/}$ improvement compared to the single-colour operation, as
indicated by the black arrow in Figure 2(c).

As a last step, we investigate the ${}^{40}{\text{K }}$atom number $N_{K}$ as
a function of the MOT loading time $t_{load}$ shown in Figure 2(c). For this,
we load the MOT for variable times at optimal parameters indicated by the
rectangles both for the $\mathcal{D}2$ -only MOT (see Figure 1(b)) and the
two-colour MOT (see Figure 2(b)i). For short loading times of
$t_{load,K}<$8\text{\,}\mathrm{s}\text{/}$$ the improvement by the two-colour
cooling scheme is marginal. However, for longer loading times
$t_{load,K}>$8\text{\,}\mathrm{s}\text{/}$$ an almost twofold increase of the
${}^{40}{\text{K }}$atom number $N_{K}$ is obtained. To extrapolate the
saturation levels of the two cooling methods, we fit both data sets in Figure
2(c) with a time dependent rate equation model, including a density dependent
two-body loss term [25], and find a threefold increased saturation level in
the two-color scenario. The loading curve is found to be well fitted by this
model, indicating that, in contrast to the single-colour MOT, even larger atom
numbers can be expected, by increasing the flux of the cold ${}^{40}{\text{K
}}$beam source. See Appendix B for details of the fit model.

##  IV Single-colour dual-species MOT

Figure 3: In (a), the potassium atom number is plotted as a function of the
intensity $I_{D2}$ and the frequency detuning $\delta_{D2}$ in the dual-
species MOT in absence of any cooling light operating on the $\mathcal{D}1$
transition. In (b), we plot the improvement factor defined as the ratio of the
normalised particle numbers $N_{K}$ found for single - and dual-species MOT
operation. In (c), we plot the particle number $N_{K}$ of the single-species
(light blue squares) and the dual-species (orange circles) MOT as a function
of the loading time $t_{load,K}$. The blue square in (a), close to the upper
left corner, indicates the optimal parameters used for measuring the loading
curve in (c). The black arrow in (c) indicates the loading time for which (a)
is obtained.

In this section, we investigate the negative effects of light-assisted hetero-
nuclear collisions (LAHNCs) on the performance of a dual-species MOT for
${}^{40}{\text{K }}$and ${}^{87}{\text{Rb }}$atoms, operating with
conventional single-colour $\mathcal{D}2$ -only cooling. Since the loading
efficiency of rubidium is much larger than that of potassium, we apply
different loading times for both species. Typically, we operate with a
variable loading time $t_{load,K}$ for ${}^{40}{\text{K }}$atoms followed by a
time window with a duration $t_{load,KRb}=$3\text{\,}\mathrm{s}\text{/}$$,
during which both species ${}^{40}{\text{K }}$and ${}^{87}{\text{Rb }}$are
loaded. During the combined loading period $t_{load,KRb}$ we see no further
increase of the ${}^{40}{\text{K }}$atom number $N_{K}$ but rather a decrease
attributed to LAHNCs. In order to consistently compare loading of
${}^{40}{\text{K }}$atoms with loading of ${}^{40}{\text{K }}$and
${}^{87}{\text{Rb }}$atoms, we equally specify the ${}^{40}{\text{K }}$atom
number $N_{K}$ and the loading time $t_{load,K}$ for both cases.

In Figure 3(a), we plot the ${}^{40}{\text{K }}$atom number $N_{K}$ as a
function of the intensity $I_{D2}$ and the detuning $\delta_{D2}$ of the
$\mathcal{D}2$ cooling light. In the conventional branch, we observe a similar
qualitative behaviour as previously found in Figure 1(b)) for the single-
species $\mathcal{D}2$ -only MOT. In Figure 3(a), the maximum particle number
$N_{K}=$2.38\text{\times}{10}^{7}$$ is found in the conventional branch for a
detuning $\delta_{D2}=$-4.6\text{\,}\Gamma$$ and an intensity of
$I_{D2}=$7.7\text{\,}\mathrm{I_{sat}}\text{/}$$. However, the side branch
obtained in Figure 1(b), vanishes. We explain this behaviour with an increased
photon scattering for cooling light tuned closer to the atomic resonance
($\delta_{D2}\sim 0$), which in consequence leads to pronounced LAHNCs and
associated two-body loss.

To further illustrate the effect, we plot the improvement factor $\varepsilon$
in Figure 3(b), which is defined as the ratio of the normalised
${}^{40}{\text{K }}$atom numbers for the single-species (Figure 1) and the
dual-species (Figure 3(a)) single-colour ${}^{40}{\text{K }}$MOT, i.e., both
in absence $\mathcal{D}1$ cooling. The red shaded areas in Figure 3(b)
(improvement factor $\varepsilon>1$) indicate regions, where the dual-species
MOT performs better compared to the single-species case, whereas the black
areas ($\varepsilon<1$) denote the regions where the $N_{K}$ is severely
reduced by the presence of ${}^{87}{\text{Rb }}$atoms.

In Figure 3(c), we investigate $N_{K}$ as a function of the loading time
$t_{load,K}$. The orange circles denote $N_{K}$ for optimal parameters
indicated by the blue rectangle in Figure 3(a). For comparison, the blue
squares repeat $N_{K}$ found in Figure 2(c) for the single-species single-
colour scenario. We see, that the ${}^{40}{\text{K }}$atom number for the
single-colour dual-species MOT is clearly reduced due to the presence of
${}^{87}{\text{Rb }}$atoms. The black arrow in Figure 3(c) marks the loading
time $t_{load,K}=$10\text{\,}\mathrm{s}\text{/}$$, for which Figure 3(a) is
obtained.

Figure 4: In (a), $N_{K}$ is shown as a function of the intensity $I_{D2}$ and
the frequency detuning $\delta_{D2}$ for a fixed value of
$I_{D1}=$1.5\text{\,}\mathrm{I_{sat}}\text{/}$$. In (b), $N_{K}$ is plotted as
a function of the intensity $I_{D1}$ and the frequency detuning $\delta_{D2}$
for a fixed value of $I_{D2}=0.5(i)/0.75(ii)/1.00(iii)\cdot I_{D2,max}$. In
(a) and (b), the blue rectangles denote the optimal MOT operation parameters.
In (c), $N_{K}$ is plotted versus the loading time $t_{load,K}$ for the
respective optimal parameters of each cooling method. The optimal parameters
for the two-colour cooling scheme is indicated by the blue rectangle in Figure
4(b,i). The red circles denote $N_{K}$ in a dual-species MOT with cooling on
both the $\mathcal{D}1$ \- and the $\mathcal{D}2$ -transition. The orange
circles denote $N_{K}$ in a dual-species MOT with conventional cooling only on
the $\mathcal{D}2$ -transition. The grey diamonds (squares) correspond to
loading curves previously obtained in Figure 2(c) (Figure 3(c)).

##  V Two-colour, dual-species MOT

Adding blue-detuned light on the $\mathcal{D}1$ transition significantly
improves the dual-species MOT performance. This central result is analysed in
the remainder of this article.

In Figure 4(a), we investigate the effects of additional cooling light
operating on the $\mathcal{D}1$ transition with an intensity of
$I_{D1}=$1.5\text{\,}\mathrm{I_{sat}}\text{/}$$ in a dual-species MOT of
${}^{40}{\text{K }}$and ${}^{87}{\text{Rb }}$. This extends the previous
investigations of $\mathcal{D}1$ line cooling in a single-species MOT for
${}^{40}{\text{K }}$shown in Figure 2. To compare our results to the previous
measurements in Figure 1(b), Figure 2, and Figure 3(a), we vary the intensity
$I_{D2}$ and the frequency detuning $\delta_{D2}$ and count the
${}^{40}{\text{K }}$atom number $N_{K}$. We observe a notably different
behaviour throughout the entire measured parameter regime. The previously
dominant conventional branch does no longer appear. Surprisingly, we find that
the inclusion of the $\mathcal{D}1$ cooling light restores the side branch and
even enhances the particle number $N_{K}$ above the saturation threshold found
for the $\mathcal{D}2$ -only dual-species MOT, as can clearly be seen in
Figure 4(a). In absence of $\mathcal{D}1$ cooling, this parameter region is
subject to significant LAHNCs and consequently low potassium particle numbers
$N_{K}$. Note, that the colour map in Figure 3 and Figure 4 is equal,
displaying a significantly larger ${}^{40}{\text{K }}$MOT in presence of
$\mathcal{D}1$ cooling. In Figure 4(b), we vary the $\mathcal{D}1$ intensity
$I_{D1}$ and the $\mathcal{D}2$ detuning $\delta_{D2}$ for three distinct
settings of the $\mathcal{D}2$ intensity $I_{D2}$ as indicated by the insets.
We observe a similar behaviour as compared to the single-species MOT and find
that the performance of the MOT is sensitive to the relative powers of
$I_{D1}$ and $I_{D2}$. We obtain a maximum number of $5\text{\times}{10}^{7}$
in the case of the two-colour dual-species MOT
($I_{D1}=$0.91\text{\,}\mathrm{I_{sat}}\text{/}$$ and
$\delta_{D2}=$-1.67\text{\,}\Gamma$$) for a parameter setting indicated by the
blue rectangle in Figure 4(b,i). This corresponds to a twofold increase for
$t_{load,K}=$10\text{\,}\mathrm{s}\text{/}$$ compared to the conventional
single-colour dual-species $\mathcal{D}2$ MOT number obtained in Figure 3(a).
Finally, we plot the potassium atom number $N_{K}$ of the dual-species MOT
versus the loading time $t_{load}$ in Figure 4(c). Here, the red circles
denote $N_{K}$ in the two-colour dual-species MOT. The orange circles mark
$N_{K}$ for the single-colour dual-species configuration of the MOT (see
Figure 3(c)). The grey data, for comparison, repeat the data shown in Figure
2(c).

For short loading times $t_{load,K}<$3\text{\,}\mathrm{s}\text{/}$$, the two
cooling methods yield comparable results. However, for longer loading times
$t_{load,K}>$3\text{\,}\mathrm{s}\text{/}$$ the potassium atom number $N_{K}$
is significantly increased by the implementation of the two-colour cooling.
For the longest loading times investigated in our experiment, we find
$N_{K}=$1.71\text{\times}{10}^{8}$$ for the two-colour cooling scheme and
$N_{K}=$5.67\text{\times}{10}^{7}$$ for the single-colour case. This is a
threefold improvement in the dual-species scenario. From the behaviour of the
loading curve it is a reasonable assumption that the improvement can be even
more significant for longer loading times as the ${}^{40}{\text{K }}$atom
number $N_{K}$ in the single-colour MOT is saturated after
$\sim$15\text{\,}\mathrm{s}\text{/}$$, while the reach of saturation of the
potassium number in the two-colour cooling scheme is significantly shifted
towards later times (cf. Appendix B).

##  VI Conclusion

In summary, we demonstrate a novel, powerful cooling scheme for preparing
mixtures of cold ${}^{40}{\text{K }}$and ${}^{87}{\text{Rb }}$atoms in a dual-
species MOT. In addition to the conventional cooling of ${}^{40}{\text{K
}}$atoms using light tuned to the red side of the $\mathcal{D}2$ -transition,
a second light component, tuned to the blue side of the $\mathcal{D}1$
-transition, is used. We have started with benchmarking the performance of a
conventional single-species MOT for ${}^{40}{\text{K }}$atoms using single
frequency cooling light with a negative detuning $\delta_{D2}<0$ with respect
to the $\mathcal{D}2$ -line and an intensity $I_{D2}$. Two domains in the
parameter space $\\{\delta_{D2},I_{D2}\\}$ are identified, dubbed conventional
branch and side branch, where the cooling efficiency attains a relative
maximum, while the global maximum is reached in the conventional branch. In a
second step, discussed in section III, we demonstrate that the inclusion of
additional light beams, blue-detuned with respect to the $\mathcal{D}1$
-transition, can increase the potassium atom number in a single-species MOT
for long loading times. In a third step, we investigate MOT loading in a dual-
species scenario of ${}^{40}{\text{K }}$and ${}^{87}{\text{Rb }}$. In section
IV, we benchmark the dual-species MOT using conventional cooling on the
$\mathcal{D}2$ -transition. Here, we find significant atomic losses due to
LAHNCs and the disappearance of the side branch. Finally, in section V, we
investigate the influence of the two-colour cooling scheme in a dual-species
MOT scenario. We observe a significant improvement of the ${}^{40}{\text{K
}}$atom number $N_{K}$, with the side branch forming the optimal parameter
region. For long MOT loading times we demonstrate a threefold improvement of
$N_{K}$. We attribute the significant reduction of saturation of
${}^{40}{\text{K }}$loading, observed in the dual-colour MOT, to a suppression
of light-assisted hetero-nuclear collisions between ${}^{40}{\text{K }}$and
${}^{87}{\text{Rb }}$atoms. As a consequence, longer loading times or an
increase of the flux of the cold ${}^{40}{\text{K }}$beam source allow for
larger $N_{K}$. Due to the similar level structure of alkali atomic species,
we suspect that the discussed cooling scheme can be a useful extension for
most modern dual-species alkali quantum gas experiments, which require high
fidelity preparation of large atomic samples with high repetition rates.

##  VII Acknowledgements

We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) through
the collaborative research centre SFB 925 (project no. 170620586, C1). M.H.
was partially supported by the Cluster of Excellence CUI: Advanced Imaging of
Matter of the Deutsche Forschungsgemeinschaft (DFG)—EXC 2056—project ID
390715994.

## References

  * Sherson  _et al._ [2010] J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Single-atom-resolved fluorescence imaging of an atomic Mott insulator., Nature 467, 68 (2010).
  * Mazurenko  _et al._ [2017] A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom Fermi-Hubbard antiferromagnet, Nature 545, 462 (2017).
  * Marco  _et al._ [2019] L. D. Marco, G. Valtolina, K. Matsuda, W. G. Tobias, J. P. Covey, and J. Ye, A degenerate fermi gas of polar molecules, Science 363, 853 (2019), https://www.science.org/doi/pdf/10.1126/science.aau7230 .
  * Schindewolf  _et al._ [2022] A. Schindewolf, R. Bause, X.-Y. Chen, M. Duda, T. Karman, I. Bloch, and X.-Y. Luo, Evaporation of microwave-shielded polar molecules to quantum degeneracy, Nature 607, 677 (2022).
  * Stevenson  _et al._ [2023] I. Stevenson, A. Z. Lam, N. Bigagli, C. Warner, W. Yuan, S. Zhang, and S. Will, Ultracold gas of dipolar nacs ground state molecules, Phys. Rev. Lett. 130, 113002 (2023).
  * Kiefer  _et al._ [2023] Y. Kiefer, M. Hachmann, and A. Hemmerich, Ultracold Feshbach molecules in an orbital optical lattice, Nature Physics 19, 794 (2023), arXiv:2302.05692 .
  * Bernien  _et al._ [2017] H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017).
  * Brown  _et al._ [2023] M. O. Brown, S. R. Muleady, W. J. Dworschack, R. J. Lewis-Swan, A. M. Rey, O. Romero-Isart, and C. A. Regal, Time-of-flight quantum tomography of an atom in an optical tweezer, Nature Physics 19, 569 (2023).
  * Schäfer  _et al._ [2020] F. Schäfer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Tools for quantum simulation with ultracold atoms in optical lattices, Nature Reviews Physics 2, 411 (2020).
  * Chomaz  _et al._ [2022] L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe-Tolra, B. L. Lev, and T. Pfau, Dipolar physics: a review of experiments with magnetic quantum gases, Reports on Progress in Physics 86, 026401 (2022).
  * Raab  _et al._ [1987] E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Trapping of Neutral Sodium Atoms with Radiation Pressure, Physical Review Letters 59, 2631 (1987).
  * Dalibard and Cohen-Tannoudji [1989] J. Dalibard and C. Cohen-Tannoudji, Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, Journal of the Optical Society of America B 6, 2023 (1989).
  * Anderson  _et al._ [1994] M. H. Anderson, W. Petrich, J. R. Ensher, and E. A. Cornell, Reduction of light-assisted collisional loss rate from a low-pressure vapor-cell trap, Physical Review A 50, 3597 (1994).
  * Goldwin  _et al._ [2002] J. Goldwin, S. B. Papp, B. DeMarco, and D. S. Jin, Two-species magneto-optical trap with 40K and 87Rb, Physical Review A - Atomic, Molecular, and Optical Physics 65, 4 (2002).
  * Ospelkaus-schwarzer [2006] S. Ospelkaus-schwarzer, Quantum Degenerate Fermi-Bose Mixtures of 40 K and 87 Rb in 3D Optical Lattices, PhD thesis, Universität Hamburg , 174 (2006).
  * Ketterle  _et al._ [1993] W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, High densities of cold atoms in a dark spontaneous-force optical trap, Physical Review Letters 70, 2253 (1993).
  * Salomon  _et al._ [2013a] G. Salomon, L. Fouché, P. Wang, A. Aspect, P. Bouyer, and T. Bourdel, Gray-molasses cooling of 39K to a high phase-space density, EPL (Europhysics Letters) 104, 63002 (2013a).
  * Höschele  _et al._ [2023] J. Höschele, S. Buob, A. Rubio-Abadal, V. Makhalov, and L. Tarruell, Atom-number enhancement by shielding atoms from losses in strontium magneto-optical traps (2023), arXiv:2302.02992 .
  * DeMarco and Jin [1999] B. DeMarco and D. S. Jin, Onset of Fermi Degeneracy in a Trapped Atomic Gas, Science 285, 1703 (1999).
  * Dieckmann  _et al._ [1998] K. Dieckmann, R. J. C. Spreeuw, M. Weidemüller, and J. T. M. Walraven, Two-dimensional magneto-optical trap as a source of slow atoms, Physical Review A 58, 3891 (1998).
  * Tiecke [2019] T. Tiecke, Properties of Potassium K (2019).
  * Salomon  _et al._ [2013b] G. Salomon, L. Fouché, P. Wang, A. Aspect, P. Bouyer, and T. Bourdel, Gray-molasses cooling of 39K to a high phase-space density, Epl 104, 10.1209/0295-5075/104/63002 (2013b), arXiv:1310.4014 .
  * Weidemüller  _et al._ [1994] M. Weidemüller, T. Esslinger, M. A. Ol’shanii, A. Hemmerich, and T. W. Hänsch, A novel scheme for efficient cooling below the photon recoil limit, Europhysics Letters 27, 109 (1994).
  * Rio Fernandes  _et al._ [2012] D. Rio Fernandes, F. Sievers, N. Kretzschmar, S. Wu, C. Salomon, and F. Chevy, Sub-Doppler laser cooling of fermionic 40 K atoms in three-dimensional gray optical molasses, EPL (Europhysics Letters) 100, 63001 (2012).
  * Grünert and Hemmerich [2001] J. Grünert and A. Hemmerich, Optimizing the production of metastable calcium atoms in a magneto-optical trap, Appl. Phys. B 73, 815 (2001).
  * Klempt  _et al._ [2006] C. Klempt, T. Van Zoest, T. Henninger, O. Topic, E. Rasel, W. Ertmer, and J. Arlt, Ultraviolet light-induced atom desorption for large rubidium and potassium magneto-optical traps, Physical Review A - Atomic, Molecular, and Optical Physics 73, 1 (2006), arXiv:0509241 [cond-mat] .
  * Hachmann  _et al._ [2021] M. Hachmann, Y. Kiefer, J. Riebesehl, R. Eichberger, and A. Hemmerich, Quantum Degenerate Fermi Gas in an Orbital Optical Lattice, Physical Review Letters 127, 33201 (2021), arXiv:2106.12241 .
  * Dinneen  _et al._ [1999] T. P. Dinneen, K. R. Vogel, E. Arimondo, J. L. Hall, and A. Gallagher, Cold collisions of ${\text{sr}}^{*}-\text{Sr}$ in a magneto-optical trap, Phys. Rev. A 59, 1216 (1999).
  * Busch  _et al._ [2006] H. C. Busch, M. K. Shaffer, E. M. Ahmed, and C. I. Sukenik, Trap loss in a dual-species $\mathrm{Rb}\text{$-$}\text{Ar}^{*}$ magneto-optical trap, Phys. Rev. A 73, 023406 (2006).

##  Appendix A 2D MOT parameters

In the source region, separated from the main chamber by a differential
pumping stage, a room temperature thermal alkali vapour is pre-cooled to
produce a collimated cold atomic beam. To increase the pressure of the alkali
gas, UV-LEDs are operated simultaneously with the loading phase. This method
has been shown to increase the loading rates of alkali MOTs [26]. In our
apparatus, the loading rate is increased almost up to tenfold using this
technique [27]. The loading rate was found to be proportional to the intensity
of the UV light.

In our case, the $\textrm{2D}^{+}$ \- MOT is formed by two pairs of counter-
propagating laser beams in a retro-reflected configuration. These pairs of
beams are used for transverse cooling of the particles. These four beams,
together with a magnetic quadrupole field, form a conventional 2D-MOT. In our
setup, however, there is an extension of this scheme, namely an additional
cooling beam aligned perpendicular to the two transversal beams, called the
axial cooling beam (hence the designation $\textrm{2D}^{+}$ \- MOT). This
axial beam is reflected from the surface of a substrate located inside the UHV
system, which has a small hole to allow the transfer of the pre-cooled atoms
into the main chamber through a differential pumping stage. The
$\textrm{2D}^{+}$ \- MOT operates only on the $\mathcal{D}2$ -line of
${}^{40}{\text{K }}$and therefore addresses the
$\ket{F=9/2}\rightarrow\ket{F^{\prime}=11/2}$ transition for cooling and
the$\ket{F=7/2}\rightarrow\ket{F^{\prime}=9/2}$ transition for repumping of
the atoms (see Figure 1(a) in main text). The magnetic quadrupole field to
generate the transversal magnetic confinement is provided by two pairs of
coils placed outside the UHV source region. Static stray magnetic fields are
compensated by additional coil pairs in the transversal direction. This
magnetic field infrastructure allows for magnetic gradients up to 20 G/cm and
homogeneous magnetic compensation fields on the order of several
$\mathrm{G}\text{/}$. The experimentally optimised parameters of the
$\textrm{2D}^{+}$ \- MOT can be found in Table 1. Efficient operation of the
$\textrm{2D}^{+}$ \- MOT is a crucial step in the experiments, since the
atomic flux determined by the quality of the $\textrm{2D}^{+}$ \- MOT strongly
influences the performance of the 3D-MOT and thus all subsequent steps in the
production of cold atoms.

Parameter | Transversal | Axial
---|---|---
magnetic gradient | $17.5\text{\,}\mathrm{G}\text{/}\mathrm{cm}$ | $0\text{\,}\mathrm{G}\text{/}\mathrm{cm}$
1/e beam diameter | $26.9\text{\,}\mathrm{mm}\text{/}$ | $14.4\text{\,}\mathrm{mm}\text{/}$
$I_{cool}$ per beam | $28\text{\,}\mathrm{I_{sat}}\text{/}$ | $70\text{\,}\mathrm{I_{sat}}\text{/}$
$I_{rep}$ per beam | $27.5\text{\,}\mathrm{I_{sat}}\text{/}$ | $14\text{\,}\mathrm{I_{sat}}\text{/}$
$\delta_{cool}$ | $-3\text{\,}\Gamma$ | $-3.6\text{\,}\Gamma$
$\delta_{rep}$ | $-0.05\text{\,}\Gamma$ | $-0.05\text{\,}\Gamma$
Table 1:  Experimentally optimised ${}^{40}{\text{K }}$2D+-MOT parameters.  Parameter | Transversal | Axial
---|---|---
magnetic gradient | $14\text{\,}\mathrm{G}\text{/}\mathrm{cm}$ | $0\text{\,}\mathrm{G}\text{/}\mathrm{cm}$
1/e beam diameter | $26.9\text{\,}\mathrm{mm}\text{/}$ | $10.8\text{\,}\mathrm{mm}\text{/}$
$I_{cool}$ per beam | $8\text{\,}\mathrm{I_{sat}}\text{/}$ | $20\text{\,}\mathrm{I_{sat}}\text{/}$
$I_{rep}$ per beam | $0.3\text{\,}\mathrm{I_{sat}}\text{/}$ | $0\text{\,}\mathrm{I_{sat}}\text{/}$
$\delta_{cool}$ | $-2.7\text{\,}\Gamma$ | $-2.7\text{\,}\Gamma$
$\delta_{rep}$ | $0\text{\,}\Gamma$ | -
Table 2:  Experimentally optimised ${}^{87}{\text{Rb }}$2D+-MOT parameters.

The rubidium $\textrm{2D}^{+}$ \- MOT is realised in the same configuration as
the potassium $\textrm{2D}^{+}$ \- MOT. The experimentally optimised
parameters of the ${}^{87}{\text{Rb }}$$\textrm{2D}^{+}$ \- MOT can be found
in Table 2. The experimentally optimised parameters of the ${}^{87}{\text{Rb
}}$and ${}^{40}{\text{K }}$3D-MOT can be found in Table 3. The parameter
values presented in the appendix of this work are not varied throughout the
series of experiments described in the main text.

Parameter | Transversal
---|---
magnetic gradient | $7.5\text{\,}\mathrm{G}\text{/}\mathrm{cm}$
1/e beam diameter | $26.9\text{\,}\mathrm{mm}\text{/}$
$I_{cool}$ per beam | $1.7\text{\,}\mathrm{I_{sat}}\text{/}$
$I_{rep}$ per beam | $0.04\text{\,}\mathrm{I_{sat}}\text{/}$
$\delta_{cool}$ | $-2.7\text{\,}\Gamma$
$\delta_{rep}$ | $0\text{\,}\Gamma$
Table 3:  Experimentally optimised ${}^{87}{\text{Rb }}$3D-MOT parameters.

##  Appendix B Long-term MOT loading behaviour

Figure 5: In (a), we repeat the data obtained in the main text of this work of
the single-species MOT (Figure 2) and plot the potassium atom number $N_{K}$
as a function of the loading time $t_{load,K}$. In (a), the salmon and red
solid line denotes the fit of the single-species data according to the correct
model for the single-colour and two-colour MOT, respectively. For details, see
text in Appendix B. In (b), we repeat the data obtained in the main text of
the dual-species MOT (Figure 4) and plot the potassium atom number $N_{K}$ as
a function of the loading time $t_{load,K}$. Here, the dotted lines denote a
fit according to the insets, where the curves fit1 and fit2 are scaled by
fitted factors $a=0.605$ (salmon) and $b=0.850$ (red), respectively.

To gain insights about the long-term loading behaviour of the different MOT
loading scenarios, we fit our experimental data obtained in the main text
(Figure 2(c) and Figure 4(c)) to a rate equation model commonly utilised
describing the loading behaviour of single-species MOTs[28, 29]:

$\frac{\partial N_{x}(t)}{\partial t}=R-\gamma N_{x}(t)-\beta_{x}N_{x}(t)^{2}$
(1)

where $N_{x}(t)$ denotes the particle number $N_{K}$ found in the single-
colour (x = D2) of dual-colour (x = D1D2) operation. We extract the constant
atomic loading rate R and the single-particle loss rate $\gamma$ with a
simultaneous fit to both loading curves shown in Figure 5 (a). The additional
free parameter $\beta_{x}$ models the density-dependent loss rate, which is
assumed to be different between the two scenarios and is therefore
individually determined. We find, that the ratio of the density-dependent loss
rate $\beta_{D2}/\beta_{D1D2}=9.73$ is far from unity, resulting in a vastly
different saturation level in both cases. Extrapolating these loading curves
beyond the measured loading duration leads to a difference in the saturation
level of $2.96$.

In the dual-species setting, isolating individual processes is much more
challenging and therefore the loading behaviour can no longer be captured with
a simple rate equation model. The inclusion of an additional inter-species
density-dependent loss term fails to accurately describe the experimental
data. In Figure 5 (b), we plot the potassium atom number $N_{K}$ of the dual-
species MOT as a function of the loading time $t_{load,K}$. The solid lines
repeat the fits obtained in (a) for comparability. Interestingly we find, that
the data is best modeled by rescaling the previously determined fit functions
fit 1, fit 2 with factors $a=$0.605$$ and $b=$0.850$$, respectively. Once
again, extrapolating beyond the measured data, we obtain a difference in
saturation level of $$2.96$*a/b=$4.15$$. However, without access to the
correct rate equation models, this result has to be taken with care.