Buffer gas loaded magneto-optical traps for Yb, Tm, Er and Ho

Direct loading of lanthanide atoms into magneto-optical traps (MOTs) from a very slow cryogenic buffer gas beam source is achieved, without the need for laser slowing. The beam source has an average forward velocity of 60-70\,m/s and a velocity half-width of ~35 m/s, which allows for direct MOT loading of Yb, Tm, Er and Ho. Residual helium background gas originating from the beam results in a maximum trap lifetime of about 80 ms (with Yb). The addition of a single-frequency slowing laser applied to the Yb in the buffer gas beam increases the number of trapped Yb atoms to 1.3(0.7) x 10^8 with a loading rate of 2.0(1.0) x 10^10 atoms/s. Decay to metastable states is observed for all trapped species and decay rates are measured. Extension of this approach to the loading of molecules into a MOT is discussed.


Introduction
The invention of laser and evaporative cooling of atoms has led to significant new research, including new frequency standards, precision spectroscopy [1], quantum computation [2,3], studies of cold collisions [4] and new degenerate quantum gases [5]. The first laser cooling experiments were done with highly 'closed cycle' species (alkali and alkaline-earth atoms), that show little spontaneous decay into metastable states. In subsequent work, species with more complex internal structure were cooled and trapped, including those with significant 'leaks' into off-resonant states. Notable examples include Yb [6], Cr [7,8], Tm [9], Er [10,11] and Dy [12]. The latter four have large magnetic dipole moments, suitable for the study of systems with longrange dipole-dipole interactions [13] and the testing of fundamental theories [12], whereas Yb has been used in quantum simulation studies [14][15][16]. Other possible uses for ultracold non Sstate atoms could include the creation of exotic quantum phases and quantum magnetism [17].
Quantum many-body and quantum information research has driven the search for new species, including polar molecules. The additional degrees of freedom in molecules offer physical effects not found in atoms. Ultracold diatomic polar molecules are proposed candidates for novel quantum information and simulation experiments [18,19] and new ultracold chemistry [20,21]. The specific molecule necessary for an experiment can depend strongly on the desired physics to be studied. A method to provide a variety of molecules at mK temperatures and at a high phase-space density is desired, but is unavailable at present.
One possible approach to useful sources of some (ultra-)cold molecules is laser cooling, including magneto-optical trapping. Recent experiments employing hydrodynamically enhanced cryogenic buffer gas beam sources (CBGBs) [22,23] have reported laser cooling of molecules that have highly diagonal Frank-Condon factors: the optical slowing and cooling of SrF [24,25]; the creation of a two-dimensional magneto-optical trap (MOT) for YO [26]; and the laser slowing of CaF [27] in a supersonic jet. Work is ongoing in several groups to create MOTs for these molecules.
In this paper, we report the successful use of a two-stage, slower CBGB for loading MOTs, including species that have leaky optical cycling transitions. This is a step toward a simple approach to loading polar diatomic molecules into a MOT. We demonstrate the method with lanthanide atoms. Employing a two-stage helium CBGB [23,28], we create cold, slow atomic beams of lanthanide atoms and load them directly into a MOT. The effects of the collisions between residual helium from the CBGB and the trapped atoms are characterized. The feasibility of loading a MOT for molecules using this source is studied. The low mean forward velocity of our beam source is ∼ − 65 m s 1 , which renders a Zeeman slower unnecessary and thus allows for a direct loading of the MOT. This demonstrates a possible experimental path to a MOT for molecules; this beam is slower than the hydrodynamic CBGB used in other laser cooling experiments and thus offers a much shorter slowing path for the molecules, before the MOT. The initial cooling stage of our experiment relies only on collisions with He atoms (and thus is not dependent on the internal structure of the species).
We demonstrate a unique flexibility of this system with regard to the choice of species by creating MOTs for the elements Yb, Tm, Er and Ho in the same apparatus with no hardware change except tuning the MOT lasers, and no additional slowing light.
In the case of Yb, we load MOTs for the isotopes of mass 170, 171, 172, 174 and 176 by changing one parameter only, the detuning of the MOT laser frequency. The total number of atoms in common MOTs for Yb using the 400 nm transition is limited to ∼ − × 4 5 10 6 [32][33][34] due to spontaneous decay into metastable states during the loading phases of these traps ( ∼ 1-10 s). We overcome this limitation with our high instantaneous flux beam source, allowing us to fully load the MOT in only a few milliseconds.

Description of atomic species
To most simply explain our method, we focus the discussion on only one species, Ho. Miao et al [35] have recently reported laser cooling and trapping of Ho. We also refer the reader to work on MOTs of the other species: Yb [6], Tm [9] and Er [10,11].
Ho has only one stable nuclear isotope, Ho

165
. With its nuclear spin quantum number of = I 7/2, it has the largest number of hyperfine states of any element, which makes it potentially useful for qubit implementations [36]. Like many other lanthanides, it has a large magnetic dipole moment ( μ 9 B ). As shown in the level scheme in figure 1( states was used for laser cooling. As with previous work on other lanthanides (see e.g. [9]), no additional repumper was necessary to trap Ho atoms in our MOT, despite the existence of possible decay channels into other hyperfine levels of the ground state manifold.

Experimental method
The apparatus is shown in figure 2. A detailed study of the two-stage buffer gas beam source is described elsewhere [22,28,37]. Briefly, the cell, operating at 2.5 K, uses a combination of hydrodynamic extraction and a second slowing stage to produce a cold and effusive-like beam Atoms are introduced into the gas phase by laser ablation of solid precursor targets with 4 ns long pulses and ∼14 mJ energy from a 532 nm Nd:YAG laser. The atoms thermalize translationally via collisions with the cold He buffer gas inside the cell to a temperature of around 2-4 K and leave the cell to form an atomic beam. We use He flow rates between 0.2-4 sccm (standard cubic cm per minute). The beam travels from the cryogenic section, through a room temperature beam region, past a mechanical shutter, and into the MOT section. Since the atoms to be trapped are present only for a few ms after the ablation pulse, the shutter keeps residual He buffer gas from entering the MOT region when the atomic species of interest is not present in the beam. For the MOT measurements reported here, the shutter is opened for 10 ms (with 3 ms delay after ablation) during the MOT loading phase. In order to keep the amount of residual buffer gas background to a minimum, each section of the chamber is pumped by a turbomolecular pump to maintain steady-state low pressures of ∼ × − 1 10 6 Torr in the beam region and ∼ × − 2 10 7 Torr in the MOT regions. We detect atoms in the MOT by imaging fluorescence onto a calibrated photomultiplier tube. To reduce background due to scattered laser light, we spatially filter the collected fluorescence using an objective that focuses the MOT image through a variable intermediate aperture with a minimal diameter of μ ∼600 m. Simulation of the imaging system using commercial raytracing software, determines the collection efficiency to be ± × − (2.5 0.5) 10 3 . MOT laser beams for each atomic species are derived from the same frequency-doubled Ti:Sapphire ring laser. Each MOT beam has ∼15 mW power with a e 1/ 2 diameter of ± 9.8 0.5 mm. The Ti:Saph laser is locked to a HeNe laser via a transfer cavity, providing <5 MHz laser linewidth, which is used to determine the error in the lifetime measurements. The quadrupole field for the MOT is generated from a pair of water-cooled coils. The coils produce an axial (radial) field gradient of × − 3.

Model for the pulsed loading process
The loading process of the MOT can be described by a phenomenological differential equation for the number of trapped particles n(t) [38], 2 where R(t) is the loading rate, α the loss due to background gas collisions and β the intra-particle two-body loss. In our measurements, no evidence for two-body effects is observed and, thus, the corresponding term will henceforth be neglected (β = 0). The loading rate is timedependent due to the pulsed nature of the loading process. We find that approximating the loading pulse by a Gaussian function as  Example of the measured time traces of the MOT loading process are shown in figure 3 along with a fit to the pulsed loading model of equation (3). We focus on the case of Ho, figure 3(c). Note that only the tail of the buffer gas beam signal between 20-30 ms is loaded into the MOT. While the beam signal represents only a velocity class corresponding to a certain detuning, the much larger MOT signal stems from particles from a range of velocities which have been actively cooled and trapped.
The resulting peak values for the observed number of atoms loaded into the MOT are given for each element in table 1. Note that the variation among the different species is not only caused by the cooling efficiency given by their corresponding natural linewidths of the cooling transition, but also by the ablation yields, which strongly vary between the specific atoms. The number of trapped atoms can be increased by applying low repetition rates of the ablation laser, leading to smaller heat loads on the buffer gas cell and more atoms below the capture velocity, and by using a single-frequency slowing laser. We demonstrate this with one of the elements, Yb; we observe a total of

Limitation of the MOT lifetime due to the helium buffer gas
Two processes compete with the trap loading and limit the MOT lifetime, namely, collisions with the background gas and decay into metastable states. The first process is dominated by   MOT lifetimes, decay rates, saturation parameters and peak number of atoms from the fit to equation (4) for every species at 0.3 sccm He flow rate and a repetition rate of the ablation laser of 1.1 Hz (except for the last two rows for Yb). Both decay rates Γ 0 and Γ 1 are determined via extrapolation to zero He flow rate.

Decay into metastable states
The large differences among the species are due to the second lifetime-limiting effect, namely the presence of decay channels to metastable states. Once the atom decays after a number of photon scattering events into such a dark state, it escapes the cooling and trapping process. In order to fully describe this decay, for example in the case of Er, 110 intermediate states have to be considered [10]. As a result, theoretical modeling of such complex atoms is daunting. Instead, we apply a simplified model [9, 10, 32] which considers a three-level system including trap losses ( figure 1). In this model, the lifetime α 1/ scales with the fractional population in the excited state and depends on the laser detuning as where Γ 0 represents the loss rate due to background collisions, Γ 1 is the decay rate into intermediate metastable states, κ = · s s 0,eff 0 is the effective saturation parameter, Δ is the laser detuning from the resonance, and Γ π Δν = × 2 , where Δν is the natural linewidth. The effective saturation parameter takes averaging over Zeeman substates and random light polarization in the MOT region into account, where κ ≈ · + + 3 F F 2 1 2 3 and F corresponds to the hyperfine quantum number of the ground state. This simplified model omits any population which gets recycled back into the ground state after the decay to the metastable state reservoir, but allows for the determination of a lower limit of the decay rate into the intermediate states.
The measurements for each species are shown in figure 5. Again, we focus on the case of Ho, figure 5(c), as an example. We observe the largest MOT fluorescence signal with a reddetuned laser at Γ ≈ − 1.3 . Although this is the optimal detuning for creating high trapped atom numbers, the longest MOT lifetime is observed at detunings further to the red. This effect is explained by the lower population in the excited state and, consequently, a lower probability of decaying into a metastable dark state. Increasing the excited state population by moving the laser frequency closer to the transition line center decreases the MOT lifetime almost by a factor of three. The strength of this effect is governed by the decay rate Γ 1 . The measurement results obtained for each atomic species are summarized in table 1. For the fitting, Γ 0 and Γ 1 were free parameters. Our measurements indicate an increase of the decay rates with an increase of the He flow rate for all species. In the Torr, which is consistent with our measurements.
The results for Γ 1 for Yb, Tm and Er are in agreement within the errors with previously reported work. For Ho, both our measurement and the result of the Saffman group [35] are currently the only experimental estimates of the decay rate to metastable states. At present, no theoretical prediction is available.

Conclusion
In conclusion, we demonstrated, using Yb, Tm, Er and Ho, the direct loading of magnetooptical traps from a cryogenic two-stage He buffer gas beam source. Despite the presence of the He background gas, we observed lifetimes of up to 80 ms (for Yb). We report a decay rate to metastable states for Ho of 1510 (203) − s 1 . For further applications, we envision an experiment where the buffer gas source and the trapping region are separated by a differential pumping stage to further reduce the residual He background pressure near the MOT. Moreover, for atoms or molecules with magnetic ground states, a magnetic guide [23] could aid in this process by redirecting only the species of interest into a ultra-high vacuum region.
The unprecedentedly high loading rate of × − 2.0 (1.0) 10 atoms s 10 1 , which we demonstrated with Yb, will allow for loading a high number of atoms with loss mechanisms that have a time-scale comparable to the trap loading time into a consecutive trap. As an example, the number of atoms in a blue Yb MOT is limited by spontaneous decay into metastable states. This is typically overcome by using an intermediate MOT with a narrow intercombination line [34]  which has no optical leaks. As an alternative, our approach would surpass the need of such an intermediate step and simplify experimental requirements. If developed further, it could produce quantum gases with larger atom number, at a higher repetition rate. This is particularly enticing as the cryogenic setup used is very straightforward.
The great flexibility and low intrinsic temperature of this atomic and molecular beam source make it a possible tool for implementing MOTs for any species that precludes the common approach of a combination of a high-temperature oven and Zeeman slower. In particular, recent experiments on slowing and cooling diatomic molecules [24][25][26], all of which successfully employ buffer gas beam sources, reflect this potential advantage.
Moreover, our approach constitutes a straightforward testbed for laser cooling and trapping of other atomic species which have not been studied yet. In particular, elements with low vapor pressures at temperatures which are feasible with common oven sources are interesting candidates since laser ablation can produce high densities of such elements in the gas phase. Since the initial cooling stage of our beam source relies solely on collisions with He, only a single laser providing the optical force of the MOT has to be adapted to the wavelength of the corresponding species. At the same time, one can imagine the simultaneous loading of multiple species out of the same source. This is a major advantage over regular setups where a separate Zeeman slower is needed for each species loaded into a MOT.