Buffer gas cooling of a continuous CO molecular beam

Buffer gas cooling of a continuous CO molecular 1 beam2 AMAN GANGWAR,1TOMMASO VEDOVELLO,2FRANCESCO PIO3 MERAFINA,3GIACOMO INSERO,1,4,6 SIMONE BORRI,1,4 PAOLO DE4 NATALE,1,4 GABRIELE SANTAMBROGIO,1,4,5,* AND SAGAR5 SUTRADHAR1,4 6 1European Laboratory for Nonlinear Spectroscopy, LENS, Via Nello Carrara 1, 50014 Sesto Fiorentino,7 Italy8 2 Dipartimento di Fisica e Astronomia, University of Florence, Via Sansone 1, 50014 Sesto Fiorentino, Italy 9 3Università di Bari, Piazza Umberto I, 1, 70121 Bari, Italy10 4Istituto Nazionale di Ottica, CNR, Largo E. Fermi 6, 50125 Firenze, Italy11 5Istituto Nazionale di Ricerca Metrologica, INRIM, Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy12 6Department of Experimental and Clinical Biomedical Sciences “Mario Serio”, University of Florence,13 Viale G. Pieraccini 6, 50139 Florence, Italy14 *santambr[email protected]15 Abstract: We characterise a new continuous buffer gas cooled source using CO molecules. We 16 show results about the source performance considering different parameters, like gas flow rate, 17 nozzle size, and internal cell volume. The beam contains 2.5×1014 molecules/(s sr) at about 18 160 m/s. Moreover, for two rotational states we observe an unexpected population distribution 19 that we tentatively attribute to a lower temperature inside the cell. Considering the importance of 20 buffer-gas cooling for experiments on ultracold molecules prepared with direct laser cooling, 21 we believe that our work will improve this key first-stage cooling, accelerating the adoption of 22 molecules in the framework of quantum technologies.23 1. Introduction24 Ultracold molecules are very promising candidates for advancing modern physics, with applica25 tions ranging from fundamental physics to frontier technologies such as quantum simulation and 26 quantum computation [1,2]. This is due to their rich internal structure, symmetry, and strong 27 intramolecular fields, which make them ideal systems for investigating new physics. However, this 28 same complexity poses significant challenges for cooling and detection, making these processes 29 much more difficult compared to atoms. To overcome these difficulties, a first cooling stage is 30 usually applied to the molecular sample. Virtually all current experiments with laser-cooled 31 molecules rely on a buffer gas source [3,4]. In this source, molecules are injected or produced 32 inside the cell, where they thermalise with a cold rare buffer gas, typically helium or neon. The 33 molecular beam exiting the source is usually in an intermediate regime between effusive and 34 hydrodynamic, i.e. experiencing almost no or a few collisions, respectively, at the exit aperture.35 Buffer gas cooling techniques have been successfully applied to a variety of species, spanning 36 a broad spectrum of chemical properties, including alkali atoms [5, 6], alkaline earths [7], 37 metals [8], chemically reactive polar molecules [9–11], and polyatomic molecules [12].38 In this work, we present our newly-developed buffer gas source that we characterize using 39 carbon monoxide. Although CO is not a particularly interesting species for laser cooling, it 40 has the advantage of being easily available in a bottle. Moreover, by exciting CO to its first 41 excited, metastable, electronic state, the 𝑎3Π state, characterisation of the beam is straightforward. 42 With the present setup for a continuously seeded buffer gas beam, we can calculate the overall 43 efficiency of the source from the know amount of gas that we let into the system and the number 44 of cold molecules in the beam. Such measurements are extremely hard when the species of 45 interest are produced via laser ablation and/or chemical reaction. Intense effusive beams can be 46 produced with other molecules, too, [7] but CO is particularly advantageous given its relatively 47 low freezing temperature.48 We optimized the source for maximal flux and minimal velocity of the molecular beam trying 49 various combinations of nozzle sizes and cell lengths. We also measure molecules in two different 50 rotational states in order to estimate rotational thermalization inside the cell and provide an 51 estimation of the beam temperature.52 2. Theoretical description of the dynamics within a buffer gas cell53 Buffer-gas cooling of atoms or molecules relies on collisions with cold buffer gas atoms at 54 cryogenic temperatures, bringing the target species to low temperatures. The buffer gas dissipates 55 the translational and internal energy of the target species, ideally without chemical reaction or 56 cluster formation. This method of energy dissipation is independent of any specific energy level 57 structure, making it applicable to a wide range of target species [7].58 A comprehensive overview of the dynamics in a buffer gas cell can be found in Refs. [4,9]. 59 Here, we focus on outlining the key parameters associated with our setup.60 Consider a buffer gas cell with a volume defined by 𝑉cell =𝐴cell ×𝐿𝑐 , where 𝐿𝑐 is the length 61 of the cell interior and 𝐴cell is the cross-sectional area. Typically, 𝐿𝑐 is of the order of a few 62 centimeters, and 𝐴cell of a few cm 2 . The cell is maintained at a fixed temperature 𝑇 by a cryogenic 63 refrigerator, typically between 1 K and 20 K. We use helium as buffer gas.64 Buffer Gas Flow through the cell65 The buffer gas exits the cell through a round aperture with diameter 𝑑aperture of a few millimeters. 66 The flow rate of the buffer gas, He in our case, is typically measured in standard cubic centimeters 67 per minute (SCCM), where 1 SCCM is approximately equivalent to a flow of 4.5×1017 gas 68 particles per second. Under steady-state conditions, the number density of helium atoms in the 69 buffer cell, 𝑛He , can be estimated by considering the constant flow of helium into the cell, 𝑓He , 70 and the pumping speed through the aperture [4],71 𝑛He =4𝑓He 𝐴aperture ¯𝑣He ,(1) where ¯𝑣He is the mean thermal velocity of the helium atoms near the aperture. For a typical flow 72 of 1 SCCM of helium through an aperture with a diameter of 3 mm in a buffer cell maintained 73 at a temperature of around 4 K, the number density is 𝑛He ≈2×1015 cm−3 . The properties of 74 the target species emerging from the buffer cell are solely determined by collisions with the 75 buffer gas, which can be quantified by the mean free path. The mean free path is defined as 76 𝜆CO =1/(𝑛He𝜎CO-He√︁𝑚CO/𝑚He +1) , where 𝜎 is a collisional cross section and 𝑚 a mass. To a 77 good approximation [9], 𝜎CO-He ≈𝜎He-He and 𝜎He-He ∼10−14 𝑐𝑚2[13].78 The Reynolds number (Re) is an important figure of merit for the description of a gas flow. 79 For the buffer gas flows through an aperture of diameter 𝑑aperture , the Reynolds number can be 80 approximated as,81 Re ≈2𝑑aperture 𝜆He ,(2) where 𝜆He is the mean free path for the collisions of buffer gas atoms and it is expressed as, 82 𝜆He =1/(√2𝑛He 𝜎He-He). Therefore, the Reynolds number can be expressed as,83 Re ≈8√2𝑓He 𝜎He-He 𝜋𝑑aperture ¯𝑣He .(3) The flow regimes can be categorised into three distinct types based on the Reynolds number, 84 which reflects the extent of collisional interactions near the cell aperture. In the effusive regime 85 ( Re ≲1 ), few or no collisions occur near the aperture, and the beam properties align with the 86 thermal distribution inside the cell. Moving into the intermediate or partially-hydrodynamic 87 regime ( 1≲Re ≲100 ), collisions begin to influence the beam properties, although the flow does 88 not yet exhibit fully fluid-like characteristics. Finally, in the hydrodynamic regime ( Re ≳100 ), 89 the buffer gas behaves like a fluid, and the beam properties start to resemble those of a supersonic 90 expansion, leading to a colder and less divergent beam.91 Extraction efficiency of the cell92 The particles of the target species can be depleted from the cooling region of the buffer cell 93 through two primary processes: diffusion and entrainment. In the diffusion process, a significant 94 fraction of particles may collide with, and adhere to, the walls of the cell, while only a very small 95 fraction diffuse out through the aperture. The effectiveness of diffusion through the aperture is 96 governed by the ratio of the aperture area to the surface area of the cooling region, which is 97 typically ≤1% . Consequently, for the remainder of this discussion, we assume that the diffusion 98 process predominantly results in particle losses, thereby limiting the extraction efficiency of 99 particles from the buffer gas cell. In contrast, the second process involves entrainment, where 100 particles are extracted or “pumped out” by the helium flow continuously emerging through the 101 aperture.102 Considering the diffusion and the entrainment processes, we define two characteristic time 103 scales for particle movement within the cell. The diffusion time scale, 𝜏diff , represents the time 104 required for particles of the target species to diffuse to the walls of the cooling region. The 105 pump-out time scale, 𝜏pump , represents the time it takes for these particles to traverse the cell 106 under the influence of helium flow. Following Ref. [4], we can write107 𝜏diff =16 𝐴cell 𝑛He 𝜎CO-He 9𝜋¯𝑣He .(4) and108 𝜏pump =4𝑉cell ¯𝑣He 𝐴aperture (5) The diffusion and pump-out times are typically around 1–10 ms. The efficiency of particle 109 extraction from the cell is governed by the interplay between these two time scales. Therefore, it 110 is instructive to define a dimensionless parameter111 𝛾cell ≡𝜏diff 𝜏pump =4 9𝜋 𝑛He𝜎CO-He 𝐴aperture 𝐿cell ≈𝜎CO-He 𝑓He 𝐿cell ¯𝑣He .(6) The value of 𝛾cell defines the regime of particle extraction. For instance, 𝛾cell ≲1 corresponds to 112 the “diffusion limit", where particles diffuse to the wall faster than they are extracted from the 113 cell. This regime results in a low output flux of target particles. In contrast, when 𝛾cell >1 , the 114 system operates in the “hydrodynamic regime", resulting in a beam rich in target species.115 While 𝛾cell can estimate the extraction efficiency well, there are instances where this simple 116 estimate breaks down. For example, 𝛾cell has no explicit dependence on the aperture diameter; 117 however, it has been observed experimentally that decreasing the cell aperture diameter can 118 reduce the extraction efficiency. [14, 15] These measurements suggest that the cell aperture 119 diameter should not be too small (less than 3 mm) to achieve good extraction. It is thus helpful to 120 determine empirically the optimal cell geometry. The gas flow regime, described by the Reynolds 121 number, Eq. (3) , and the extraction parameter 𝛾cell , Eq. (6) are related by a factor that depends on 122 geometry:123 𝛾cell Re ∝𝑑aperture 𝐿cell .(7) This means that, at least in principle, it is possible to separately control the extraction efficiency 124 (governed by 𝛾cell ) and the flow regime (governed by Re). Most buffer gas sources operate in 125 either the effusive or the intermediate flow regimes, and it is experimentally challenging to design 126 a beam that is completely effusive, has good extraction, and has sufficient thermalization.127 Thermalization of CO molecules128 As previously mentioned, the characteristics of the target particles emerging from the buffer cell 129 are determined by the collisions with buffer gas atoms. The translational temperature of the CO 130 molecules, 𝑇CO , after undergoing 𝑁 collisions with the buffer gas, can be estimated as follows [4], 131 𝑇CO (𝑁) 𝑇He ≈1+𝑇CO (0) 𝑇He 𝑒−𝑁/𝜅,(8) where 𝜅=(𝑚CO +𝑚He)2/(2𝑚CO 𝑚He) , 𝑇He is the temperature of the buffer gas atoms in the 132 cell, ∼4 K, and 𝑇CO (0) is the temperature of the target particles when they are introduced 133 into the cell, ∼70 K (see below). Using this formula, we estimate that for CO molecules in 134 the buffer cell, about 30 collisions are needed to translationally cool the molecules from room 135 temperature to within 2.5% of the temperature of the buffer gas atoms. For typical values of 136 𝜎CO-He ≈10−14 cm2 and He number density of 10 15−16/cm3 , the mean free path is 0.01−0.2mm . 137 Therefore, the thermalization length for the species in the buffer gas cell is typically no more 138 than 30 ×0.2mm =6mm.139 Apart from translational cooling of the target species, buffer gas cooling is also effective 140 at rotational quenching which is driven by the anisotropy of the helium interaction with the 141 molecule [16]. Typical rotational relaxation cross sections for molecules with helium buffer gas 142 are of the order 𝜎rot ∼10−(15−16)cm2 [17], which means that around 𝜎CO-He/𝜎rot ∼10 −100143 collisions are required to relax a rotational state. With the parameters given above, we estimate 144 that a cell length of 9–90 mm is required for full rotational quenching.145 Forward Velocity of the CO beam146 In the intermediate regime, the average velocity of the Helium, ¯𝑣He , is higher than that of CO, 147 ¯𝑣CO , by a factor of √︁𝑚CO/𝑚He . The collisions of the Helium atoms with the CO near the aperture 148 are predominantly in the forward direction. Therefore, the CO molecules are accelerated in the 149 forward direction, which results in a velocity larger than the thermal velocity of the CO molecules 150 in the cell.151 CO molecules undergo approximately Re 2 collisions near the aperture [14]. For a small number 152 of collisions, the resulting forward velocity is given by [4],153 𝑣CO ≈¯𝑣CO +0.6 ¯𝑣He Re 𝑚He 𝑚CO (9) This suggests a linear increase of forward velocity with Re (1≲Re ≲10) and therefore with 154 buffer gas flow. However, as 𝑣CO approaches ¯𝑣He , the above model breaks down, as the maximum 155 possible forward velocity of the CO molecules is 1.4¯𝑣He as determined by the fully hydrodynamic 156 expansions of the helium atoms [4]. We therefore expect that the forward velocity should saturate 157 to this value at large enough 𝑅𝑒 . For Re ≳10 , the forward velocity is described by the “sudden 158 freeze” model,159 𝑣CO (Re) ≈ 1.4¯𝑣He 1−4 Re4/5(10) The transition to sudden-freeze model occurs at the flow rate for which there are collisions at a 160 distance larger than one aperture diameter from the aperture. This happens for Re ≳10 [14]. For 161 sufficiently high Re (specifically Re ≳100), species can achieve a forward velocity of162 𝑣CO ≈1.4¯𝑣He (11) 3. Experimental system163 A schematic of the vacuum system is shown in Fig. 1. The vacuum system consists of two 164 chambers. The first chamber contains the buffer gas cell, which is connected to a two-stage 165 pulse tube cryostat (PT425, Cryomech). The second chamber houses the detection region. Both 166 chambers are pumped by turbo-molecular pumps, HiPace 1200 and HiPace 300 (Pfeiffer Vacuum), 167 for the first and second chamber, respectively. The system typically operates at a pressure of 168 approximately ∼10−7 mbar, which limits the number of collisions with background gas, thereby 169 facilitating the formation of a molecular beam. The pressure is measured in both chambers at the 170 room-temperature part of the chambers.171 x y z 40K stage 4K stage Buffer gas cell PMT Aluminium shield 206 nm laser beam Molecular beam axis (a) Charcoal fins Buffer gas cell 40K stage 4K stage z y x(b) Fig. 1. Overview of the overall vacuum system (a) and a detailed arrangement of the buffer cell (b). Charcoal grains are glued to copper fins (as described in the text) and attached to a 4K cold head. For the visual clarity, only one of the charcoal fin arrangement is shown, on two different sides in the two pictures to avoid obstructing the view of the cell. The bottom of the radiation shield is closed by a series of copper stripes arranged in a chevron shape. An aluminum shield is mounted in contact with the 40-K stage of the cryostat, while the buffer 172 cell is attached to the 4-K stage. The aluminum shield functions as a radiation shield, effectively 173 reducing the thermal radiation load on the buffer cell. A ∼ 23 mm hole at the front of the radiation 174 shield serves as an aperture for the molecular beam to emerge. Additionally, two orthogonal 175 ports on the radiation shield, positioned perpendicular to the molecular beam, provide access for 176 the excitation laser. The excitation laser intercepts the molecular beam approximately 30 mm 177 after the cell nozzle. To further minimize the thermal load on the buffer cell, the radiation shield 178 is wrapped 10 layers of polyester foil, double-sided aluminized, perforated and interleaved with 179 10 layers of non-woven polyester spacer material.180 Charcoal at cryogenic temperatures is well known for its ability to efficiently absorb helium. [18] 181 In many cryogenic buffer gas beam sources, the cell is surrounded by a small metal enclosure 182 maintained at 4K, with charcoal glued on its interior walls. Instead, we developed a skeletal 183 like copper structure mounted to the 4K head of the cryostat. Fine charcoal grains are glued 184 to the copper fins using a thin layer of thermally conductive epoxy glue. These fins are then 185 integrated into the copper framework, which is connected to the 4K cold head. This solution 186 substantially increases the area covered by charcoal, thereby enhancing helium pumping capacity, 187 while maintaining good conductance toward the turbo pump. The large copper surface covered 188 by charcoals allows for continuous pumping of 20 SCCM of Helium for over 2 days without 189 using the turbo pump before heating the system to release the adsorbed helium, a value much 190 higher compared to other systems.191 3.1. Design of the buffer gas cell192 The schematic of the buffer gas cell is shown in Fig. 2. The top part of the cell is attached to the 193 4K cold head of the cryostat. The cell is machined from a copper block and features a cylindrical 194 region, which we refer to as the “cooling region”. The temperature measured at the cell under 195 normal operation conditions is of 3.7 K.196 To 4K stage Helium tube Cartridge heater CO tube PEEK Brass Aperture diameter: 5mm Cooling region bore diameter: 15 mm length: 20 mm Cylindrical PEEK piece z y x Fig. 2. The cross-sectional view of the buffer cell illustrates the arrangement of the aperture and the gas inlet tubes for CO and helium. A polyether ether ketone (PEEK) component is employed to thermally isolate the CO inlet tube from the cold buffer cell, as described in the text. Furthermore, a cylindrical PEEK piece is integrated to precisely control the length of the cooling region. The temperature of the CO tube near the buffer cell is regulated using a cartridge heater mounted on a copper element. The nozzle of the cell is machined from a separate copper piece and subsequently attached to 197 the buffer cell with a specific threading, facilitating a systematic study of how aperture dimensions 198 determine the system performance. The cooling region is designed as a cylinder with a diameter 199 of 15 mm. The exit nozzle has a conical shape, as outlined in [19]. The gas inlet configuration 200 for the buffer cell is depicted in Fig. 2. To precisely control the cooling region length, cylindrical 201 PEEK pieces are attached to the back end of the cell. These PEEK pieces feature appropriately 202 sized holes to allow helium flow into the cooling region, as shown in Fig. 2. By incorporating 203 these pieces, we reduced the overall length of the cell, allowing for controlled variation of the 204 cooling region length. In this study, we tested nozzles with diameters of 2, 3, 4, and 5 mm, and205 cooling region lengths of 2, 3, 4, and 5 cm.206 Helium and CO gases are supplied to the buffer gas cell from their respective bottles, with the 207 flow rates of both gases controlled by flowmeters (MCE-20SCCM-D-6MMCOMP for helium 208 and MCE-1SCCM-D-6MMCOMP for CO, by Alicat). The helium line passes through a cooling 209 cell soldered to the 4-K stage of the cryostat. The cold helium is injected into the buffer cell 210 via a stainless steel capillary tube with an outer diameter of 3.2 mm, as depicted in Fig. 2. The 211 CO gas is introduced from the back end of the cell through a 3.2-mm-outer-diameter copper 212 capillary tube. This tube is thermally isolated from the buffer cell by a PEEK piece, and cartridge 213 heaters are used to keep the CO line at 70 K by a PID controller to prevent freezing. This heating 214 arrangement is illustrated in Fig. 2. Under standard pressure, CO liquefy at 81.15 K and freezes 215 at 74.15 K.216 3.2. Optical transitions, detection, and the laser system217 BGC 30 mm 70 mm 245 mm Top view Molecular beam axis 206 nm laser beam 40-K shield aperture 23 mm x z y PMT . Side view Fig. 3. Scheme of the molecular beam and detection system. To detect CO molecules emerging from the buffer cell, we first excite them to a metastable triplet 218 state with a pulsed laser. 1 mJ of light at 206 nm saturates the spin-forbidden transition 𝑎3Π1(𝑣=219 0, 𝐽 =1) ← 𝑋1Σ+(𝑣=0) . The 𝑎3Π1(𝑣=0, 𝐽 =1) has a lifetime of 2.63 ms. [20] Then, 220 we detect their phosphorescence on a photo-multiplier tube (PMT) (9813BQ, ET Enterprises), 221 positioned approximately 24.5 cm downstream from the excitation region. It has an efficiency of 222 30% at 206 nm and it is mounted behind a quartz window with a transmission of 90% at 206 nm. 223 The PMT is 117 mm from the axis of the molecular beam and has an effective entrance aperture 224 of 35 mm in diameter. Such geometry allows for the collection of phosphorescence signal under 225 0.07 sr. All together these parameters yield a total detection efficiency of 0.135%. We show a 226 scheme of this setup in Figure 3. We acquire the phosphorescence signal with 13 𝜇 s resolution. 227 For the range of velocities studied in this work (100–250 m/s), this set of parameters yields a 228 velocity resolution of about ± 10 m/s and detection efficiency is independent on velocity in first 229 approximation. A first aperture in the 40-K shield reduce the divergence of the beam, but the field 230 of view of the PMT further reduce the portion of the beam that is detected, yielding an overall 231 divergence of 0.012 sr. This value is large but we believe that it is a useful measure because with 232 high-power lasers one can decelerate and transverse-cool beams with such characteristics.233 The electronic ground state 𝑋1Σ+ is best described in Hund’s case (b), where the rotational 234 states are fully characterized by the rotational quantum number 𝑁 . The parity of the rotational 235 states follows (−1)𝑁 . In contrast, the rotational structure of the electronically excited state 𝑎3Π1 236 is described by the total angular momentum quantum number 𝐽 . We characterized the buffer gas 237 cell by exciting the CO molecules from the rotational levels 𝑁=0 to the lower component of the 238 Λ doublet in the 𝑎3Π1 ( 𝐽=1 ) state. Only for the data shown in Figure 8, we excite molecules 239 also from the 𝑁=1 level to the upper component of the Λ doublet in the 𝑎3Π1 ( 𝐽=1 ) state. A 240 more detailed description of the energy levels can be found in Ref [21].241 We employed a laser system similar to that described in Ref [22], which generates a pulsed 242 beam with an energy of approximately 1 mJ at 206 nm, a repetition rate of 10 Hz, a pulse duration 243 of around 6 ns and a linewidth of approximately 200 MHz.244 4. Results and discussions245 480.0 240.0 160.0 120.0 96.0 80.0 Velocity (m/s) 0.5 1.0 1.5 2.0 2.5 3.0 Time (ms) 0 1 2 3 4 5 Molecules / (sr s) (×1013) 0 SCCM He 12 SCCM He 16 SCCM He 20 SCCM He Fig. 4. Arrival time of CO molecules in front of the PMT with 1 SCCM of CO, and 0 and 12, 16, 20 SCCM of helium, a 3-cm cell length and 5-mm aperture, solid lines. The dashed lines are the fit of a Maxwell-Boltzmann distribution to the data. On top, the arrival time is converted into the correspondent molecular velocity. Figure 4 shows the phosphorescence signal detected by the PMT, both in the presence and 246 absence of helium flow in the cell. We correct for the exponential decay of the population in the 247 excited states and take the overall detection efficiency into account to calculate the number of 248 molecules/(s sr) that have been prepared by the laser in a single quantum state.249 Knowing the CO excitation time and the phosphorescence time, and the distance between 250 excitation laser and PMT, we calculate the velocity of the molecular beam, shown on the horizontal 251 axis on top of the graph. The shift in the overall profile and in the forward velocity in dependence 252 of the helium flow clearly indicate the cooling effect on CO. We attribute this effect to the 253 thermalization of CO molecules within the buffer cell. Collisions with He atoms might transfer 254 part of the metastable population to the lower rotational states of the Ω = 0 manifold on the 𝑎3Π255 state. However, the lifetime of those states are about two orders of magnitude longer than from 256 the Ω = 1 states. Therefore, we consider their contribution to the observed signal to be negligible. 257 Fitting the time of flight profiles in Figure 4 to a Maxwell-Boltzmann distribution yields 258 temperatures of 69.2±0.1K and 6.9±0.2K for helium flow rates of 0 and 20 SCCM, respectively. 259 Two different effects are responsible for the observed data. Collisions with helium lower the CO 260 2 4 6 8 10 12 14 16 18 20 Helium Flow Rate (SCCM) 0.0 0.2 0.4 0.6 0.8 1.0 Integrated signal (a. u.) 3 mm Aperture, 2 cm Cell 4 mm Aperture, 2 cm Cell 5 mm Aperture, 2 cm Cell 3 mm Aperture, 3 cm Cell 4 mm Aperture, 3 cm Cell 5 mm Aperture, 3 cm Cell 3 mm Aperture, 4 cm Cell 4 mm Aperture, 4 cm Cell 5 mm Aperture, 4 cm Cell 3 mm Aperture, 5 cm Cell 4 mm Aperture, 5 cm Cell 5 mm Aperture, 5 cm Cell Fig. 5. Integrated phosphorescence signal in dependence on He flow rate, for all aperture diameters and cell lengths. In all cases, larger He flow yields larger CO signal. velocity from the over 250 m/s expected for CO at around 70 K (temperature of the CO line) to 261 below 150 m/s. However, by further increasing the He flow, we increase the Reynolds number 262 and slightly accelerate CO molecules.263 Figure 5 shows the CO phosphorescence signal in dependence on the He flow rate, for all 264 source configurations. We see a monotonic signal increase with increasing flow, up to 20 SCCM, 265 which is the limit of our He flowmeter. The same is true for the CO flow rate, which is limited to 266 1 SCCM by the CO flowmeter. Therefore, all data shown in the following are measured with 1 267 SCCM of CO and 20 SCCM of He.268 We test Eq. (6) by measuring the phosphorescence signal in dependence on the cell length for 269 various nozzle sizes, Figure 6. A shorter cell minimizes the probability of diffusion to the walls 270 and thus increases the extraction efficiency, 𝛾 . Measured data show a qualitative agreement with 271 theory. However, although we do not expect significant dependence on the nozzle sizes, we know 272 from the literature that lower output is expected when the nozzle is too small, see Ref. [14]. This 273 is in fact what we observe with a nozzle diameter of 3 mm.274 We then investigate the dependency of the forward velocity on the nozzle diameter, which 275 influences the Reynolds number characterizing the flow at the source exit. Data are shown in 276 Figure 7. We fit a Maxwell-Boltzmann curve to the recorded phosphorescence signal and extract 277 a peak forward velocity. Although we observe an overall velocity reduction upon nozzle diameter 278 enlargement, we also see large difference depending on cell length. With longer cells, CO 279 molecules undergo more collisions and are thus more likely to diffuse to the walls. Therefore, we 280