Heteronuclear collisions between laser-cooled metastable neon atoms
Phys. Rev. A 86, 022713 (2012)
We investigate heteronuclear collisions in isotope mixtures of laser-cooled metastable () neon. Experiments are performed with spin-polarized atoms in a magnetic trap for all two-isotope combinations of the stable neon isotopes Ne, Ne, and Ne. We determine the rate coefficients for heteronuclear ionizing collisions to cm/s, cm/s, and cm/s. We also study heteronuclear elastic collision processes and give upper bounds for heteronuclear thermal relaxation cross sections. This work significantly extends the limited available experimental data on heteronuclear ionizing collisions for laser-cooled atoms involving one or more rare gas atoms in a metastable state.
Due to their high internal energy which surpasses the ionization energy of almost all neutral atomic and molecular collision partners, metastable rare-gas atoms (*) prepared by laser cooling techniques Vassen et al. (2012) present a unique class of atoms for the investigation of cold and ultracold collisions Weiner et al. (1999). With lifetimes ranging from 14.73 s (neon) Zinner et al. (2003) to 7870 s (helium) Hodgman et al. (2009), the first excited metastable states present effective ground states for applying standard laser cooling techniques. The resulting extremely low kinetic energy of the laser-cooled atoms ( eV) stands in strong contrast to the high internal energy between 8 eV (xenon) and 20 eV (helium). This offers unique conditions not accessible with samples of laser-cooled alkali-metal atoms. In particular, the high internal energy of the metastable state allows for Penning (PI) and associative (AI) ionizing collisions,
to dominate losses in trapped * samples at high densities. Since direct detection of the collision products (using electron multipliers) as well as of the remaining * atoms is possible with high efficiency, detailed studies of homonuclear ionizing collisions have been carried out for all rare gas elements (see Vassen et al. (2012) for an overview). Additional motivation for these investigations arises from the fact, that favorable rate coefficients for inelastic but also for elastic collisions are essential for the achievement of quantum degeneracy which for * atoms so far has only been demonstrated for He Robert et al. (2001); Pereira Dos Santos et al. (2001); Tychkov et al. (2006); Dall and Truscott (2007) and He McNamara et al. (2006).
For unpolarized * samples, two-body loss rate coefficients for PI not (a) between for Xe Walhout et al. (1995) and for Ne van Drunen (2008) have been measured. Spin polarizing the atoms to a spin-stretched state may suppress PI: In a collision of atoms in spin-stretched states the total spin of the reactants is larger than the total spin of the products. Thus, if spin is conserved, PI collisions should be significantly reduced. In the case of He* in the state, a suppression of four orders of magnitude has been observed Tychkov et al. (2006); Stas et al. (2006). For the heavier rare gases, however, the metastable state is formed by an exited electron and a core with orbital momentum . This leads to an anisotropic quadrupole-quadrupole interaction between the colliding atoms that limits the amount of suppression Doery et al. (1998). In the case of neon, suppression rates of 77 for Ne and 83 for Ne, respectively, have been determined Vassen et al. (2012); van Drunen (2008), but no suppression has been found for Kr* Katori et al. (1995) and Xe* Orzel et al. (1999).
In contrast to the case of homonuclear collisions, the number of experimental studies of cold heteronuclear ionizing collisions with at least one * atom is very limited. To our knowledge, there exists only one investigation involving heteronuclear pairs of * atoms, performed with metastable helium McNamara et al. (2007), and only two experiments involving one * atom in combination with a ground state alkali-metal atom: Ar* and Rb Busch et al. (2006) and He* and Rb Byron et al. (2010). It is the purpose of the present work to extend the available experimental data by the investigation of heteronuclear collision between all possible combinations of the stable isotopes of neon. There exist two stable bosonic isotopes, Ne (natural abundance: 90.48%) and Ne (9.25%), and one fermionic isotope, Ne, with an abundance of 0.27% Rosman and Taylor (1998). This work complements our previous measurements on homonuclear collisions for the bosonic isotopes Ne and Ne Spoden et al. (2005).
In this paper we report on trapping of all three stable isotopes and all two-isotope mixtures of laser-cooled Ne* in a magnetic trap. We present measurements on the rates of heteronuclear ionizing collisions and heteronuclear thermal relaxation cross sections in isotope mixtures of spin-polarized Ne*. Specific emphasis has been put on the preparation of spin-polarized samples in order to have clear experimental conditions avoiding unambiguity arising from averaging over different internal state combinations during collisions. We also address the question of whether the rates for heteronuclear collisional interactions are favorable for sympathetic cooling between different neon isotopes, as is the case for He* McNamara et al. (2006). Sympathetic cooling of Ne, which has a positive scattering length of , Spoden et al. (2005) using Ne as a coolant might open a novel route to produce quantum degenerate bosonic Ne*. Sympathetic cooling of Ne, using one of the bosonic isotopes as a coolant, could allow for the creation of a cold, dense sample of spin-polarized fermionic neon which could complement experiments with fermionic He for studying, e.g., the effect of Pauli blocking DeMarco et al. (2001) on Penning ionization for heavier rare-gas atoms Orzel et al. (1999).
i.1 Experimental setup
In our experiment Zinner et al. (2003); Spoden et al. (2005), neon atoms are excited to the metastable state in a dc discharge, then optically collimated, Zeeman decelerated, and captured in a magneto-optical trap. For laser cooling, the transition at 640.4 nm is used. While the bosonic isotopes have no nuclear spin, Ne has a nuclear spin of which causes a hyperfine structure of the atomic states. Ne is trapped in the state with total angular momentum and the transition is used for laser cooling. After magneto-optical trapping, the atoms are spin polarized to the substate ( in the case of Ne) using circular polarized light and are transferred to an Ioffe-Pritchard magnetic trap (see Spoden et al. (2005) for details). As a last step of preparation, we apply one-dimensional Doppler cooling Schmidt et al. (2003) by irradiating the magnetically trapped atoms with circular polarized, red-detuned laser light along the symmetry axis of the trap.
The different laser fields for decelerating, cooling, optical trapping, and detecting the atoms of one isotope are derived from a single dye laser using acousto-optic frequency shifters. In order to trap Ne, in addition to the cooling light, we superimpose “repumping” light () on all laser beams. This light pumps atoms that have been off-resonantly excited to the state and have spontaneously decayed to the state back into the cooling cycle. In order to maximize the number of trapped Ne atoms, we pump atoms that have been initially excited to the or states by the discharge source into the cooling cycle. For this purpose, we add laser light tuned between the closely spaced and transitions in the optical collimation zone directly after the discharge source (see Feldker et al. (2011) for details).
The isotope shift of the cooling transition is MHz for Ne Ne and MHz for Ne Ne, respectively Feldker et al. (2011). In order to trap two isotopes simultaneously, we use two dye lasers with the frequency of each laser being stabilized to the cooling transition of the respective isotope and a non polarizing beam splitter to overlap their output light. Typical atom numbers of two-isotope mixtures of magnetically trapped atoms, compared to single isotope samples, are presented in Table 1. The atom numbers in two-isotope samples are slightly lower than in the single isotope cases. The number of Ne and Ne atoms is limited due to inelastic collisions between trapped atoms, while the number of Ne atoms is limited by the maximum available loading duration of 0.7 s in our setup. After one-dimensional Doppler cooling, the mean temperatures are typically 300 K for single isotopes and 500 K for two-isotope mixtures.
For the bosonic isotopes, the number of trapped atoms is determined by absorption imaging. The images are taken 3 ms after the trap has been switched off. Knowing the trapping potential, these images also allow for a determination of the ensemble temperatures from the widths of the atom clouds. In the case of isotope mixtures, the images are taken using light resonant with the cooling transition of one of the isotopes. Since the isotope shift of the cooling transition is at least 600 MHz, the presence of another isotope does not influence the imaging process. For the given densities, absorption imaging is limited to atom samples of more than atoms. In order to determine the number of Ne atoms, either fluorescence imaging or electronic detection are used. For fluorescence imaging of the magnetically trapped atoms, we illuminate the atoms with the magneto optical trap (MOT) beams for 100 ms and collect the fluorescence light with the CCD camera. The signal is well pronounced even for small samples but does not reveal information about the temperature of the cloud. For electronic detection, we use a double micro channel plate (MCP) detector which is placed 13.9 cm below and 2.7 cm sideways with respect to the trap center. From the time-of-flight signal of Ne* released from the magnetic trap, the number of atoms as well as the temperature of the atom sample can be determined. To distinguish between different isotopes we push away the atoms of the unobserved isotope using slightly blue-detuned MOT light. We do not see any influence of this light on the remaining atoms of the observed isotope.
|Single-isotope samples||Two-isotope mixtures|
|Ne||Ne + Ne|
|Ne||Ne + Ne|
|Ne||Ne + Ne|
Since one-dimensional Doppler cooling is more efficient along the beam axis (i.e., the symmetry axis of the Ioffe-Pritchard trap) Schmidt et al. (2003), we obtain ensembles not in three-dimensional thermal equilibrium after the preparation process. In each dimension, however, energy equipartition is fulfilled and the ensembles can be described by independent temperatures in axial and in radial directions. A mean temperature defined as is used to describe the thermal energy of the atom sample. The absorption images are taken perpendicular to the symmetry axis of the trap and allow for a determination of and simultaneously. From the time-of-flight signal on the MCP detector only can be deduced directly since mainly influences the total number of atoms hitting the detector. However, by calibrating the MCP signals with corresponding fluorescence images, we can derive axial and radial temperature for electronic detection as well.
Ii Heteronuclear ionizing collisions
We performed number decay measurements for all spin-polarized two-isotope mixtures in the magnetic trap for trapping times between 0.2 s and 4 s [see Fig. 1 (left)]. After the trap is switched off, an individual image is recorded for one isotope and after a second identical repetition of the experimental run a corresponding image for the other isotope is taken. For Ne, in an additional run the time-of-flight signal on the MCP detector is recorded in order to gain full information about atom number , , and for all isotopes.
From the number decay, we determine the rate coefficients of binary inelastic collisions. The decrease in atom number of isotope Ne originates from one-body losses ( with rate constant ) as well as homonuclear ( with rate constant ) and heteronuclear ( with rate constant ) two-body losses. We have no signature of higher order loss processes in our measurements. One-body losses are mainly caused by the 14.73 s lifetime of the state and by background gas collisions. Two-body losses are almost entirely caused by ionizing collisions which we confirmed by simultaneously measuring the trap loss by absorption imaging and detecting the rate of ions escaping from the trap using the MCP in previous measurements for the bosonic isotopes Spoden et al. (2005). Spin-changing two-body collisions play an insignificant role in two-body loss for our experimental conditions. We infer that this is also valid for Ne since hyperfine state changing collisions are energetically suppressed due to the inverted hyperfine structure.
The trap loss can be described by
with densities of isotope Ne. The trap potential can be calculated from the known geometry and the currents that are supplied to the coils of the trap which, together with the measured temperatures and , allows for a computation of the the effective volumes and . For temperatures above 300 K the atoms are not fully localized in the harmonic region of the trap. Therefore, instead of assuming Gaussian density profiles, we perform the spatial integration numerically, also accounting for different and . All measurements were performed in the trap configuration that is used for Doppler cooling without further compression of the trap. Here, the trap is operated with an offset field of 2.6 mT and the calculated vibrational trap frequencies for Ne are s in axial and s in radial directions.
We find that the effective volumes increase in time due to heating of the ensembles Spoden et al. (2005). This heating is mainly caused by the higher rate of ionizing collisions at the trap center, involving atoms with an energy below average (cf. Sec. III). Explicit evaluation of Eq. (II) would require a detailed knowledge of the heating mechanisms, so we formally integrate Eq. (II) to obtain
resulting in a linear relation with slope and offset . For Ne and Ne the homonuclear two-body loss coefficients and are known Spoden et al. (2005). For Ne homonuclear collisions can be neglected due to the small number of Ne atoms relative to the numbers of Ne and Ne (see Table 1). All other quantities needed to calculate and can be derived from experimental data by means of numerical integration.
The number decay of Ne and Ne in a two-isotope mixture is shown in Fig. 1 (left). The data points present averages of six measurements. The number decay of Ne represented according to Eq. (4) is shown in Fig. 1 (right). We observe the expected linear dependence and by a least-square fit we derive a one-body loss coefficient of s and a heteronuclear two-body loss coefficient of . The coefficient determined from the complementary number decay of Ne in the same measurement agrees within the error margins not (b). Similar analysis for the other isotope combinations yield and , respectively. In the latter two cases, only the decay of Ne can be analyzed since the effect of heteronuclear two-body loss induced by Ne on one of the other isotopes is negligible due to the low number of trapped Ne atoms.
The measured values for the rate coefficients of heteronuclear ionizing collisions together with the previously measured homonuclear rate coefficients for Ne and Ne are summarized in Table 2. We find heteronuclear rate coefficients that are a factor of 2-6 larger than the homonuclear rate coefficients. A larger rate coefficient for heteronuclear collisions has also been observed in the corresponding measurements in He* McNamara et al. (2007).
The quoted uncertainties are the combined statistical and systematic uncertainties. They are dominated by systematic uncertainties in atom density, depending on atom number and effective volume. The evaluation procedure according to Eq. (4) is especially sensitive to the initial atom number. Other, also included but less dominant contributions to the uncertainties are given by the uncertainties of the homonuclear two-body loss coefficients. For Ne, additional uncertainties arise due to the indirect measurement of and larger statistical uncertainties because of the low atom number.
Iii Heteronuclear elastic collisions
We also analyzed the heteronuclear elastic collision rates for magnetically trapped spin-polarized Ne*. In addition to the importance for completing the available database for metastable neon atoms, efficient sympathetic cooling between different isotopes requires a large ratio of elastic to inelastic collision rates. Therefore, we studied the heteronuclear elastic collision rates between isotope Ne and Ne by determining internuclear thermal relaxation rate constants , defined by
Since depends on the densities and temperatures of the ensembles involved, it is useful to define an effective relaxation cross section
where is the average relative velocity of the colliding atoms.
We prepare two-isotope mixtures in the magnetic trap with a temperature difference between the isotopes by applying one-dimensional Doppler cooling with different efficiencies to the two isotopes. For all isotope combinations, we find that heteronuclear thermal relaxation is outbalanced by intrinsic heating caused by ionizing collisions: Since ionizing collisions occur preferentially at the center of the trap, where the density is highest and the energy of the atoms is lowest, these collisions remove atoms with below average energy. This leads to an effective heating of the remaining atoms (see also Söding et al. (1998); Spoden et al. (2005)). The heating rate per ionizing collision depends on the mean energy carried away by the collision products relative to the mean energy of all atoms in the trap. The heating rate is given by Söding et al. (1998)
with . We calculate assuming a velocity-independent cross section and Gaussian density distributions. For homonuclear collisions ; for heteronuclear collisions depends on the temperatures of the two isotopes and is limited to .
The time evolution of , thus can be described by
with an additional constant heating rate accounting for density-independent heating effects. Again, we can formally integrate Eq. (8) to obtain
resulting in a linear relation with the slope given by . Again, all quantities needed to calculate and can be derived from experimental data by means of numerical integration.
We performed relaxation cross-section measurements for all two-isotope combinations. As an example, the time evolution of the dimensionally averaged temperatures of spin-polarized Ne and Ne in a two-isotope mixture and the representation of according to Eq. (III) are shown in Fig. 2. All measurements reveal the systematic problem that the time evolution of the temperature in all cases is dominated by intrinsic heating: The temperature for all isotopes is increasing during the trapping time and thermal relaxation is not sufficiently efficient to equilibrate the temperatures of the different isotopes. Additionally, the large uncertainties in (and thus in the heating rates) and in density lead to huge uncertainties in the extracted relaxation cross sections. As a consequence, only upper bounds for the values of can be determined.
For the data presented in Fig. 2 (right), we observe the expected linear dependence and by a least-square fit we determine . Homonuclear collisions of Ne and effects of Ne on Ne can be neglected due to the low number of Ne atoms. The time evolution of is used to determine the constant heating rate . A respective analysis for a Ne-Ne mixture yields . In case of Ne-Ne mixtures, the time evolution of as well as can be fitted. Analysis of yields . By fitting we get a value for consistent with this upper bound but exhibiting even stronger heating effects not included in our model based on Eq. (7). This might indicate that the assumption of a velocity-independent cross section is not valid or that the differences in and need to be taken into account in a more sophisticated fashion not (b).
The resulting upper bounds of for all two-isotope mixtures are summarized in Table 3 and compared to previously measured homonuclear thermal relaxation cross sections of the bosonic isotopes Spoden et al. (2005). The values for homonuclear and the upper bounds for heteronuclear cross sections have the same order of magnitude, although significantly smaller values for the heteronuclear cross sections could be possible. In any case, the resulting upper bounds exclude the possibility that strongly enhanced heteronuclear thermalization could lead to efficient two-isotope evaporative cooling.
We measured the rate coefficients for heteronuclear ionizing collisions of spin-polarized Ne* and determined upper bounds for the thermal relaxation cross sections. We found that the heteronuclear ionizing collision rate coefficients are a factor of 2 to 6 larger than their homonuclear counterparts, while the heteronuclear and homonuclear thermal relaxation cross sections are expected to have comparable values. This shows that the heteronuclear collisional interaction properties are not favorable for hetero nuclear sympathetic cooling and that the “good-to-bad” ratio in the collisional properties is worse in the heteronuclear than in the homonuclear cases.
Acknowledgements.This work was supported in part by the German Research Foundation (DFG) (Contract No. BI 647/3-1) and by the European Science Foundation (ESF) within the Collaborative Research Project CIGMA of the EUROCORES program EuroQUAM.
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