Magnetic Trapping of NH Molecules with 20 s Lifetimes

. Buﬀer gas cooling is used to trap NH molecules with 1 /e lifetimes exceeding 20 s. Helium vapor generated by laser desorption of a helium ﬁlm is employed to thermalize 10 5 molecules at a temperature of 500 mK in a 3.9 T magnetic trap. Long molecule trapping times are attained through rapid pumpout of residual buﬀer gas. Molecules experience a helium background gas density below 1 × 10 12 cm − 3 .


Introduction
Avid interest in cold molecules arises from their potential utility in diverse areas of physics. Cold molecules are employed in studies of the temporal variation of fundamental constants [1,2] and in searches for a permanent electric dipole moment of the electron [3,4]. Infrared spectroscopy of molecules provides important information about their abundance in stellar environments like cold dark clouds [5,7,6] and can thus give insight into the evolution of these environments. The strong electric dipole-dipole interaction between molecules polarized by external electrical fields may lead to the creation of condensed matter systems with novel properties [8] and the use of molecular ensembles as bits in quantum computers [9,10].
In many experiments, the trapping of molecules facilitates their study. Trapped molecular samples are useful in understanding spin depolarization and collisional quenching [11,12]. The spontaneous radiative decay of molecules in rovibrationally excited levels is directly and most precisely measured by observing the temporal evolution of excited state populations [13,12]. These transitions, typically having lifetimes of several milliseconds, can be monitored when dilute samples of molecules are confined in free space using electromagnetic fields. Techniques to increase molecular phase space densities through collisions also benefit from increased confinement times, as efficient cooling requires sufficient time for molecule populations to thermalize to the temperature of the refrigerant (in sympathetic cooling) [15,14] or to rethermalize (evaporative cooling) [16,18,17]. Trap lifetimes of around ten seconds were required to evaporate the first atomic samples to quantum degeneracy [19].
This letter reports the use of a variant of the buffer gas technique to cool and magnetically trap NH molecules with 1/e lifetimes exceeding 20 s. We have previously reported the use of the buffer gas technique to study the spin relaxation of NH molecules in collisions with helium [11]. In the trapping conditions of that experiment (T = 710 mK, B max = 3.9 T, η = µB max k B T = 7.5, n He ∼ 5 × 10 14 cm −3 , where T is the temperature, B max is the depth of the magnetic trap, µ is the magnetic moment of the molecule and n He is the helium density), molecule trap lifetimes were limited to around 200 ms by inelastic buffer gas collisions. Enhanced molecule lifetimes in the current experiment are achieved through a thousand-fold reduction in the helium background density on a timescale shorter than the trapping time.
To dissipate the translational and rotational energy of the molecules we produce from our room temperature source, we require helium densities of approximately 1×10 15 cm −3 . At these densities, the molecule trap lifetime is determined by the competing effects of diffusion and spin depolarization. Diffusion enhancement of the trap lifetime is proportional to n He ; spin depolarization produces loss that reduces the trap lifetime as 1/n He . As the buffer gas density is reduced from the densities required for loading our magnetic trap, diffusion and spin depolarization become less significant and the effect of trap evaporation (expulsion of molecules due to elastic collisions with the buffer gas) dominates. Trap evaporation has a roughly exponential dependance on both the  trapping parameter η and the helium density. Longer trapping durations may thus be achieved by reducing the ambient helium density, trapping colder molecules and employing deeper magnetic traps. Previous work [20] has shown that reductions in the helium density must occur rapidly compared to the molecule trap lifetime for a significant number to be retained in low background gas conditions . Trap evaporation is studied by performing a Monte Carlo simulation of molecule trajectories [21,22]. Figure [1] presents the results of the simulation of NH molecules embedded in a helium vapor background. Collisions are modeled as hard sphere scattering events. The buffer gas temperature is assumed to be 500 mK, the cell temperature. The elastic collision cross-section between NH and 3 He is assumed to be the experimentally measured value of 2.7× 10 − 14 cm −2 [11] . Red triangles show the effect of elastic collisions between molecules and buffer gas atoms. In the absence of inelastic collisions, a minimum lifetime is predicted to occur at a density of approximately 10 14 cm −3 , when the background gas is too dilute to enforce diffusive motion but frequent collisions can eject molecules from the trap. The spin depolarization rate for NH-3 He collisions, k in (studied in reference [11]), was found to be 3.0 ± 0.9 × 10 14 cm 3 s −1 . The blue circles result from including the effects of spin-depolarizing collisions on the molecule lifetime.

Experimental Apparatus and Technique
The experimental apparatus employed to trap molecules for longer durations, Figure  [ 2], is similar to that described in reference [11]. NH molecules, produced in the form of a supersonic beam by glow discharge of ammonia, are injected into a copper cell housed in the bore of a superconducting magnet (anti-Helmholtz configuration). The cell is thermally anchored to a 3 He refrigerator and sits at approximately 500 mK. In the previous experiments, the molecules thermalized to the cell temperature through collisions with helium supplied by steady flow through a fill line attached to the cell. The fixed flux into the cell through the fill line and out of the cell through the 1 cm diameter front aperture established a constant helium density within the cell. In the current apparatus, a rapid reduction in the helium density after loading is attained by creating an additional 3.80 cm diameter aperture at the back end of the cell. A pulse of helium gas, provided by an external reservoir physically disconnected from the trapping cell, is used to thermalize the injected molecues in lieu of the steady helium flow.
The helium reservoir is a copper chamber with a fill line for gas supply and an aperture that permits the gas to be delivered to the cell. The reservoir volume is 200 cm 3 ; the aperture diameter is 0.64 cm. A phosphor bronze spring presses a PTFE disc against the bottom reservoir flange to seal the aperture. Thermal connection to the 3 He refrigerator fixes the reservoir temperature at 900 mK.
The molecule loading procedure is as follows. The reservoir seal is opened and helium fills the cell at an approximate density of 10 15 cm −3 for 20 ms. The molecule beam is fired into the helium vapor, which flows out of the cell and into the vacuum space. The molecules persist in the trap with 1/e lifetimes of a few seconds (Figure [ The lifetime limit imposed by film desorption may be circumvented by a modification of the loading procedure. The reservoir is again used to fill the cell with helium. The film is then allowed to thin over time. 45 s after the actuation of the reservoir, 4 mJ of energy from a 532 nm YAG laser is incident on the cell; the YAG pulse elevates the cell temperature from 520 mK to 590 mK and desorbs helium from the cell walls. The molecular beam is timed to fire with the YAG pulse, and the desorbing helium thermalizes a portion of the molecules, which are retained in the trap. From the measured lifetime and the Monte Carlo simulation, we infer a background helium density between 10 11 cm −3 and 10 12 cm −3 in the trapping region. shows fluorescence spectra at different times. The red trace shows a spectrum recorded 150 ms after the firing of the molecular beam. The blue circles are a spectrum measured 10 s after the molecular beam launch. The fluorescence signal for the early time specrum is reduced by a factor of 300 to permit comparison to the spectrum at longer time. Optical pumping by blackbody radiation has been shown to limit trapping times in room temperature experiments [23]. Hoekstra et al calculate maximal room temperature trapping lifetime for NH to be under 10 s. At the 1 K temperature of our experiment, the black body pumping rate is strongly suppressed (by a factor of ∼ 10 10 ) and plays no part in determining the molecule lifetime.

Conclusions
The trapping of molecules in conditions of lower buffer gas density increases the prospects of success for a number of collisional experiments. We have previously demonstrated the simultaneous loading and magnetic trapping of nitrogen atoms and NH molecules [24]. The interaction of these species in an environment with a low density of helium will facilitate more sensitive study of the collisional properties of this system. Favorable collisional properties (low inelastic loss rates), could lead to nitrogen being used as a refrigerant for the NH molecules, enabling the sympathetic cooling of the molecule. We also expect increased loading efficiency if the molecules are supplied to the trapping region as a 4 K effusive beam. We have developed such beams [25,26] with a variety of species. Higher densities of accumulated molecules and long trapping times could allow us to study low temperature molecule-molecule interactions. While our molecule temperatures currently exceed those attained using other methods (such as Stark deceleration techniques), additional cooling steps may permit dramatic temperature reductions and increases in molecular phase space densities [27]. Long trapping times in our experiment might also permit us to perform high precison measurements of the lifetimes of the metastable states of radical species. In our measurement of the radiative lifetime of the first vibrational level of NH, the 37 ms lifetimes was a significant fraction of the 200 ms trapping time; extraction of the radiative lifetime required correction for the effect of a finite trapping time. In the conditions of the current experiment, the radiative lifetime is less than one percent of the molecule trapping time. The reduction in the ambient helium density also minimizes uncertainties associated with the quenching of the excited vibrational state (our dominant systematic uncertainty) and facilitates the measurement of longer lifetimes for metastable states of other trappable species.
The low helium background present in the experiment also suggests that this variant of buffer gas loading can be applied to thermalize and trap particles with unfavorable ratios (γ = σ elastic σ inelastic ) of elastic to inelastic cross-sections, potentially extending the number of species that can be studied. High rates of inelastic loss due to collisions with helium limited the trapping lifetimes of the highly paramagnetic molecules chromium hydride (γ ∼ 9000) and manganese hydride (γ ∼ 500) to hundreds of milliseconds [28]. Employing a transient burst of helium to thermalize the molecules and then rapidly removing the residual gas could lead to trap lifetimes of several tens of seconds for these molecules.
In conclusion, we have been able to demonstrate the confinement of 10 5 NH molecules in a magnetic trap with lifetimes exceeding 20 s. The long trap lifetimes are obtained by using a loading technique that creates a background gas density between 10 11 cm −3 and 10 12 cm −3 . Trapping is accomplished in a cryogenic environment, avoiding constraints imposed by the optical pumping of molecules by blackbody radiation.
The authors thank Nathan Brahms for his assistance with the simulation.