Beyond the limits of conventional Stark deceleration

Stark deceleration enables the production of cold and dense molecular beams with applications in trapping, collisional studies, and precision measurement. Improving the efficiency of Stark deceleration, and hence the achievable molecular densities, is central to unlock the full potential of such studies. One of the chief limitations arises from the transverse focusing properties of Stark decelerators. We introduce an operation strategy that circumvents this limit without any hardware modifications, and experimentally verify our results for hydroxyl radicals. Notably, improved focusing results in significant gains in molecule yield with increased operating voltage, formerly limited by transverse-longitudinal coupling. At final velocities sufficiently small for trapping, molecule flux improves by a factor of 4, and potentially more with increased voltage. The improvement is more significant for less readily polarized species, thereby expanding the class of candidate molecules for Stark deceleration.

Figure 1

Beyond the limits: conventional Stark deceleration (left column) and transversely focusing variants (middle and right columns). Conventional Stark deceleration utilizes a single distribution of electric field (A, top) and its translation plus ${90}^{\circ }$ rotation (${\mathrm{A}}^{\prime }$, middle) in an alternating fashion termed “S = 1” operation (bottom, aligned) [16]. The bottom panel describes S = 1 by plotting the potential experienced by an ideal “synchronous molecule” as it propagates exactly down the center axis of the decelerator (bold). Abrupt changes (bold dashed lines) in the potential the synchronous molecule experiences are achieved by rapidly switching between A and ${\mathrm{A}}^{\prime }$ (labels indicate where each is active) via fast high-voltage switches. Distribution A scarcely focuses, and is not active where it most strongly focuses ($z=7.5\mathrm{mm}$, note increasing field strength of axis). Distributions are shown in the diagonally slicing plane visible in the 3D render (top right, pink). A new focusing mode (F, middle column) circumvents this focusing limitation through the incorporation of new distributions B and C (and their primes, not shown, which relate as do A and ${\mathrm{A}}^{\prime }$). These distributions do not focus on their own but only when averaged together. A and ${\mathrm{A}}^{\prime }$ are still used close to 5 and 10 mm as in S = 1, with the result that the energy removed per pin pair (total length of bold dashed lines) is equivalent to S = 1. Mode SF (strong focusing, right column) simply replaces B, C, and their primes with D, which is more strongly focusing but challenging to implement experimentally.

Figure 2

Simulation results of different deceleration modes. (a) Simulated phase-space volume captured by different modes of operation, for varying decelerations and elapsed time fixed at 3 ms. A 10-kV peak-to-peak traveling wave (TW) deceleration and $\pm 12.5\mathrm{kV}$ S = 3 are also plotted for comparison. Three solid dots correspond to the deceleration used in (b) and (c), about $200{\mathrm{km}/\mathrm{s}}^2$. (b) Equipotentials of the traveling trap generated for three modes. Lack of closure of an equipotential indicates the possibility of molecule escape. The $z$ axis corresponds to the longitudinal direction. (c) Phase-space fillings, both longitudinal (top) and transverse (bottom), for the labeled operation modes after $3\text{ms}$ of travel. The surviving number of molecules is $3.0\times {10}^3$, $1.1\times {10}^4$, and $2.4\times {10}^4$, respectively. Note dramatic improvements in homogeneity and flux, without significant broadening to larger velocity classes.

Figure 3

The molecular signal and enhancement between the F mode and conventional S=1 deceleration over a range of final speeds. Data are collected with a beam of hydroxyl radicals expanded in neon at an initial speed of $825\mathrm{m}/\mathrm{s}$ and deceleration up to $200{\mathrm{km}/\mathrm{s}}^2$. The inset shows the time-of-flight signal from the valve pulse for F (orange) and S = 1 (blue) modes measured at the end of the decelerator when slowing to $50\mathrm{m}/\mathrm{s}$, demonstrating a factor-of-4 improvement at trappable final speeds. Here the decelerator voltage is 12.5 kV.

Figure 4

Comparisons of decelerated populations between the F mode and S = 1 mode at different applied voltages with a final velocity of $50\mathrm{m}/\mathrm{s}$. The points represent experimental results, while the lines are calculated via Monte Carlo simulation. Instead of showing saturation behavior as S = 1, the decelerated population using the F mode increases with higher applied voltage.