Nonadiabatic transitions in a Stark decelerator arXiv:1001.3222v2 [physics.atom-ph] 4 Mar 2010 T. E. Wall, S. K. Tokunaga, E. A. Hinds, and M. R. Tarbutt ∗ Centre for Cold Matter, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK In a Stark decelerator, polar molecules are slowed down and focussed by an inhomogeneous electric field which switches between two configurations. For the decelerator to work, it is essential that the molecules follow the changing electric field adiabatically. When the decelerator switches from one configuration to the other, the electric field changes in magnitude and direction, and this can cause molecules to change state. In places where the field is weak, the rotation of the electric field vector during the switch may be too rapid for the molecules to maintain their orientation relative to the field. Molecules that are at these places when the field switches may be lost from the decelerator as they are transferred into states that are not focussed. We calculate the probability of nonadiabatic transitions as a function of position in the periodic decelerator structure and find that for the decelerated group of molecules the loss is typically small, while for the un-decelerated group of molecules the loss can be very high. This loss can be eliminated using a bias field to ensure that the electric field magnitude is always large enough. We demonstrate our findings by comparing the results of experiments and simulations for the Stark deceleration of LiH and CaF molecules. We present a simple method for calculating the transition probabilities which can easily be applied to other molecules of interest. PACS numbers: 37.10.Mn, 37.20.+j, 31.50.Gh Beams of fast-moving polar molecules can be brought to rest using a Stark decelerator [1]. The molecules ex- perience a force in the inhomogeneous electric field of the decelerator. By switching the field on and off in a carefully tailored sequence this force always opposes their forward motion. The Stark decelerator was first demon- strated for metastable CO [2] and several other molecules have since been decelerated this way. The decelerator works best for molecules in low-field seeking states since they are easy to focus through the device. For the de- celerator to work it is crucial that the molecules remain in the same quantum state throughout the deceleration process. The timing sequence that needs to be applied to the decelerator electrodes depends on the Stark shift and, since different states have different shifts, a molecule that changes state will no longer be decelerated. Moreover, if the state change is to one of the high-field seeking states, the molecule will be attracted to the electrodes where the field is strongest, and it is unlikely to be transmitted. The unwanted change of state can occur because the molecules experience a time-varying electric field as they move through the decelerator and as the decelerator is switched from one field configuration to another. Tran- sitions between states will only be significant if the time-varying electric field has frequency components that approach the frequency splitting between those states. Some simple order-of-magnitude reflections provide con- siderable comfort in this respect - in a typical deceleration experiment the Stark shifts are tens of GHz, whereas the molecule takes about 10 µ s to travel from one stage to the next and the rise and fall times ( τ ) of the switching need only be 10 times smaller than that for the deceleration to be efficient. Nevertheless, we must consider carefully those cases where energy levels happen to be very close, as occurs at an avoided crossing, or when the electric field becomes so small that states differing only in their ori- entation with respect to the field are nearly degenerate. It is important to distinguish these two cases. In the de- celerator, molecules need to traverse an avoided crossing diabatically so that the gradient of the Stark shift is the same on both sides of the crossing. That may be difficult to arrange if the energy gap at the avoided crossing is too large. Conversely, to preserve its orientation in low field, the molecule must follow the changing field adiabatically , which can be arranged by ensuring that the electric field in the decelerator is never too small. When the decelerator switches, both the magnitude and the orientation of the electric field changes. It is the rotation of the electric field that is responsible for the orientation-changing transitions. On the axis of the de- celerator the electric field vector rotates through 90 ◦ each time the decelerator switches. The rotation rate of the field vector depends on the position within the decelera- tor. At positions where the field magnitude is small prior to switching and large afterwards (or vice versa), the ma- jority of the 90 ◦ rotation occurs in a small fraction of τ , meaning that the rotation rate reaches values very much larger than τ − $^{1}$. In fact, as we shall see, the rotation rate is at its largest at a point in space and time where the energy splittings are at their smallest and the molecules most vulnerable to nonadiabatic transitions. It is these rotation-driven transitions that are the main subject of this paper. Losses due to nonadiabatic transitions and due to avoided crossings have been considered previously in the literature on Stark deceleration. For the deceleration of $^{∗}$Electronic address: m.tarbutt@imperial.ac.uk I. INTRODUCTION