11 transitions. Taking OH in the $^{2}$Π$_{3}$$_{/}$$_{2}$ ,J = 3 / 2 state as an example, and neglecting hyperfine structure, Λ- doubling separates the low-field seeking components from the high-field seeking ones by almost 10 $^{10}$rad/s at zero field. Therefore, there are never any transitions between the two Λ-doubled states. Within the upper Λ-doubled manifold, the states differing in M have very different Stark shifts, one being far larger than the other, and so transitions between these M states, which are degenerate at zero field, could still result in loss. However, because of the relatively small splitting between the Λ-doubled components, the Stark shift becomes linear in relatively small fields. As a consequence, the Stark splitting of the two low-field seeking states is large enough to avoid nona- diabatic transitions for all electric fields typically found in the decelerator, even when there is no bias field. For example, this splitting is 2 . 6 × 10 $^{9}$rad/s at 2 kV/cm. Another interesting and relevant example is the | J,K 〉 = | 1 , 1 〉 state of ammonia. Its Stark shift changes from a quadratic to a linear dependence on the field mag- nitude once the Stark shift exceeds the inversion split- ting. In $^{14}$NH$_{3}$ the inversion splitting is large and the Stark shift is quadratic for fields up to ∼ 20 kV/cm. At a field of 2 kV/cm, the splitting between neighbouring M states is 1 . 5 × 10 $^{8}$rad/s. In $^{14}$ND$_{3}$ on the other hand, the inversion splitting is far smaller and the Stark shift becomes linear for fields greater than ∼ 5 kV/cm. At a field of 2 kV/cm, the splitting between neighbouring M states is 1 . 9 × 10 $^{9}$rad/s, more than 10 times larger than for NH$_{3}$. These observations suggest that, unless a bias field is used, Stark deceleration experiments on NH$_{3}$ will exhibit loss of the non-decelerated group due to nonadi- abatic transitions, whereas for ND$_{3}$ no such loss should occur. We have shown that the transition probability is a strong function of the position in the decelerator, and that the decelerated group tends to be immune to nona- diabatic transitions because these molecules are always in a large field when the decelerator switches. This is particularly true when the synchronous phase angle is large. The fact that this loss mechanism distinguishes between the trapped and untrapped molecules could be used to filter out only those molecules that are being de- celerated. This might be useful in experiments with slow molecules where the non-decelerated molecules present an unwanted background. Our experiments on the decel- eration of LiH and CaF show clear evidence for loss due to nonadiabatic transitions. As expected, they show that the loss is far greater for the non-decelerated group of molecules and that this loss can be eliminated by apply- ing a bias field of an appropriate size. The experimental results are in excellent agreement with simulations that include the transitions between the M states. We thank Jony Hudson and Ben Sauer for helpful dis- cussions regarding this work. We are grateful to Jon Dyne, Steve Maine and Valerijus Gerulis for their expert technical support. This work was funded by the UK EP- SRC and STFC, and by the Royal Society. The research leading to these results has received funding from the European Community’s Seventh Framework Programme FP7/2007-2013 under the grant agreement 216774. We have presented a simple formalism for calculating the M -changing transition probabilities. The formalism is based on linear rigid rotor molecules, but with some modifications could also be applied to other molecules of interest, e.g. asymmetric rotors. Hyperfine structure complicates the calculation of the transition probabili- ties. However, if the hyperfine structure is small com- pared to the Stark shift at the minimum field encoun- tered, as for LiH for example, it can be neglected. Our consideration of the hyperfine structure of CaF suggests that although this structure is large enough to be impor- tant, and though we have not done the complete calcu- lations, the full results will not differ greatly from those obtained with hyperfine structure omitted. Consider some general Hamiltonian which we write as a sum of two parts ˆ H ( t ) = ˆ H$_{1}$ ( t ) + ˆ H$_{2}$ ( t ), and where the instantaneous eigenvalues and eigenvectors of ˆ H$_{1}$ ( t ) are ϵ$_{m}$ ( t ) and | m ( t ) 〉 : ˆ H$_{1}$ ( t ) | m ( t ) 〉 = ϵ$_{m}$ ( t ) | m ( t ) 〉 . Using a basis formed by these instantaneous eigenvectors, we can For molecules that are not Σ states, we expect Λ- doubling to suppress the probability of nonadiabatic Acknowledgments Appendix A: Time evolution in an adiabatic basis states, some of which are high-field seeking. The transi- tion probability depends on how the rotation rate of the field vector compares to the splitting between neighbour- ing M states. In order to ensure adiabatic behaviour, the electric field in the decelerator should always be large enough that the minimum splitting between states greatly exceeds the maximum rotation rate. This can be achieved by applying a bias electric field, and choosing switching rise and fall times that are as slow as possible while still being compatible with efficient deceleration. For a typical deceleration experiment, the maximum ro- tation rate is about 10 $^{8}$rad/s. This sets the scale for the size of the bias field required, which will depend on the molecular species. A magnetic field could also be used to suppress nonadiabatic transitions for some molecules, but its magnitude would need to be at least 0.01 T for it to be effective. This would not be useful for Σ states where the only relevant magnetic interaction is with the electron spin (if there is one). In this case it is the com- bination of the Zeeman interaction and the spin-rotation interaction that removes the degeneracy at zero electric field, and the induced splittings are small because the spin-rotation interaction is small.