The result obtained agrees very well with profile (ii) of Fig. 9(a), showing that the molecules do indeed follow the field adiabatically once V$_{lo}$ = 1 . 45 kV, and showing that their motion through the decelerator is well understood in this case. The central peak in the simulation is slightly broader and slightly smaller than in the experiments, but we find these features to be sensitive to the initial spatial distribution of molecules in the source, which is quite uncertain. In this paper we have shown, both theoretically and experimentally, that nonadiabatic transitions occurring in a Stark decelerator can result in a significant loss of molecules. When the decelerator switches, the rotation of the electric field vector drives transitions to other M Figure 9(b) shows the results of simulating these CaF experiments. We simulate the motion of molecules in all 9 M$_{N}$ substates of N = 4, and then use our knowledge of the correlation between the M$_{N}$ states at high field and the F states at low field to calculate how many molecules are detected in F = 5 (see Fig. 7). Profile (i) is the result expected when the field is static, and serves to normalize the other profiles, exactly as for the experimental data. Almost all of the molecules transmitted are those in the M$_{N}$ = 0 and 1 states, as expected since these are the low-field seeking states. Profile (ii) is the result obtained when the decelerator is switching and we assume that molecules always follow the field adiabatically. Again, although we simulate all the M$_{N}$ states only the 0 and 1 states make a substantial contribution to the final signal. To obtain profile (iii) we have simulated the case of V$_{lo}$ = 0, where the loss due to nonadiabatic transitions is most severe. If we do this simulation in the same way as we did for the LiH case, assuming that molecules are immediately lost if they are switched out of the M$_{N}$ = 0 state, we find that the only molecules transmitted are the small bunch that are phase-stable. All of the un-trapped molecules are lost because the transition probability is high over a substantial region of the decelerator. This is not what happens in the experiments. Molecules are focussed in both the M$_{N}$ = 0 and M$_{N}$ = 1 states, and those that enter the decelerator in a high-field seeking state, or are switched into a high-field seeking state, may subsequently be switched to a low-field seeking state and thereby be transmitted. Indeed, the transition proba- bilities are so high that we can expect many of the un- trapped molecules to undergo several changes of state as they propagate through the machine. For the simu- lation that leads to profile (iii), we have tried to cap- ture this complexity. We first calculate the position- dependent probability for transitions between each and every M state, using the same parameters as in the exper- iment, neglecting the dependence of the probabilities on the transverse coordinates, and neglecting the hyperfine structure. For each molecule, we assign an initial M state at random, solve the motion up to the moment of the first switch, re-assign the M state according to the molecule’s position and the pre-calculated probabilities, solve the motion up to the moment of the second switch, and con- tinue with this procedure until the molecule crashes or ex- its the end of the decelerator. Unlike the adiabatic case, we find that molecules in all initial M states contribute to the final signal, though 0 and ± 1 still contribute the most. The simulated profile obtained this way agrees remarkably well with the experimental data, suggesting that the calculated transition probabilities are approxi- mately correct despite the neglect of hyperfine structure, that the motion of the molecules in all relevant quantum states is well understood, and that the approximations we have made are reasonable. proximately adiabatic in this case. We observe a narrow central peak that corresponds to a bunch of molecules that are close in phase space to the synchronous molecule. This bunch is trapped in the moving potential well of the decelerator. We also see four smaller narrow peaks, two on either side of the main peak, and these correspond to bunches of molecules with speeds close to the syn- chronous speed but positions that are one and two po- tential wells ahead or behind the central bunch. Further out again are a pair of broader peaks corresponding to molecules that are not phase-stable, meaning that they are not trapped in the potential wells of the decelerator. Nevertheless, they are focussed through the decelerator, though not as effectively as in the case of static fields because the position-averaged field is only half as great when the decelerator is switching. We note that increas- ing V$_{lo}$ beyond this value of 1.45 kV does not change the time-of-flight profile, indicating that the fully-adiabatic regime has been reached. For profile (iii) the decelerator was switched between 14 kV and ground, i.e. V$_{lo}$ = 0. For this case, the minimum field is 2.7 kV/cm and the minimum splitting is 1 . 0 × 10 $^{7}$rad/s. The number of non phase-stable molecules is drastically reduced as we would expect since the maximum rotation rate is considerably larger than the minimum Stark splitting and so the loss due to nonadiabatic transitions is severe. The number of phase-stable molecules is also reduced but by a much smaller factor. This is what we expect for a synchronous phase angle of zero because, taking snapshots at each of the switch moments, the phase-stable molecules follow closed trajectories centred on θ = 0 in the phase-space plot of Fig. 1(c), and only some fraction of those trajecto- ries overlap the zone around − 90 ◦ where transitions are likely. The total number of molecules transmitted by the decelerator in this case is 22% of the number transmitted in the adiabatic case. For profile (iv) the value of V$_{lo}$ is 500 V. In this case, the minimum field is 5.3 kV/cm and the minimum Stark splitting is 4 . 0 × 10 $^{7}$rad/s. This is still not sufficient to avoid transitions and we see that the degree of loss is intermediate between cases (ii) and (iii) as we would expect. Again, the broad wings of the time-of-flight profile are reduced in amplitude far more than the central narrow peak. IV. CONCLUSIONS 10