9 2.0 2.2 2.4 2.6 Time of flight (ms) Normalized signal (a) (i) (ii) (iv) (iii) 0.2 0.4 0.6 0.8 1.0 Normalized signal (b) 0.2 0.4 0.6 0.8 1.0 0.0 0.0 2.0 2.2 2.4 2.6 Time of flight (ms) (i) (ii) (iii) 1.5 2.0 2.5 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Normalized signal Time of flight (ms) (a) (b) (c) FIG. 8: (Color online) Time of flight profiles of LiH molecules decelerated from an initial speed of 420 m/s to a final speed of 213 m/s. The deceleration parameters are V$_{hi}$ = 9 . 5 kV, V$_{lo}$ = 0, and φ$_{0}$ = 51 $^{◦}$. (a) Lower trace, experimental data. (b) Middle trace, simulation including nonadiabatic loss. (c) Top trace, simulation for the adiabatic case. In all cases the signal is normalized to that obtained in dc mode. The traces are offset for clarity. FIG. 9: (Color online) (a) Experimental time of flight profiles for CaF in the N = 4 state with a synchronous phase angle of 0 ◦ (no deceleration), a synchronous speed of 370 m/s, and an applied voltage of V$_{hi}$ = 14 kV. (i) No switching. (ii) V$_{lo}$ = 1 . 45 kV. (iii) V$_{lo}$ = 0. (iv) V$_{lo}$ = 0 . 5 kV. (b) Simulations of these experiments. All the results share a common baseline. effect on the decelerated bunch of molecules. The modi- fied simulation matches the experimental data very well indicating that this is the right loss mechanism, and that the simple procedure we have applied is a good one in this case. This procedure involves a number of simplifi- cations. We take the transition probability to be inde- pendent of the transverse coordinates. We have neglected the hyperfine structure, which is a good approximation for LiH as discussed above. By simply multiplying tran- sition probabilities, we are assuming that the superpo- sition state rapidly decoheres, which is reasonable given the field inhomogeneity. Finally, instead of calculating the trajectories of molecules that have changed state we assume that they are lost rapidly from the decelerator by being pulled onto the electrodes. In principle, a LiH molecule transferred to the | 1 , 1 〉 state during one switch could be transferred back to the | 1 , 0 〉 state during a sub- sequent switch and so be recaptured in the decelerator before being lost. However, a LiH molecule in the | 1 , 1 〉 state is lost from the decelerator on the timescale of a few switch periods, and since the transition probability is quite small everywhere, there is very little chance of this recapture process occurring. focussed through the decelerator and the time-of-flight profile is a direct reflection of the velocity distribution in the beam. For this data, the mean speed is 368m/s and the translational temperature is 5 K. The amplitudes of all the profiles are normalized to the peak of this one. For the other three profiles in Fig. 9(a) the decelera- tor is switched with a synchronous phase angle of 0 ◦ (no deceleration) and a synchronous speed of 370 m/s. The only parameter that changes between these three profiles is the value of V$_{lo}$ . For profile (ii) the decelerator was switched between V$_{hi}$ = 14 kV and V$_{lo}$ = 1 . 45 kV. In this case, the minimum electric field on the axis of the deceler- ator is raised to 12.0 kV/cm, and the corresponding min- imum splitting between the M = 0 and M = ± 1 states is 2 . 0 × 10 $^{8}$rad/s. This is larger then the maximum rotation rate (see Fig. 3) and we expect the evolution to be ap- Figure 9(a) shows experimental time-of-flight data ob- tained for CaF in the N = 4 state, when the deceler- ator high voltage is V$_{hi}$ = 14 kV. Profile (i) is the one obtained when the high voltage is applied statically to all the electrodes of the decelerator. The molecules are