Zeeman deceleration of H and D

Hydrogen and deuterium atoms in supersonic jet expansions have been decelerated using a multistage Zeeman decelerator. The properties of the decelerator have been completely characterized in a series of experiments in which (i) the initial longitudinal velocities of the decelerated atoms, (ii) the maximum magnetic field strength, and (iii) the duration of zero-field intervals between successive field pulses in neighboring deceleration stages were systematically varied. Experiments using Ar and Kr as carrier gases have clearly revealed that the H atoms are located at the surface of the jet expansion cone in each case. Comparison of the results of these experiments with numerical simulations of the atom trajectories through the decelerator provides a full description of the phase-space distribution of the decelerated atoms. Evidence is presented of transverse guiding of the beam and of a partial redistribution of the H atom population among the $M_F$ components of the $F=1$ manifold at times when the magnetic field strength approaches zero.

Figure 1

Schematic diagram of the experimental setup (not to scale). The H (D) atomic beam is prepared in a pulsed supersonic expansion by $193\mathrm{nm}$ photolysis of $\mathrm{N}{\mathrm{H}}_3$ or $\mathrm{N}{\mathrm{D}}_3$, respectively. After propagating through a $2\mathrm{mm}$ diameter skimmer, the beam enters the Zeeman decelerator. The TOF from the point of production of the H (D) atoms to the end of the decelerator is measured by two photon excitation to Rydberg states followed by pulsed electric field ionization. The resulting ions are then detected on a microchannel plate (MCP) detector (not pictured). The phase angle $\varphi$ with respect to the first solenoid of the decelerator is indicated in the lower part of the figure (see text for details).

Figure 2

(a) Measurement of the temporal profile of the magnetic field on axis at the center of one of the decelerator solenoids made via integration of the electrical potential generated in a small pick-up solenoid. For this particular solenoid, the rise time $\delta t_r$ and fall time $\delta t_f$ amount to 4.7 and $3.9\mu \mathrm{s}$, respectively. (b) Schematic timing diagram indicating the definition of the time delay $\Delta t$ between the initiation of the switch-off and switch-on of the magnetic field in adjacent solenoids (labeled $n$ and $n+1$) in the decelerator.

Figure 3

(Color online) (a) The Zeeman effect in the $1{}^{2}S$ ground state of atomic hydrogen. The hyperfine interaction splits the ground state into $F=0$ and $F=1$ states, where $F$ is the total spin quantum number. Upon application of the magnetic field, the $F=1$ state splits into a manifold of three $M_F$ states, two of which are shifted to higher energies and one to lower energy as the field strength increases. (b) Map of the longitudinal and radial magnetic field distribution in each solenoid of the Zeeman decelerator calculated for an operating current of $250\mathrm{A}$. The position and spatial extension of the solenoid is indicated by the thick black line on the axis representing the longitudinal position.

Figure 4

(a) General timing scheme for the operation of the Zeeman decelerator. The H atoms are produced at time $t_{\mathrm{exc}}$ with the first solenoid of the decelerator then switched off at time $t_0$ such that the synchronous atom enters the decelerator at a predefined phase angle. The two-photon excitation and field ionization take place at a time $t_{\det }$ such that the TOF is given by $t_{\det }-t_{\mathrm{exc}}$. (b) A typical computer controlled pulse sequence calculated to decelerate a bunch of H atoms with a mean initial longitudinal velocity of $527\mathrm{m}∕\mathrm{s}$ to a final velocity of $415\mathrm{m}∕\mathrm{s}$ over seven decelerator stages switched at a 55° phase angle and operated at a current of $250\mathrm{A}$. The temporal overlap $\Delta t$ between consecutive pulses in this sequence is $-1\mu \mathrm{s}$ (see Fig. 2). As the atoms lose longitudinal kinetic energy, the pulses become longer as can be seen in (c) where the duration of the pulses applied to each of the solenoids is plotted against the time at which each is switched on.

Figure 5

TOF profiles demonstrating the deceleration of H atoms using pulse sequences calculated for synchronous atoms with initial longitudinal velocities of 569, 548, 527, and $506\mathrm{m}∕\mathrm{s}$ when the decelerator was operated at a current of $250\mathrm{A}$ and a phase angle of 55°. (a) Experimental TOF profiles, (b) simulated TOF profiles. The final velocities of the decelerated atoms determined from the simulations are indicated alongside the vertical arrows in panel (b). The bottom profile in each panel represents the TOF of the H atoms with the decelerator off. For clarity of presentation the upper profiles in each panel are vertically offset.

Figure 6

(Color online) Simulated characteristics of the beam of H atoms. (a) Color map indicating the H atom signal as a function of longitudinal velocity and TOF. The decelerator is assumed to operate at $250\mathrm{A}$ with a pulse sequence calculated to decelerate a synchronous atom with an initial longitudinal velocity of $506\mathrm{m}∕\mathrm{s}$ to a velocity of $390\mathrm{m}∕\mathrm{s}$ at a 55° phase angle. The color gradient indicates the number of atoms with a particular longitudinal velocity. The feature enclosed by box A corresponds to the bunch of atoms unaffected by the operation of the decelerator, that in box B arises as a result of the combination of longitudinal bunching and transverse guiding in the decelerator, and that labeled C represents the bunch of decelerated atoms. The TOF profile corresponding to this velocity distribution is represented in (b) by the solid curve, while the dashed curve represents the simulated TOF profile with the decelerator off.

Figure 7

TOF profiles demonstrating the deceleration of H atoms at different decelerator operating currents. The deceleration pulse sequence was calculated for a synchronous atom with an initial longitudinal velocity of $506\mathrm{m}∕\mathrm{s}$ and for a phase angle of 55°. The current at which the decelerator was operated was varied from $50\text{to}250\mathrm{A}$ (corresponding to a maximum magnetic field strength on axis in each solenoid of 0.3 and $1.4\mathrm{T}$, respectively). (a) Experimental TOF profiles, (b) simulated TOF profiles. The final velocities of the decelerated atoms determined from the simulations are indicated alongside the vertical arrows in panel (b). The bottom profile in each panel represents the TOF of the H atoms with the decelerator off. For clarity of presentation the upper profiles in each panel are vertically offset.

Figure 8

TOF profiles recorded for a pulse sequence calculated for a synchronous atom with an initial longitudinal velocity of $506\mathrm{m}∕\mathrm{s}$ traversing the decelerator at a phase angle of 55° as a function of the delay time $\Delta t$ between the switch-off and switch-on of adjacent solenoids. The decelerator was operated at a current of $250\mathrm{A}$ in each case. The bottom profile is the TOF of the H atoms to the detection point when the decelerator is off. For clarity of presentation the upper profiles are vertically offset.

Figure 9

Simulated TOF profiles for pulse sequences calculated for a synchronous atom with an initial longitudinal velocity of $506\mathrm{m}∕\mathrm{s}$ traversing the decelerator at a phase angle of 55°. (a) The probability $p$ of an $M_F$-changing transition occurring at the switch-off of each of the solenoids increases in increments of 0.1 for each of the profiles moving down the figure. The decelerator was considered to operate at a current of $250\mathrm{A}$ throughout. The bottom profile is the simulated TOF of the H atoms to the detection point when the decelerator was off. (b) Comparison between simulated TOF profiles calculated assuming that $p=0$ and using pulse sequences for which $\Delta t=-1\mu \mathrm{s}$ (upper trace) and $\Delta t=4\mu \mathrm{s}$ (middle trace), and for which $\Delta t=4\mu \mathrm{s}$ with $p=0.4$ (bottom trace). For clarity of presentation the upper profiles in each figure are vertically offset.

Figure 10

TOF profiles demonstrating the deceleration of H atoms seeded in Kr for which the synchronous atom has an initial longitudinal velocity of $422\mathrm{m}∕\mathrm{s}$ and traverses the decelerator at a phase angle of 55°. The current at which the decelerator was operated was varied from $50\text{to}250\mathrm{A}$ (i.e., the maximum magnetic field strength on axis in each solenoid was varied from $0.3\text{to}1.4\mathrm{T}$). The left panel (a) contains the experimental data with the simulated data presented in the right panel (b). The simulated final velocities of the atoms are indicated by the vertical arrows in panel (b). The bottom profile in each panel represents the TOF of the H atoms when the decelerator was off. For clarity of presentation the upper profiles in each panel are vertically offset.

Figure 11

TOF profiles for (a) H atoms and (b) D atoms seeded in Kr. In both cases the solid curves indicate the measured TOF profiles for pulse sequences calculated for the deceleration of a synchronous atom with an initial longitudinal velocity of $422\mathrm{m}∕\mathrm{s}$ that traversed the decelerator at a phase angle of 55°. The decelerator was operated at a current of $250\mathrm{A}$ in each case (i.e., the maximum magnetic field strength on axis in each solenoid was $1.4\mathrm{T}$). The dashed curves indicate the measured TOF profiles at the detection point when the decelerator was off.