EPJ manuscript No.
(will be inserted by the editor)
Accumulation of Stark-decelerated NH molecules in a
magnetic trap
Jens Riedel
1,2
, Steven Hoekstra
1,3
, Wolfgang Jäger
4
, Joop J. Gilijamse
1
, Sebastiaan Y.T. van de Meerakker
1
, and
Gerard Meijer
1
1
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
2
Present address: Bundesanstalt für Materialforschung und -prüfung, Richard-Willstätter-Str. 11, D-12489 Berlin, Germany
3
Present address: Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, 9747 AA Groningen, The
Netherlands
4
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
Received: date / Revised version: date
Abstract. Here we report on the accumulation of ground-state NH molecules in a static magnetic trap. A
pulsed supersonic beam of NH (a
1
∆) radicals is produced and brought to a near standstill at the center of a
quadrupole magnetic trap using a Stark decelerator. There, optical pumping of the metastable NH radicals
to the X
3
Σ
−
ground state is performed by driving the spin-forbidden A
3
Π←a
1
∆ transition, followed by
spontaneous A → X emission. The resulting population in the various rotational levels of the ground state is
monitored via laser induced fluorescence detection. A substantial fraction of the ground-state NH molecules
stays confined in the several milliKelvin deep magnetic trap. The loading scheme allows one to increase the
phase-space density of trapped molecules by accumulating packets from consecutive deceleration cycles in
the trap. In the present experiment, accumulation of six packets is demonstrated to result in an overall
increase of only slightly over a factor of two, limited by the trap-loss and reloading rates.
1 Introduction
Cold and ultra-cold atoms have had a major impact on
modern physics and the ensuing studies have revolution-
ized our view of the quantum world. An analogous gener-
ation of studies on cold and ultra-cold neutral molecules
promises to have similar, perhaps even farther reaching,
consequences. The added degrees of freedom in molecu-
lar systems, such as rotation, vibration and electric and
magnetic moments, provide additional handles by which
to manipulate them. For these reasons, research on cold
and ultra-cold molecules has rapidly become a mature re-
search field [1].
Cold and ultra-cold molecules are anticipated to have
widespread applications, and the field is characterized by
the enormous variety of experimental methods that have
been developed to produce samples of these. The atomic
physicists in this field have perfected the methods to as-
semble ultra-cold molecules from ultra-cold atoms using
photoassociation or association through magnetically tuned
Feshbach resonances. These methods are limited mainly to
alkali atoms, but can produce dense samples of molecules
in the ultra-cold regime [2]. The molecular physicists have
developed methods to bring pre-existing molecules to low
temperatures by, for instance, thermalizing them with a
cryogenic buffergas [3] or by manipulating their motion
with external fields [4]. While applicable to a wider vari-
ety of molecular systems, these techniques only reach into
the cold (1 mK - 1 K) regime with considerable lower num-
ber densities. Nevertheless, these methods can be used to
load neutral molecules into magnetic or electrostatic traps
in which a further phase space density increase might be
obtained via cooling through, for example, evaporative or
laser cooling [5].
An alternative approach to increase the phase space
density of trapped ground-state molecules is to add new
molecules to the trap, without losing or heating the ones
that are already trapped. Here, we experimentally demon-
strate the accumulation of ground-state NH radicals in a
magnetic trap, following a detailed proposal and ending a
ten year quest [6]. The essence of the proposal is that NH
(a
1
∆) radicals, brought to a standstill using electric fields,
can be transferred to the X
3
Σ
−
ground state via optical
pumping on the spin-forbidden A
3
Π←a
1
∆ transition fol-
lowed by spontaneous emission to the ground state. This
laser induced spontaneous emission process provides a uni-
directional path from the metastable state to the ground
state of NH. In their ground state, the NH radicals are
hardly influenced by electric fields, but can be trapped
using magnetic fields. By repeating this scheme, ground-
state NH molecules can be accumulated in the magnetic
trap. The crucial step in this approach is the transfer of
stationary molecules into a trap in a dissipative fashion,
and the underlying strategy is much more generally appli-
cable than just to NH; similar schemes have been proposed
2 Jens Riedel et al.: Accumulation of Stark-decelerated NH molecules in a magnetic trap
and used by others to accumulate atoms or molecules in
magnetic or optical traps [7,8].
X
3
Σ
-
A
3
Π
Transfer
(584 nm)
a
1
Δ
0 100 200
10
20
-1
0
1
Magnetic Field (Gauss)
Electric Field (kV/cm)
Energy (GHz)
0
M''
-0.5
0.0
0.5
0 100 200
0
2
4
-2
0
2
-4
Energy (cm-1)
M
Ω
Electric Field (kV/cm)
-2
4
Decay
(336 nm)
(τ
>2.7 s)
(τ
=450 ns)
metastable
ground state
Fig. 1. Schematic representation of the electronic states of NH
that are of relevance to the accumulation scheme. In the long-
lived a
1
∆(v = 0, J = 2) state, the NH radicals experience a
large Stark shift, as shown in the inset. Both the Stark shift
(dashed curve) and the Zeeman shift (solid curves) of the lowest
rotational level (N” = 0, J” = 1) in the X
3
Σ
−
state are shown
as well. For the Stark shift, the different M-components are
unresolved. Note the different scales for both insets (reprinted
from [6]).
In Figure 1 the electronic states of the NH molecule
that are of relevance to the accumulation scheme are schemat-
ically shown. The spin-forbidden A
3
Π(v
0
= 0)←a
1
∆(v =
0) transition around 584 nm, via which the NH molecules
are optically pumped to the X
3
Σ
−
(v” = 0) ground state,
has been observed and analyzed in detail before [9]. In
that work, the (efficiency of the) various pathways to bring
the metastable NH radicals to the lowest rotational level
in the electronic and vibrational ground state has been
discussed. We report here on the direct probing of the
resulting population distribution of the rotational levels
in the ground state of NH, using a pump-probe detec-
tion scheme. The production of an intense pulsed beam
of metastable NH radicals, their deceleration to a stand-
still and their subsequent confinement in an electrostatic
trap has also been previously reported upon [10]. Here,
we report on the implementation of a quadrupole mag-
netic trap directly behind the Stark decelerator, following
the approach demonstrated by others for ground-state OH
radicals [11]. We first demonstrate magnetic trapping of
the NH radicals in their metastable state. We then induce
the unidirectional transfer of the metastable molecules to
the ground state, and demonstrate magnetic trapping of
ground-state NH molecules. By repeating the trap load-
ing process, ground-state NH molecules from consecutive
loading cycles are accumulated in the trap.
2 Experimental
For the formation of NH, a molecular beam of ≈1 vol %
hydrazoic acid (HN
3
) seeded in Kr is intersected with a fo-
cused 50 mJ/pulse beam of the fourth harmonic (λ = 266
nm) of a pulsed Nd:YAG laser (Quanta Ray, Indi Se-
ries) near the exit of a silica capillary mounted on the
tip of a pulsed supersonic valve (Parker, General Valve).
The HN
3
was prepared by the thermic reaction of sodium
azide (NaN
3
, Sigma Aldrich) with an excess of lauric acid
at T=80
◦
C and p=1 mbar [12]. In this photodissociation
scheme the majority of NH is formed in the desired a
1
∆
state [13]. We used Kr as carrier gas even though its expan-
sion forms a relatively fast beam (v≈ 420−480 m/s, ∆v
20% FWHM) since the heavier Xe is known to efficiently
quench the NH (a
1
∆) molecules [13]. While the supersonic
jet expansion assures an efficient rovibrational cooling of
the nascent NH molecules in the a
1
∆ electronic state, no
electronic relaxation occurs. After passing a skimmer, a
hexapole is used to couple the metastable NH radicals that
are in low-field-seeking levels into the Stark decelerator.
The molecular beam machine that has been used for these
experiments [14] and its application to the deceleration of
metastable NH radicals [10] have been described in detail
before. For the experiment reported here, the decelerator
serves the purpose to produce a spatially well-defined and
slow packet of NH radicals in the a
1
∆(v = 0, J = 2) level.
Long. Position / mm
Magnetic field
Electric field ( / 10)
Potential energy / cm
-1
Permanent Magnets
Laser Beam
a)
b)
c)
-4 -2 0 2 4
0.00
0.05
0.10
Fig. 2. Schematic drawing (a) and photograph (b) of the
permanent magnetic trap. In (c) the loading potential and
the trapping potential for NH (a
1
∆(v = 0, J = 2)) radicals is
shown with respect to the midpoint between the two disc-
shaped electrodes.
After deceleration to a speed of about 20 m/s the
molecular packet enters the magnetic trap. The trap con-
sists of two disc-shaped nonmagnetic stainless steel elec-
trodes placed 10 mm apart. Inside these electrodes strong
permanent magnets are embedded, forming a quadrupole
magnetic trap. Some of the technical details as well as a
photograph of the trap can be seen in Figure 2. When the
molecules enter this trap through a center hole in the first
electrode, voltages of ± 20 kV are applied to the two elec-
trodes. The slow molecules in their low-field-seeking state
are stopped by the resulting electric field configuration
that peaks in the center between the electrodes; there, the
potential energy (Stark energy) of metastable NH radicals
in the J = 2, M
J
Ω = −4 level amounts to ≈ 0.35 cm
−1
.
The two permanent NdFeB N50 magnetic discs (IBS Mag-
Jens Riedel et al.: Accumulation of Stark-decelerated NH molecules in a magnetic trap 3
net, Berlin) are aligned parallel to the electrodes and cre-
ate a zero of the magnetic field at a position that is 2 mm
closer to the exit of the decelerator than where the maxi-
mum of the electric field is. The depth of the magnetic trap
is limited by the presence of the electrodes to 0.035 cm
−1
(5.0 mK) and 0.053 cm
−1
(7.6 mK) for metastable NH
molecules in the (J = 2, M = 2) level and for ground-state
NH molecules in the (N” = 0, J” = 1, M” = 1) level, re-
spectively. The laser light for the optical pumping and
detection of the molecules passes through the center of
the magnetic trap, perpendicular to the molecular beam
axis. The laser induced fluorescence (LIF) is collected by a
fused silica lens through a central hole in the last trapping
electrode, spectrally filtered and detected by a photomul-
tipler tube.
The NH (a
1
∆) radicals are detected by observing the
A
3
Π → X
3
Σ
−
fluorescence after driving the spin-forbidden
A
3
Π ← a
1
∆ transition with the ≈ 50 mJ output of a
pulsed dye amplifier (Sirah, pumped by a Powerlite, Con-
tinuum), seeded at λ = 584 nm by a SHG Nd:YVO
4
(Mil-
lenia V, Spectra-Physics) pumped ring-dye laser (380A,
Spectra-Physics). To probe the NH molecules in their X
3
Σ
−
ground state, ≈ 3 mJ of the λ = 305 nm output of a
Nd:YAG (Surelight, Continuum) pumped pulsed dye laser
(Narrowscan, Radiant-dyes) is used to excite the A
3
Π, v
0
= 1
← X
3
Σ
−
, v” = 0 transition. As the electronic relaxation
occurs predominantly via the diagonal v
0
= 1 → v” = 1
band, the fluorescence at λ = 336 nm can be readily sep-
arated from the scattered light of the excitation laser.
3 Results
3.1 Magnetic trapping of NH (a
1
∆)
To optimize the relevant timings of the deceleration pro-
cess, such as to produce a cloud of NH radicals with the
highest possible density and the lowest possible tempera-
ture at the center of the magnetic trap, it is rather conve-
nient that these radicals can also be magnetically trapped
while in the metastable state. For optimum loading of the
trap, the molecules need to have just the right amount
of kinetic energy to overcome the potential barrier near
the entrance of the magnetic trap and to subsequently be
stopped by the electric field near the trap center. The den-
sity of magnetically trapped NH (a
1
∆, v = 0, J = 2, M = 2)
radicals was maximized by iteratively changing the exper-
imental conditions while monitoring the intensity of the
LIF at 336 nm. For this procedure, a set of parameters
obtained from a one-dimensional trajectory calculation
served as an initial guess. During the manual optimiza-
tion, not surprisingly, the timings of the last few stages
of the decelerator ("buncher" in Figure 2a) and of the
loading potential proved to be most critical.
The measured intensity of the LIF signal at optimum
settings is depicted in Figure 3 as a function of time after
production of the metastable NH molecules via photoly-
sis. The first maximum after around 8 ms results from the
molecules that come to a standstill on the electrostatic
stopping slope. The decelerated NH molecules are in the
5 10 15 20 25 30 35 40 45
0.0
0.2
0.4
0.6
0.8
1.0
1.2
!
!
LIF- intensity-/-a.-u.
time-/-ms
0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
!
!
LIF-intensity -/-a.-u.
time-/-s
Fig. 3. Intensity of the LIF signal of NH (a
1
∆, v = 0, J = 2)
radicals at the center of the magnetic trap as a function of time.
The slow metastable molecules enter the magnetic trap about
8 ms after their production in the beam source. Only half of the
injected molecules will be in a magnetically low-field-seeking
level and remain in the trap. Oscillations of the density of
trapped metastable NH radicals at the trap center are clearly
observed. In the inset, the intensity of the LIF signal is shown
on a longer time-scale, both with (solid black squares) and
without (open circles) metastable NH molecules in the trap,
from which a 1/e trapping time of 350 ± 40 ms is deduced.
M
J
Ω = −4 component of the J=2 level (the M
J
quantum
number refers to the projection along the electric field),
which splits into a M = 2 and a M = −2 component (M
now refers to the projection along the magnetic field) in
the magnetic field. Only the M = 2 component is low-field
seeking in a magnetic field, thus explaining the reduction
in fluorescence intensity after the first peak. As the trap-
ping volume is large compared to the volume of the incom-
ing packet of molecules and compared to the interaction
volume with the laser, oscillations are observed in the flu-
orescence intensity. These oscillations, with a period of
about 6 ms, reflect a ’breathing’ like motion of the molec-
ular ensemble in the trap. In the inset, the LIF signal is
shown on a timescale of 1 second. The density in the trap
is seen to exponentially decay with time, and a 1/e decay
time of 350 ± 40 ms is extracted from these data. The
dominant trap-loss channel is collisions with background
gas in the approximately 3 · 10
−8
mbar vacuum.
3.2 Optical pumping to the ground state
The uni-directional spontaneous decay from the A
3
Π state
to the ground state is an essential step for the accumula-
tion of ground-state NH molecules in a magnetic trap.
The distribution over the ground-state ro-vibrational lev-
els that occurs after spontaneous emission is governed by
the Franck-Condon and Hönl-London factors. The A − X
transition in NH is almost perfectly diagonal and the v
0
= 0
−v” = 0 band has a Franck-Condon factor of better than
0.999 [15]. To optimize the build-up of density in a single
rotational level, preferentially the rotational ground state,
4 Jens Riedel et al.: Accumulation of Stark-decelerated NH molecules in a magnetic trap
only the intermediate rotational level in the A
3
Π, v
0
= 0
state needs to be chosen appropriately.
32760 32780 32800 32820 32840 32860
0.0
0.2
0.4
0.6
0.8
1.0
1.2
LIF-intensity-(arb.units)
laser-frequency-(cm
?1
)
1.2
1.4
1.6
1.8
2.0
2.2
N’’=0,-J’’=1
(0,F
3
)
(3,F
1
)
(2,F
2
)
(2,F
1
)
(1,F
3
)
(1,F
2
)
(0,F
3
)
(2,F
1
)
(1,F
2
)
(0,F
3
)
(3,F
1
)
(2,F
2
)
Fig. 4. Observed fluorescence excitation spectra, prob-
ing the population in the ground state of NH on the
A
3
Π, v
0
= 1 ← X
3
Σ
−
, v” = 0 transition, together with simu-
lated spectra. The upper and the lower spectrum, vertically
offset for clarity, have been obtained after optical pumping
from the metastable state via the positive and negative par-
ity component, respectively, of the J’=1 rotational level in the
A
3
Π
1
, v
0
= 0 spin-orbit multiplet. The lines in the upper spec-
trum originate from the N"=0, J"=1 level when indicated and
from the N"=2 level otherwise; all lines in the lower spectrum
originate from the N"=1 level. The (J’, F
i
) labeling of the ro-
tational levels in the A
3
Π state is given in the spectra.
In Figure 4, two different fluorescence excitation spec-
tra, probing the population in the lowest rotational levels
of the electronic and vibrational ground state, are shown.
As the Λ-doublet splitting of the a
1
∆, v = 0, J = 2 level is
sub-MHz [16], both parity components of this metastable
level are expected to be populated under our experimental
conditions. The upper (lower) spectrum is obtained after
optical pumping from the metastable state via the upper
(lower) Λ-doublet component of the J
0
= 1 level in the
A
3
Π
1
spin-orbit manifold, via which exclusively ground-
state levels with negative (positive) parity can be reached.
The parity of the rotational levels in the X
3
Σ
−
state is
given by (−1)
N”+1
, e.g. the N” = 0, J” = 1 ground-state
level can only be reached via the upper Λ-doublet com-
ponent of the A
3
Π
1
, J
0
= 1 level. Simulated spectra, using
the known Hönl-London factors for the spontaneous decay
from the selected rotational levels in the A
3
Π, v
0
= 0 state
as well as for the excitation from the ground state to the
A
3
Π, v
0
= 1 state, are shown as solid curves in both spec-
tra and are seen to reproduce the observations very well.
The three strongest lines in the upper spectrum all origi-
nate from the lowest rotational level in the X
3
Σ
−
, v” = 0
ground state of NH, as explicitly indicated in the Figure;
the four remaining fitted lines originate from the different
spin components of the N"=2 level. The
R
P
31
(1) transi-
tion around 32860 cm
−1
is observed to be stronger than
expected from the simulations; although care was taken
not to saturate the transitions, this has probably not been
completely avoided in the measurements. All fitted lines in
the lower spectrum originate from the different spin com-
ponents of the N"=1 level. To identify the transitions, the
(J’, F
i
) labeling of the rotational levels in the A
3
Π state
(F
1
for
3
Π
2
; F
2
for
3
Π
1
; F
3
for
3
Π
0
) is given in the spec-
tra [17]. The small peaks in the measured spectra around
32807 and 32857 cm
−1
originate from rotational transi-
tions in the c
1
Π, v
0
= 1 ← a
1
∆, v = 0 band that happen
to lie in the same spectral region.
0 . 0 0 . 2 0 . 4 0 . 6
0 . 0
1 . 0
2 . 0
L I F i n t e n s i t y / a . u .
t i m e / s
Fig. 5. Intensity of the LIF signal of trapped ground-state
NH molecules as a function of time. At time equal zero the
ground-state molecules are produced. The measured LIF signal
is shown after a single loading event (open circles) and over the
course of six consecutive loading cycles (solid squares), together
with the best fitting curves, shown in blue and red, respectively.
The intensity of the LIF signal immediately after a loading
event converges to the value indicated by the dashed horizontal
line.
3.3 Accumulation of ground-state NH molecules
The slow ground-state NH molecules are created near the
center of the quadrupole magnetic trap and can remain
trapped, provided they have a sufficiently low kinetic en-
ergy. To detect these trapped molecules, the same off-
resonant LIF detection scheme as described in the pre-
vious paragraph is used. By recording the LIF signal as
a function of time after production of the ground-state
molecules, the time-dependence of the density in the trap
can be monitored. In Figure 5 the LIF signal of trapped
NH (X
3
Σ
−
, v” = 0, N” = 0, J” = 1, M” = 1) molecules is
shown after loading a single packet into the magnetic trap
Jens Riedel et al.: Accumulation of Stark-decelerated NH molecules in a magnetic trap 5
(open circles). It is difficult to extract the density of trapped
molecules from a measurement of this type, but we esti-
mate to have about 10
4
ground-state NH molecules in the
trap, at a density of about 10
5
/cm
3
. From a fit of these
data to an exponentially decaying curve, a 1/e trapping
time of τ = 180 ± 20 ms is deduced. This trapping time is
shorter than observed for the metastable NH molecules,
probably because the background pressure was slightly
higher during the accumulation measurements.
As the pulsed molecular beam machine and the laser
systems are running at a repetition frequency f of 10 Hz,
every 0.1 s a new packet of Stark-decelerated NH mole-
cules arrives near the trap center and can be transferred
to the ground state. Although the pulsed beam of carrier
gas and undecelerated NH radicals also passes through the
trap, its density is rather low there and is not expected to
lead to any observable trap loss. The intensity of the LIF
signal that is observed when six consecutive packets of NH
molecules are accumulated in the magnetic trap is shown
in Figure 5 as well (solid black squares). At any time dur-
ing the trapping process, the LIF signal is expected to
show an exponential decay with the same time constant τ
mentioned above. Under the assumption that the density
of molecules that is added to the trap per deceleration cy-
cle is always the same, the LIF signal immediately after
loading the n-th (n ≥ 1) packet is a factor
n−1
X
i=0
e
−i/fτ
(1)
larger than the signal immediately after loading the first
packet. A fit of the data according to this model, in which
the overall vertical scale is the only adjustable parameter,
is shown as well. The sum in the equation above converges
to a value of 1/(1 − e
−1/f τ
), which is indicated by the hor-
izontal dashed line in Figure 5. In the present experiment,
we can at most increase the density of accumulated mo-
lecules by a factor 2.35 (± 0.20) relative to the density
after a single loading event. This limiting value is already
almost reached after loading six packets, which is why we
limited the loading sequence to this.
4 Conclusions
The results presented here demonstrate that the scheme
proposed about a decade ago to accumulate ground-state
NH radicals in a magnetic trap indeed works [6]. At the
same time, it shows the limitations of this approach, as
the gain in density that has been obtained thus far has
only been slightly more than a factor of two. One might
wonder whether an equally large gain could have been ob-
tained by using a single loading cycle and by having the
molecular beam source further optimized instead, for in-
stance, and this might indeed well have been the case. If
one would like to pursue accumulation of multiple packets
in the trap in the future, one has to make the product f τ
(which is the convergence limit of the sum in equation (1)
when f τ >> 1) as large as possible, i.e. one has to increase
the product of the repetition frequency with which the
trap can be reloaded and the trapping time. Given that in
the present experiment the NH molecules are transferred
into the magnetic trap within 10 milliseconds after they
leave the beam source, the repetition frequency could in
principle be an order of magnitude larger. To increase the
trapping time, the rate of collisions with background gas
has to be reduced, i.e. the vacuum needs to be improved.
Losses due to nonadiabatic transitions near the trap cen-
ter have to be avoided as well, and a Ioffe-Pritchard type
magnetic trap might be required. At some point, losses
due to optical pumping by blackbody radiation will be-
come the dominating loss channel [18], in which case one
would need to cool the trap. It has recently been demon-
strated that in a cryogenic setup, ground-state NH mo-
lecules can be magnetically trapped with 1/e lifetimes of
over 20 seconds [19]. In such a cryogenic trap, the density
could be increased by more than a factor of 200 via this
accumulation scheme, even with reloading at the present
frequency of 10 Hz.
5 Acknowledgements
This work is supported by the ESF EuroQUAM programme,
and is part of the CoPoMol (Collisions of Cold Polar Mo-
lecules) project. We thank Henrik Haak for the design of
the integrated magnetic trap and Boris G. Sartakov for
his help with the analysis of the observed LIF spectra.
WJ thanks the Alexander von Humboldt Foundation for
a Research Award.
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![Fig. 1. Schematic representation of the electronic states of NH that are of relevance to the accumulation scheme. In the longlived a1∆(v = 0, J = 2) state, the NH radicals experience a large Stark shift, as shown in the inset. Both the Stark shift (dashed curve) and the Zeeman shift (solid curves) of the lowest rotational level (N” = 0, J” = 1) in the X3Σ− state are shown as well. For the Stark shift, the different M-components are unresolved. Note the different scales for both insets (reprinted from [6]).](/figures/fig-1-schematic-representation-of-the-electronic-states-of-4ytpq6qa.webp)
