Storage and adiabatic cooling of polar molecules in a microstructured trap.

Abstract

We present a versatile electric trap for the exploration of a wide range of quantum phenomena in the interaction between polar molecules. The trap combines tunable fields, homogeneous over most of the trap volume, with steep gradient fields at the trap boundary. An initial sample of up to 10(8), CH(3)F molecules is trapped for as long as 60 s, with a 1/e storage time of 12 s. Adiabatic cooling down to 120 mK is achieved by slowly expanding the trap volume. The trap combines all ingredients for opto-electrical cooling, which, together with the extraordinarily long storage times, brings field-controlled quantum-mechanical collision and reaction experiments within reach.

Full text

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arXiv:1107.2821v1 [quant-ph] 14 Jul 2011
Storage and Adiabatic Cooling of Polar Molecules in a Microstructured Trap
B.G.U. Englert, M. Mielenz, C. Sommer, J. Bayerl, M. Motsch,∗P.W.H. Pinkse,†G. Rempe, and M. Zeppenfeld‡
Max-Planck-Institut f¨ ur Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
(Dated: July 15, 2011)
We demonstrate loading, trapping and adiabatic cooling of polar molecules in a new type of
electric trap. The trap consists of two microstructured capacitor plates with an additional perimeter
electrode, allowing for homogeneous fields in the trap volume and steep fields at the trap boundary.
CH3F molecules are trapped up to 60 seconds, with a 1/e storage time of 12 seconds. Applying
different electric fields in two halves of the trap, adiabatic cooling is achieved by slowly expanding
the trap volume. The trap is ideally suited for precision studies of ultracold molecular collisions
and spectroscopy. Moreover, it combines all ingredients for the recently proposed opto-electrical
molecular cooling scheme [M. Zeppenfeld et al., Phys. Rev. A 80, 041401(R) (2009)].
PACS numbers: 37.10.Mn, 37.10.Pq
Keywords: adiabatic cooling, cold molecules, electrostatic trapping
Precise control of the motional degrees of freedom of
cold atoms has resulted in fundamental achievements in
precision measurements and quantum technology. Com-
pared to the previous focus on atomic systems, molecules
offer novel possibilities due to additional internal de-
grees of freedom and strong long-range interactions. For
example, cold molecules are promising candidates for
precision tests of fundamental symmetries [1, 2], allow
unique approaches to quantum computation [3, 4], offer
new quantum-mechanical reaction channels [5, 6], and
can condense to new quantum phases of matter [7, 8].
However, realizing a comparable degree of control over
molecules as for atoms remains a challenge, mainly due
to the general lack of fast optical cycling transitions. In
this respect, it is advisable to make use of any advan-
tages offered by molecules, in particular the strong in-
teraction of dipolar molecules with electrostatic fields.
A primary application for these interaction is the trap-
ping of molecules [9–12]. By providing long interrogation
times in a compact environment, electric traps hold great
promise for fascinating applications [13–15]. Not least, a
suitable electric trap is a key component of opto-electrical
cooling [16], a general Sisyphus-cooling scheme for polar
molecules.
In this Letter we present the experimental realization
of a novel electric trap, featuring several key innovations.
Specifically, molecules are trapped in a box-like poten-
tial where tunable homogeneous offset electric fields can
be applied to a large fraction of the trap volume. High
trapping fields exist only at the trap boundary.
mogeneous fields allow molecular transitions to be ad-
dressed by lasers or microwaves with strongly suppressed
Stark broadening.Furthermore, an offset field in the
central trap region greatly reduces the presence of field
zeros, thereby suppressing losses via non-adiabatic tran-
sitions [17]. In fact, molecules are stored for up to a
minute with a 1/e time of up to 12 seconds. To achieve
such long storage times, the two trap outlets required for
loading and unloading of the molecules are closed electri-
Ho-
perimeter electrode
(a)
(c)(d)
-
++
--
+
Ez
(b)
microstructured
electrodes
substrate
3Vµ
+Vµ
-Voffset
+Voffset
region 1 region 2
-Vµ
3mm
0.9mm
+Vµ -Vµ
400µm
Ey
FIG. 1: (Color online).
(not to scale). The trap consists of a high-voltage perimeter
electrode and capacitor plates with microstructured surface
electrodes. Trap dimensions are 4cm × 2cm × 3mm. (b)-(d)
Details of the electric-field configuration and microstructure
electrode design as discussed in the text.
(a) Side view of the electric trap
cally. A unique feature of our trap is the subdivision into
two trap regions where homogeneous electric fields can be
applied independently. This allows for additional control
of the motion of the molecules, which we demonstrate
by cooling of the molecules via an adiabatic expansion in
the trap.
A schematic of the trap is presented in Fig. 1(a). Two
parallel capacitor plates produce arbitrary homogeneous
electric fields in a large fraction of the two trap regions 1
and 2.To prevent molecules from colliding with the
plate surfaces, a planar array of equidistant (400µm)
microstructured electrodes is deposited on the capaci-
tor plates. Applying opposite-polarity voltages ±Vµ to
adjacent electrode stripes creates large repelling electric
fields near the plate surfaces that exponentially decay
away from the plates [18, 19].
background field is produced by applying additional off-
set voltages ±Voffset to the two plates. Transverse con-
finement of the molecules is achieved by a high-voltage
electrode between the plates that surrounds the perime-
Between the plates, a

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2
QMS
ionization
volume
guide 1 guide 2guide 3
bend for longitudinal filtering
(radius 3.5mm)
effusive source
(N2-cooled, T=105K)
collimating
guide exit
electric trap and
ring electrode
region 2
region 1
4cm
2cm
quadrupole guide
FIG. 2: (Color online). Schematic of the setup. The slowest
molecules from a liquid-nitrogen-cooled reservoir are loaded
into the electric trap via a quadrupole guide connected to the
trap. For detection, an exit quadrupole guides the molecules
to a quadrupole mass spectrometer (QMS).
ter of the trap.
To suppress trap losses, attention must be paid to the
details of the electric fields. As shown in Fig 1(b), the in-
terference of the microstructure field with a homogeneous
offset field gives rise to a zero electric field (indicated by
crosses in Fig. 1(b)) above every second microstructure
electrode. These zeros cause trap losses in two ways:
First, molecules are likely to undergo non-adiabatic tran-
sitions, so-called Majorana flips, to states that are no
longer trapped [17]. Second, these zeros continue under-
neath the perimeter electrode, allowing molecules to leak
out of the trap volume. To reduce Majorana flips, the
microstructured electrode stripes are slightly wedged as
shown in Fig. 1(c). This produces an additional com-
ponent of the electric field Ez parallel to the stripes,
thereby eliminating the electric field zero. To avoid “leak-
ing” of the molecules from the trap, the microstructured
electrodes with the same polarity as the perimeter elec-
trode are interconnected under the perimeter electrode
(Fig. 1(d)), causing the holes to lead back into the trap.
Operating the trap requires a suitable source of
molecules and a means for their detection. This leads
to an integration of the trap in the experimental setup
as shown in Fig. 2. As a source of molecules we em-
ploy velocity filtering with an electric quadrupole guide
from a liquid-nitrogen-cooled effusive nozzle as described
in detail elsewhere [20]. This method has the advantage
of providing a large continuous flux of molecules using a
very robust setup. The geometry of the trap is specif-
ically chosen to permit the connection to a quadrupole
guide. Here, interrupting the perimeter electrode of the
trap allows two opposing electrodes of the quadrupole
guide to be connected to the trap. The other two elec-
trodes of equal polarity merge with the microstructured
plates. After trapping, the molecules are guided to the
ionization volume of a quadrupole mass spectrometer
(QMS), enabling time-resolved measurements. For sig-
nal enhancement, the guide electrodes at the exit of the
guide are bent outwards which, similar to a microwave
horn antenna, collimates the molecules onto the ioniza-
tion volume of the QMS. Note that the guide used in our
experiment consists of three independently switchable
segments, allowing loading and unloading of molecules
to be switched on or off without affecting the trapping
fields.
Great care has been taken to ensure that the molecules
experience a similar potential depth everywhere.
particular, this calls for appropriate voltage ratios to
be applied to the various electrodes.
mum used electric field strength of 60kV
±Vµ= ±1.8kV is applied to the microstructure, whereas
the perimeter electrode voltage and the voltage difference
applied to the 1stand 3rdguide during trap loading and
unloading is Vperimeter= 3Vµ= 5.4kV. For a molecular
state with an effective dipole moment of 1D, this corre-
sponds to a potential depth of kB× 1.45K. For other
trap depths, all voltages are scaled accordingly.
The measurements are carried out with fluoromethane
(CH3F), a lightweight symmetric-top molecule, but in
principle all molecules with significant Stark shifts can
be used. The density of trapped CH3F-molecules for the
maximum trapping fields is approximately 108cm−3, as
has been determined via a QMS calibration [21]. Note
that this value mainly reflects the density of molecules in
the source.
For trap characterization, we first determined the trap
lifetime by varying the holding time for molecules in
the trap. Loading and unloading is carried out at
reduced trap and guiding fields, allowing us to filter
molecules with smaller velocities and efficiently extract
these molecules, respectively. During the holding time
the voltages are increased, resulting in a deep confine-
ment for the loaded molecules. This leads to the follow-
ing experimental protocol: Initially, molecules are contin-
uously loaded into the trap for a time interval tload= 3s
at a reduced confinement field Eload. This establishes a
steady state in the trap. Measurements were performed
for two loading fields, Eload= 20kV
corresponding to slower and faster molecules, respec-
tively [20]. This allows us to analyze the dependence of
the trap lifetime on the initial velocity distribution of the
molecules. After the loading process, the trapping fields
are increased to Ehold= 60kV
cmto confine the molecules in
the trap during the holding time, thold, ranging from 1 to
60s. During this time, high negative voltages are applied
to the 1stand 3rdguide. This creates a repelling electric
field at the gaps between the guides so that molecules
that attempt to leave the trap via the entrance or exit
guide are reflected back into the trap, thereby electri-
cally closing the two outlets of the trap. After thold, the
trap and the 3rdguide are switched back to a guiding
configuration with Eunload = Eload and the molecules
are extracted from the trap during the unloading time
tunload= 3s.
Fig. 3(a) shows typical time-of-flight (TOF) signals for
In
For the maxi-
cm, a voltage of
cmand Eload= 30kV
cm,

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3
QMS Signal (counts/s)
2468 10
t (s)
1214 1618 20
0
100
200
300
400
500
600
(a)
(b)
Molecule Signal
0 102030
thold (s)
405060 70
101
102
103
100
Fit: τ=12.2(2)s
Fit: τ=9.4(2)s
Eload=20kV/cm
Eload=30kV/cm
?
FIG. 3: (Color online). (a) Trap unloading signal for Eload=
30kV
ing the trap. (b) Integrated unloading signal of the molecules
as a function of thold for two loading field strengths (20kV
and 30kV
cm). The blue (dashed) and the red (solid) line are
exponential fits for the determination of the lifetime.
cmand different holding times tholdversus time t after clos-
cm
the unloading process for different holding times. Upon
switching the 3rdguide to guiding configuration after
thold, the QMS signal increases due to the arrival of
molecules. This increase is followed by a slow decay as
the number of molecules left in the trap decreases. In
Fig. 3(b) the integrated molecule signal for the two differ-
ent loading fields is plotted as a function of thold. As can
be seen, even after thold= 60s we still measure molecules
from the trap. To determine the trap lifetime for slower
(Eload = 20kV
the data are fitted with an exponential decay function.
Evidently, slower molecules have a longer trap lifetime
which is consistent with Majorana flips being one of the
main loss mechanisms for molecules in the trap. Addi-
tional contributions might be due to collisions with the
background gas (the pressure is ∼ 1× 10−10mbar in the
trap chamber) or remaining holes in the trap. Lastly,
note that the data show slight deviations from the ex-
ponential decay function. This is due to a larger initial
decay rate which is again consistent with faster molecules
getting lost from the trap at a higher rate.
As a second test, we demonstrate the versatility of our
trap by performing adiabatic cooling of the molecules.
Here, the temperature is reduced by adiabatically ex-
panding a molecular gas from one to both trap regions.
This doubling of the trap volume is implemented by
ramping down a potential step in the middle of the trap.
As for the previous measurements, molecules are loaded
into the trap during tload= 3s with Eload= 20kV
sequently all voltages are ramped up and an electric offset
field of 20kV
cmis applied between the plates in region 1,
creating a large potential step in the trap. Due to the
large voltages, the confinement field between one of the
plates in region 1 and the perimeter electrode is zero,
causing all molecules not confined to region 2 to be lost
from the trap during the emptying time tempty= 500ms.
cm) and faster (Eload = 30kV
cm) molecules,
cm. Sub-
0
2004006008001000
1.1
1.2
1.3
1.4
1.5
170
160
150
140
130
120
tramp (ms)
1.0
Factor of Cooling
Temperature (mK)
180
190
(a)
QMS Signal (a.u.)
t (s)
(c)
?
0
tramp=5ms
tramp=1000ms
0.511.522.533.5
(b)
normalized
00.10.2
FIG. 4: (Color online). (a) Molecule temperature and cooling
factor for the adiabatic cooling versus the ramping time. (b)
Typical TOF signal. Molecules with tramp = 1000ms arrive
later and decay slower than molecules with tramp = 5ms. (c)
Close-up of the normalized rising edge signal.
Next, the offset field in region 1 is ramped down to
the offset field in region 2 in the ramping time tramp,
thereby doubling the trap volume. This expansion pro-
cess is expected to conserve the phase-space density of
the molecules if it is done adiabatically. Therefore, in
the experiment trampis varied to analyze the timescale of
adiabaticity; the subsequent holding time is chosen such
that tramp+ thold= 1.1s = const. Finally, molecules are
unloaded during tunload= 3.5s.
Figs. 4(b) and (c) compare the TOF unloading signal
for the slowest (tramp = 1000ms) and fastest (tramp =
5ms) ramping; for these two cases the most significant
signal difference is expected. As can be seen, for slower
ramping of the electric fields the molecules arrive later at
the QMS, demonstrating a slower velocity distribution.
This is corroborated by the slower decay for the 1000ms
ramp since slower molecules have a lower trap loss rate
as shown by the trap lifetime measurement. The overall
number of measured molecules is even slightly higher for
tramp= 1000ms than for tramp= 5ms. This is clear evi-
dence that the velocity reduction is not due to a filtering
process but rather that a new, shifted velocity distribu-
tion is created by the ramping process.
We estimate the molecular temperature T for the dif-
ferent ramping times according to kBT/2 = m?vz?2/2
from the rising edge of the normalized TOF signal
S(t). Here, ?vz? is the mean of the longitudinal veloc-
ity distribution ρ(vz)dvz in the exit guide which deter-
mines the normalized TOF signal. Noting that S(t) =
?∞
we find
L/tρ(vz)dvzwith L being the length of the third guide,
?vz? = L
?∞
0
1
t2S(t)dt.(1)

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4
In addition to the temperature T, we define the cooling
factor F for each ramping time as the ratio in T between
the given ramping time and the fastest ramping time.
The resulting values of T and F are shown in Fig. 4(a)
as a function of the ramping time. As expected for a
transition from a non-adiabatic to an adiabatic process,
we see a steep initial increase of the cooling factor fol-
lowed by a plateau. The transition between the two at
tramp≈ 100ms corresponds to a molecule with a typical
velocity of 6m/s traveling back and forth the full 4cm
length of the trap a total of maximally 8 times. Given the
need for a molecule to switch regions several times for the
process to be adiabatic, the frequent change in direction
of a molecule upon reflection from the microstructure
field and the need for the various velocity components
to mix, this 100ms timescale of adiabaticity therefore
seems reasonable. For tramp= 1000ms we determine a
maximum cooling factor Fmax = 1.53 ± 0.03, with the
corresponding minimal temperature Tmin= 121 ± 2mK.
To estimate the yield of the adiabatic cooling we com-
pare the experimental results with the maximum cooling
factor we expect from theory.
only confined in trap region 2. When the initial kinetic
energy of the molecules exceeds the potential barrier due
to the high electric fields in region 1, the molecules can
enter this region where they lose energy due to the po-
tential step. If this expansion of the molecular gas to
double its volume is done adiabatically, the phase-space
density is conserved and the molecular temperature is re-
duced by a theoretical factor of Fopt= 22/d, with d = 3
being the spatial degree of freedom of the contribut-
ing velocities.Comparing this theoretically expected
maximum cooling factor Fopt= 1.59 to the experimen-
tally measured value results in an experimental yield of
log(Fmax)/log(Fopt) = 92±3%. The main limitation in
the experiment is given by the non-zero ramping time of
the fastest ramping which is used as the non-adiabatic
reference point Tmax for all data points. Faster ramp-
ing than 5ms could result in the demonstration of even
higher yields, but is hard to implement due to technical
limitations of our voltage supplies.
In summary, we have presented the first experimental
demonstration of a microstructured box-like electric trap
with adjustable homogeneous offset fields. Molecules are
stored for up to 60s with a trap lifetime of 12.2 ± 0.2s
which, to our knowledge, is the longest lifetime shown for
an electric trap to date. Additionally, adiabatic cooling
has been demonstrated with a cooling factor of up to
1.53±0.03corresponding to a cooling yield of at least 92±
3%. This controlled microstructure-based manipulation
of molecules is a major step towards scalable trapping
systems as in atom chip experiments [22].
Notwithstanding the excellent performance of the trap,
further improvements are possible. For example, non-
adiabatic transitions as one of the main loss mechanisms
can be suppressed by better tailoring the microstructure
At first, molecules are
electrodes. The density of molecules in the trap can be
increased by combining the trap with, e.g., velocity fil-
tering from a cryogenic buffer-gas cooled source [21] or
via laser-induced accumulation of molecules inside the
trap [16]. Further increasing the electrode voltages also
increases the density.
Already the present trap enables a number of mea-
surements.For example, the addition of suitable mi-
crowave and optical fields will allow cooling of both the
motional and the internal degrees of freedom of polar
molecules [16, 23, 24]. Homogeneous offset fields and the
long trap lifetime can be used for precision Stark spec-
troscopy [25] or the investigation of weak transitions [13].
Finally, tuning of the offset field will allow field-induced
collision resonances to be investigated [14].
We acknowledge support by the Deutsche Forschungs-
gemeinschaft through the excellence cluster “Munich
Centre for Advanced Photonics”.
∗Present
Chemie, ETH Z¨ urich, CH-8093, Switzerland
†Present address: MESA+ Institute for Nanotechnology,
University of Twente, 7500AE, The Netherlands
‡Electronic address: martin.zeppenfeld@mpq.mpg.de
[1] E.A. Hinds, Phys. Scr. T70, 34 (1997).
[2] J. J. Hudson et al., Nature 473, 493 (2011).
[3] D. DeMille, Phys. Rev. Lett. 88, 067901 (2002).
[4] A. Andr´ e et al., Nat. Phys. 2, 636 (2006).
[5] R.V. Krems, Phys. Chem. Chem. Phys. 10, 4079 (2008).
[6] P. S. Zuchowski and J. M. Hutson, Phys. Rev. A 79,
062708 (2009).
[7] K. G´ oral, L. Santos, and M. Lewenstein, Phys. Rev. Lett.
88, 170406 (2002).
[8] A. Micheli, G.K. Brennen, and P. Zoller, Nat. Phys. 2,
341 (2006).
[9] S.Y.T. van de Meerakker et al., Phys. Rev. Lett. 94,
023004 (2005).
[10] T. Rieger et al., Phys. Rev. Lett. 95, 173002 (2005).
[11] J. Kleinert et al., Phys. Rev. Lett. 99, 143002 (2007).
[12] S.D. Hogan, Ch. Seiler, and F. Merkt, Phys. Rev. Lett.
103, 123001 (2009).
[13] S.Y.T. van de Meerakker et al., Phys. Rev. Lett. 95,
013003 (2005).
[14] A. V. Avdeenkov and J. L. Bohn, Phys. Rev. A 66,
052718 (2002).
[15] M.R. Tarbutt et al., Faraday Discuss. 142, 37 (2009).
[16] M. Zeppenfeld et al., Phys.Rev.A80,041401(R)(2009).
[17] M. Kirste et al., Phys. Rev. A 79, 051401 (2009).
[18] S.J. Wark and G.I. Opat, J. Phys. B 25, 4229 (1992).
[19] S. H. Schulz et al., Phys. Rev. Lett. 93, 020406 (2004).
[20] T. Junglen et al., Eur. Phys. J. D 31, 365 (2004).
[21] C. Sommer et al., Faraday Discuss. 142, 203 (2009).
[22] A.D. Cronin, J. Schmiedmayer and D.E. Pritchard, Rev.
Mod. Phys. 81, 1051 (2009).
[23] I. S. Vogelius, L. B. Madsen and M. Drewsen, Phys. Rev.
Lett. 89, 173003 (2002).
[24] G. Morigi et al., Phys. Rev. Lett. 99, 073001 (2007).
[25] M. Motsch et al., Phys. Rev. A 76, 061402(R) (2007).
address: Laboratorium f¨ urPhysikalische