Electrostatic trapping of metastable NH molecules

0.44 MB·English

by  Steven Hoekstra

February 2, 2008
Electrostatic trapping of metastable NH molecules
∗
Steven Hoekstra, Markus Mets¨al¨a, Peter C. Zieger, Ludwig Scharfenberg,
Joop J. Gilijamse, Gerard Meijer, and Sebastiaan Y. T. van de Meerakker
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
We report on the Stark deceleration and electrostatic trapping of 14NH (a1∆) radicals. In the
trap,themoleculesareexcitedonthespin-forbiddenA3Π←a1∆transitionanddetectedviatheir
subsequent fluorescence to the X3Σ− ground state. The 1/e trapping time is 1.4 ± 0.1 s, from
whichalowerlimit of2.7 sfortheradiativelifetime ofthea1∆,v=0,J =2stateisdeduced. The
spectralprofileofthemoleculesinthetrappingfieldismeasuredtoprobetheirspatialdistribution.
8
ElectrostatictrappingofmetastableNHfollowedbyopticalpumpingofthetrappedmoleculestothe
0
electronic ground state is an important step towards accumulation of these radicals in a magnetic
0
trap.
2

n PACSnumbers: 37.10.Pq,37.10.Mn,37.20.+j,33.55.Be
a
J

7 I. INTRODUCTION tion of cooling schemes like evaporative or sympathetic
cooling.
]
h An obvious route towards higher number densities
Theabilitytoconfinecoldgas-phase(polar)molecules
p in the trap is the accumulation of several packets of
in traps has increased interest in gas-phase molecular
-
m physics in recent years. This interest stems from the ex- molecules that are produced in distinct cycles of the ex-
periment. Although an increase of the phase-space den-
o otic and intriguing phenomena that are predicted to be
sity in this way is forbidden by Liouville’s theorem, a
t observable in these cold molecular gases, ranging from
a reloading scheme has been proposed for the NH radi-
chemistry at ultralow temperatures [1] to the engineer-
.
s ing of macroscopic collective quantum states [2]. The cal that circumvents this fundamental obstacle [14]. In
c this scheme, NH radicals that are produced in the long-
field of (ultra)cold molecules might revolutionize molec-
si ular physics. It even has the potential to affect physics lived metastable a1∆ state are Stark decelerated to a
y standstilland subsequently optically excitedto the A3Π
at large, just as the first successful production of (ul-
h state. Spontaneous fluorescence from the A3Π state
p tra)cold atoms has led to spectacular advances far be- to the X3Σ− ground state provides the required uni-
[ yond the realm of classical atomic physics. The tech-
directionalpathway. Amagneticquadrupoletrapcanbe
niques to produce cold molecules are slowly maturing;
2 placed at the end of the Stark decelerator, such that the
photo-association [3], buffer gas cooling [4], and Stark
v
createdgroundstatemoleculesaremagneticallytrapped.
2 deceleration[5]havealreadyresultedinthethreedimen-
TheStarkinteractioninthe groundstateisratherweak,
1 sional trapping of molecules. Many other techniques are
therefore the Stark deceleratorcanbe usedto decelerate
2 currently being developed by various groups.
3 the next pulse of metastable NH radicals without affect-
. The method of Stark deceleration and electrostatic ingthetrappingpotentialforgroundstateNHmolecules.
9 trapping combines molecular beam technologywith con- A number of prerequisites for the successful implemen-
0
cepts from charged particle accelerator physics. In tation of this accumulation scheme have already been
7
0 essence, a part of a molecular beam pulse of polar neu- experimentally demonstrated. The hitherto unobserved
: tral molecules can be decelerated to a standstill and A3Π←a1∆transitionwasfoundandcharacterized[15],
v
confined in a trap, exploiting the interaction of polar and in a preliminary deceleration experiment, a beam of
i
X molecules with inhomogeneous electric fields. The tech- metastable NH radicals was Stark decelerated from 550
r nique works for a large class of polar molecules, and has m/sto330m/s[16]. However,the intensityofthe decel-
a resulted to date in the trapping of ND3 molecules [5], eratedpacketwasratherpoor,andpreventedthedemon-
OHradicals[6, 7]andmetastableCO molecules[8]. The stration of deceleration to lower velocities.
density of the decelerated and trapped molecular pack-
Herewepresentthedecelerationandelectrostatictrap-
ets has proven to be sufficient for a number of experi-
ping of a pulsed beam of NH (a1∆) radicals. The trap-
ments [9,10, 11, 12, 13]. However,it is stilla formidable
ping time of the metastable radicals in the quadrupole
challenge to reachhigh enoughdensities in the trapthat
electrostratic trap is measured. A laser-baseddiagnostic
collisions occur between the trapped molecules on the
method has been used to characterize the spatial distri-
trapping time scale. This is required to be able to ex-
bution of the trapped cloud.
perimentally study the interactions between the trapped
molecules, and it is a prerequisite for the future applica- The NH radical has several additional properties that
make this species of interest for cold molecule experi-
ments. In fact, NH in the a1∆ state is one of the prime
candidates for the Stark deceleration and trapping tech-
∗Electronicaddress: [email protected] nique. The Stark shift over mass ratio (the parameter
2
PMT dissociation of about 1 vol % hydrogen azide (HN3)
seededinKryptonbyfocussingthe6mJoutputofaArF
LIF zone
excimerlaseronasmallquartzcapillarythatismounted
trap
on the tip of a pulsed supersonic valve. Gaseous HN3 is
detection laser preparedbythereactionofsodiumazide(NaN3)withan
(584 nm) excess of lauric acid under vacuum. The reaction starts
Stark decelerator A 3Π1 (v'=0, J'=1) at approximately 348 K and proceeds smoothly at 353-
363K.TheNHradicalsareproducedbothintheX3Σ−
skimmherexapole 1.31 m 584 nm ground state and in the metastable a1∆ electronically
excited state. With Krypton as a carrier gas the molec-
336 nm a 1Δ (v=0, J=2)
ular beam has a forwardvelocity centered at about 450-
500 m/s with a full-width half-maximum (FWHM) ve-
photodissociation
pulsed valve laser (193 nm) X 3Σ-(v''=0) locity spread of about 20 %. The use of Xenon as a
carrier gas, which would result in a lower initial veloc-
ity, is not possible since it is known to efficiently quench
FIG. 1: Scheme of the experimental setup. NH molecules in
thea1∆statearecreatedbyphotodissociationofHN3seeded tehxepamnesitoanst,ambolestNmHolmecoulleecsuilnesth[2e3a].1∆Afetleercttrhoensicupsteartseonreic-
in Kr. The beam passes througha skimmer, a hexapole, and
a Stark decelerator. The decelerated molecules are subse- side in the v =0,J =2 ro-vibrationalgroundstate. The
quently loaded into an electrostatic trap. The molecules are StarkshiftofthislevelisshownintheupperpartofFig-
probed at the center of the trap by a far off-resonant laser- ure2. Onlymoleculesinthelow-fieldseekingMJΩ=−4
induced fluorescence detection scheme, that is shown in the component are decelerated and trapped in the experi-
inset. A photograph of the Stark decelerator is shown in the ments.
upperleft corner.
Onasmallerenergyscale,inthelowerpartofFigure2,
theeffectofthehyperfinestructureof14NHontheStark
splittingbecomesvisible. Duetothenuclearspinofboth
thatdeterminestheefficiencyofthedecelerationprocess) the 14N and the H nucleus, the a1∆,J =2 level is split
is significantly larger than for the OH radical, a system
intosixhyperfinelevelsthatarelabelledbythequantum
that is extensively used in deceleration and trapping ex-
periments. In the X3Σ− ground state, its 2 µB mag- number F. The Λ-doublet splitting of the J =2 level is
only116kHz [24], andisnotvisible onthis energyscale.
netic moment makes the molecule a good candidate for
The hyperfine splitting is therefore (much) larger than
magnetic trapping experiments. Recently, ground state
the Λ-doubletsplitting, andthe low-andhigh-fieldseek-
NH molecules have been magnetically trapped using the
ing MF components of the different hyperfine states in-
buffergascoolingtechnique[17],takingadvantageofthe
teractstrongly. Thisunusualsituationisratherdifferent
favorable properties of He-NH collisions [18]. The elec-
tric dipole allowed A3Π,v′ = 0 ← X3Σ−,v′′ = 0 tran- from that in the molecules that have been used in Stark
deceleration experiments thus far, and one may wonder
sition has an unusually large Franck-Condon factor [19],
(and worry) if this complex energy level structure could
which offers interesting prospects for direct laser cool-
resultinaredistributionovertheMJΩ statesduringthe
ing. It has also been predicted that NH in the ground
deceleration process.
state has favorable properties to perform evaporative
cooling [20]. Finally, interesting collision properties are Approximately 3 cm downstream from the nozzle ori-
expectedbetweencoldNH(X3Σ−)moleculesandultra- fice, the molecular beam passes through a skimmer, and
cold Rb atoms [21, 22]. enters the decelerator chamber. The molecules are fo-
cussed into the Stark decelerator by a short hexapole.
The Stark decelerator that is installed in the trapping
machine consists of 108 electric field stages with a cen-
II. EXPERIMENT
ter to center distance of 11 mm. Each stage consists
of 2 parallel 6 mm diameter electrodes that are placed
The experiments to decelerate the NH radicals, and aroundthe molecularbeamaxis to providea 4 × 4 mm2
theexperimentstosubsequentlyconfinethemoleculesin opening area for the molecular beam to pass. A voltage
an electrostatic quadrupole trap, are performed in two difference of 40 kV is applied to the electrodes. At the
different pulsed molecular beam machines, operating at endofthedeceleratoranelectrostaticquadrupoletrapis
a repetition frequency of 10 Hz. The deceleration ex- mounted. The trap loading procedure is similar to that
periments are performed in a newly constructed Stark used to trap OH [6]. The Stark decelerator that is used
deceleration molecular beam machine; for the trapping in the deceleration experiments consists of 104 electric
experimentsthesamesetupisusedasinourOHtrapping field stages. The electrode geometry of this decelerator
experiments. The latter setup is schematically depicted is identical to that of the other decelerator, except for
inFigure1,andhasbeendescribedindetailelsewhere[6]. an overall scaling factor of 0.75, i.e., the electrodes have
a 4.5 mm diameter, are placed 8.25 mm apart, and pro-
AmolecularbeamofNHmoleculesisformedbyphoto- vide a 3 × 3 mm2 aperture. However, the same voltage
3
pulsed dye amplifier pumped by a frequency-doubled in-
jection seeded Nd:Yag pump laser. For the excitation, a
3 mm diameter laser beam with a pulse energy of up to
25 mJ in a 5 ns duration pulse, with a bandwidth of ap-
proximately130MHz,isused. Thisintensityissufficient
to saturate even this weak spin-forbidden transition. In
the deceleration experiment, the laser beam excites the
molecules just behind the last electrodes of the decel-
erator. In the trapping experiments, the laser beam is
directed through holes in the center trap electrode, and
the fluorescence is collected through a 6 mm hole in the
end-capelectrode. Thefluorescenceisimagedwithalens
ontoaphotomultiplier tube. Unless statedotherwise,all
electrodesaregrounded10µsbeforethelaserexcitesthe
molecules.
III. RESULTS AND DISCUSSION
A. Deceleration of NH (a1∆) radicals
Atypicaltime-of-flight(TOF)profileofNH(a1∆,v =
0,J = 2) radicals that is observed in a deceleration ex-
periment is shown in curve (a) of Figure 3. In this ex-
periment, a packet of molecules with an initial velocity
of 520 m/s is selected, and the Stark decelerator is pro-
grammed to extract 1.6 cm−1 of kinetic energy from the
packet in every electric field stage. The selected frac-
FIG. 2: The Stark shift of the metastable a1∆(v = 0,J = tion of the molecular beam pulse that is decelerated to
2) state. In the upper panel the energy splitting (in cm−1) a final velocity of 84 m/s arrives in the detection re-
in strong electric fields is shown, not resolving the hyperfine gion about 3 ms after production, and is split off from
structure. The lower panel shows the energy splitting (in the remaining part of the beam that is not decelerated.
MHz) in low electric fields, including the hyperfine structure The TOF profile that is obtained from a three dimen-
of 14NH. sional trajectory simulation of the experiment is shown
in curve (b), and is seen to quantitatively reproduce the
observed TOF profile. In the simulations, the NH radi-
difference of 40 kV is applied to the electrodes. A pho- cals are assumed to be produced in each of the six MJΩ
tograph of the latter decelerator is shown in the upper components of the J = 2 state with equal probability.
left corner of Figure 1. As can be seen from this pho- In the curves (c), (d), and (e) the individual contri-
tograph, the last 8 electric field stages are mounted on butions of the MJΩ = −4, the MJΩ = −2, and both
conically shaped rods to provide an optimal solid angle MJΩ = 0 components to the TOF profile are shown,
for fluorescence collection. respectively. The decelerated packet of molecules exclu-
The NH (a1∆) radicals that exit the decelerator are sively consists of molecules in the J = 2,MJΩ = −4
state-selectively detected using a far off-resonant Laser state,butmolecules inthe MJΩ=−2state significantly
Induced Fluorescence (LIF) scheme that is schemati- contribute to the signal of the non-decelerated part of
cally shown in the inset of Figure 1. The molecules the beam. The MJΩ = 0 components hardly contribute
are excited to the upper Λ-doublet component of the to the signal as molecules in these components do not
A3Π1,v = 0,J = 1 level on the P2(2) line of the spin- experience transverse focussing forces as they progress
forbidden A3Π ← a1∆ transition around 584 nm [15], throughthedecelerator. Moleculesinthehigh-fieldseek-
and the subsequent fluorescence to the X3Σ− ground ingMJΩ=+2andMJΩ=+4componentsaredeflected
state around 336 nm is recorded. Although the use of a from the molecular beam axis and do not reach the exit
spin-forbiddentransitionforLIFdetectionofmoleculesis of the Stark decelerator.
unconventional, this scheme is advantageous as it allows From these simulations, the MJΩ composition of the
almost background-free detection by blocking the stray- structuredTOFprofileofthenon-deceleratedpartofthe
light from the excitation laser with optical filters. The beam is easily identified. This structure, and in particu-
584 nm light is generated by a narrow-bandpulsed laser lar also the ratio between signal intensity of the deceler-
system. Inthis laserthe output ofafrequency stabilized ated and non-decelerated part of the beam pulse, is well
single mode ring dye laser is amplified in a three stage reproduced by the simulations. This is a strong indica-
4
FIG. 4: The arrival of undecelerated NH molecules in the
trap center is followed by the steady signal of trapped NH
molecules. The molecules are brought to a standstill 6 ms
after their production. At that moment the trap is switched
FIG.3: Ameasuredtime-of-flight(TOF)profileofmetastable on. In the inset the population of electrostatically trapped
NHmoleculesobservedinadecelerationexperiment(a),com- NH(a1∆,v = 0,J = 2) molecules is plotted as a function of
pared with the outcome of a numerical simulation (b). The time. Thesolidlineisasingleexponentialfittothedatawith
molecules are decelerated from 520 m/s to a final velocity of an 1/e lifetime of 1.4 s.
84 m/s. The contribution of individual MJΩ components to
the simulated TOF-profile is shown in the lower part of the
figure.
0.36 s−1. The most abundant collision partner for the
trapped metastable NH radicals is Krypton, the car-
tion that there is no significant redistribution over the rier gas used in these experiments. Unfortunately this
variousMJΩcomponentswhenswitchingfromonehigh- loss factor can not be quantified because the NH(a1∆)-
voltageconfigurationtothenextintheStarkdecelerator. Krypton collision cross-section is unknown. The radia-
tive lifetime of the a1∆ state of NH is not known ac-
curately, but is expected to be on the order of a few
B. Trapping of NH (a1∆) radicals seconds (see [25] and references therein). When we com-
binethemeasuredtrappingtimewiththecalculatedloss
rate due to blackbody radiation pumping and when we
When the molecules are brought to a standstill the
assume no loss due to collisions with the background
electrostatic trap is switched on. The details of the trap
gas, we find a lower limit for the radiative lifetime of
loading process are published elsewhere [6]. The inten-
sityoftheLIFsignalofNH(a1∆,v =0,J =2)radicals, the NH(a1∆,v =0,J =2) state of 2.7 seconds.
detected atthe center ofthe trap,is shownasa function The number of trapped molecules can be estimated
of time in Figure 4. The trap is switched on about 6 ms from the intensity of the detected fluorescence. The av-
after the NH radicals are produced. After a few initial eragednumberofdetectedphotons,after200msoftrap-
oscillations a steady signal of the trapped molecules re- ping, is 2.4 per excitation laser pulse. From this the
mains. In the inset the signal of the trapped molecules number of trapped NH(a1∆,v = 0,J = 2) molecules is
is plotted on a longer time scale. We have fitted a single estimatedtobeabout104,correspondingtoadensityon
exponentialdecaytothedata,resultingina1/etrapping theorderof106 moleculescm−3. Thisisaboutoneorder
time of 1.4 ± 0.1 s. of magnitude less than in our OH trapping experiments,
There are three main processes that limit the trap- reflecting the inferior beam intensity of NH(a1∆) radi-
ping time: rotational excitation due to absorption of cals. The production of NH(a1∆) radicals in the beam
room-temperature blackbody radiation, collisions with can be improved when the HN3 molecules are photodis-
the background gas and the spontaneous decay of the sociated using the 266 nm light of a Nd:Yag laser. In
metastable state itself. In a recent study, the effects of this scheme, the production of NH (X3Σ−) is spin for-
blackbody radiation have been quantified for OH/OD, bidden, and the NH radicals are exclusively produced in
and tabulated for a variety of molecules [13]. For the a1∆ state [26]. Alternatively, NH (a1∆) molecules
NH(a1∆,v = 0,J = 2) the loss rate due to optical canbeproducedwithahighquantumyieldbyphotodis-
pumping by room-temperature blackbody radiation is sociation of HNCO at 193 nm [27].
5
Simulations the 584 nm radiation can safely be used to excite the
moleculeswhile the trapelectrodesarestill onhighvolt-
es II II
ul age. Inthe mainpartofFigure 5three different spectral
c
e 1
mol x3 profiles of the P2(2) line are shown, all recorded after 16
of msoftrapping. Theoriginofthehorizontalaxisissetat
ber III III the center of the field-free line profile, indicated as pro-
m
nu file (I). This line profile is measured 10 µs after the trap
0.0 0.1 0.2 0.3 0.4 0.5 0 5 10 15 20 25 electrodes are switched off and grounded. This time in-
Stark shift (cm-1) speed (m/s)
tervalissufficientlyshortthatthemoleculesdonotmove
significantly,while being long enoughto ensure field-free
conditions. A near-Gaussianlineshape with a FWHM of
∼ 130MHz, mainly determined by the bandwidthof the
laser,isobserved. Weakshouldersdue topartlyresolved
hyperfinestructureandtheintrinsicspectralstructurein
the laser pulse can be recognized in this profile.
-8 -6 -4 -2 0
Also shown are two broadened line profiles, (II) and
(III),observedwhenthemoleculesareexcitedinthepres-
ence ofthe trappingpotential. In the electric field ofthe
FIG. 5: Spectral profiles obtained by scanning the detec- trap, the trapped molecules in the a1∆,v = 0,J = 2
tion laser frequencyoverthehighest frequencycomponentof level and the A3Π1,v′ = 0,J′ = 1 level both experience
theP2(2)transition,whichexcitesthetrappedNHmolecules
from the a1∆ to the A3Π state. The field-free profile (I) is apositive Starkshift. Since the Stark shiftfor molecules
trapped in the a1∆ state is considerably larger than the
shown, scaled down by a factor 3, together with the profiles
obtained while the shallow (II) or deep (III) trapping field is StarkshiftintheexcitedA3Π1 state,abroadenedprofile
on. In the inset the result of numerical simulations is given, of the P2(2) line results that is shifted to lower frequen-
showing the number of trapped molecules as a function of cies. The difference betweenprofile(II)and(III) reflects
their Stark shift and speed. the difference in the depth and slope of the trapping po-
tentials that are being used; the deceleration and trap
loading process is identical in both cases. Profile (II) is
C. Spectral profiles recordedwhentheringelectrodeofthetrapisgrounded,
whereasavoltageof+15kVisappliedtothiselectrodeto
recordprofile (III). The endcaps ofthe electrostatic trap
An important property of the trapped gas is the tem-
are at a potential of -15 kV in both cases. The resulting
perature. Measuring the temperature, however, is no-
trap potentials therefore differ in slope and depth by a
toriously difficult. The temperature can in principle be
factor of two, and are referred to hereafter as ’shallow’
determined by measuring the spatial distribution of the
(II) and ’deep’ (III).
molecular cloud, as the spatial and velocity distribution
of the molecules in the trap are coupled. In trapping ex- The laser excitation and fluorescence detection in the
perimentswithND3 molecules,thataredetectedusinga experiment is done through holes in the trap electrodes,
Resonance Enhanced Multi Photon Ionization (REMPI) inevitablyrestrainingaccesstothetrappingvolume. For
schemewithafocussedlaser,thespatialdistributioncan adirectdeterminationofthe temperatureofthetrapped
be measured by mechanically scanning the laser focus molecules from the measured line profiles a complicated
alongasymmetryaxisofthetrap[28]. Thisstrategycan instrumentfunctionwouldhavetobetakenintoaccount;
onlybeimplementedifthedetectionlaserbeamis(much) the laser position, its spatial intensity profile and the
smaller than the size of the molecular cloud. When LIF spatial sensitivity of the detection system have to be ac-
isusedasadetectionscheme,thelaserbeamcanusually curately known. Therefore, a detailed analysis of the
not be made small enough to measure the spatial distri- line profiles intrinsically has many uncertainties. How-
bution this way. When the laser beam is comparable in ever, information on the energy and the position of the
sizetothemolecularcloud,however,thetemperaturecan molecules in the trap can also be obtained in a straight-
be deduced from the spectral profile of the molecules in forwardmannerbycomparingtheexperimentallinepro-
thepresenceofthetrappingpotential,amethodthathas, files with each other. In such a comparison, complica-
for instance, been applied to magnetically trapped CaH tions related to details of the excitation- and detection-
molecules[4]. Unfortunately,iftheexcitationwavelength processes cancel out.
is in the ultraviolet part of the spectrum, scattered pho- Theintegratedsignalofthethreelineprofilesis,within
tons can release electrons from the trap electrode mate- experimentalaccuracy,thesame. Moreover,ifprofile(II)
rial. This can cause electricalbreakdownin electrostatic is stretched out in frequency by a factor of two, and re-
traps, and has thus far hampered the application of this duced in intensity by a factor of two, it is virtually iden-
method to electrostatically trapped molecules. ticalto profile(III). This aloneindicates thatthe spatial
The detection scheme that is used in the present distribution of the trapped molecules in the shallow and
experiments does not suffer from these limitations, as deep potential are the same. This in turn implies that
6
theinitialkineticenergyofthemolecules,atthemoment erated, and loaded into an electrostatic trap. The den-
thatthetrapisswitchedon,issmallrelativetothedepth sity of the trapped sample is on the order of 106 cm−3,
ofthetrappingpotentials. Theenergydistribution(tem- which can be further enhanced by implementing more
perature)isthereforemainlydeterminedbythetrapping efficient production schemes. The 1/e trapping lifetime
potential, and is about a factor of two different for the is determined as 1.4±0.1 s, which yields a lower limit of
shallow and the deep trap. 2.7 s for the radiative lifetime of the a1∆,v = 0,J = 2
This conclusionis supported by numericalsimulations state. The spatial distribution of the trapped cloud is
of the deceleration and trapping process. The inset in probed by performing spectroscopy on the molecules in
Figure5showstheresultsofthesesimulations,indicating the presence of the trapping field. This experiment is
the number of trapped molecules as a function of their an important step towards the accumulation of multi-
Starkshiftandspeed,forbothtrappinggeometries. The ple packets of Stark-decelerated molecules in a magnetic
moleculesintheshallowtrappotential(II)haveasmaller trap,whichisapromisingroutetowardshigherdensities
Stark shift and a narrower speed distribution than the ofcoldmolecules. Modificationstothemachinethatwill
molecules trapped in the deep trap potential (III). The enable the transfer of the NH radicals into a magnetic
simulated speed distribution can be characterized by a trap are currently being implemented.
temperature, which is on the order of 60 mK and 100
mK for the molecules trapped in the shallow and deep
trap potential, respectively.
V. ACKNOWLEDGEMENTS
IV. CONCLUSIONS WeacknowledgetheexperimentalsupportfromHenrik
Haak and Sandy Gewinner, and the theoretical support
A pulsed molecular beam of NH radicals in the from Boris Sartakov. M.M. is grateful to the Academy
metastable a1∆ state has been produced, Stark decel- of Finland for financial support.
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