Single atom detection of calcium isotopes by atom trap trace analysis

0.76 MB·English

by  S. Hoekstra

Single atom detection of calcium isotopes by atom trap trace analysis
S. Hoekstra, A. K. Mollema, R. Morgenstern, H. W. Wilschut and R. Hoekstra
Atomic Physics, KVI, Rijksuniversiteit Groningen,
Zernikelaan 25, 9747 AA, Groningen, The Netherlands
(Dated: February 2, 2008)
Wedemonstrateacombinationofanisotopically purifiedatombeamandamagneto-opticaltrap
whichenablesthesingle atomdetection ofallstableisotopes ofcalcium (40,42, 43,44, 46and48).
5 Theseisotopes range in abundancefrom 96.9 %(40Ca) to0.004 %(46Ca). Thetrap isloaded from
0
an atomic beam which is decelerated in a Zeeman slower and subsequently deflected over an angle
0 ◦
of 30 by optical molasses. The isotope selectivity of theZeeman slower and the deflection stage is
2
investigated experimentally and compared with Monte Carlo simulations.

n
a
J I. INTRODUCTION tweenneighboringisotopes. Forthe calciumisotopesthe

4 isotope shift is about five times the natural linewidth;
therefore isotope selectivity in laser pumping of calcium

] Trace analysis of long-lived isotopes has become an
isotopes is possible. Reducing the Doppler broadening
h
important tool in modern science. From medical sci-
p ofthe transitionis anessentialingredientfor the isotope
ence to environmental research, from nuclear safety to
- selectivity. Therefore, cold atoms are an ideal and nec-
m archeology,the capability to detect low-abundance long-
essarytool for ultra-sensitive isotope detection. Samples
lived isotopes has opened many research fields [1]. For
o of cold atoms can be obtained by laser cooling and trap-
t the detection of trace elements Atom Trap Trace Anal- ping in a magneto-opticaltrap (MOT) [13], which is the
a
ysis (ATTA) is a promising and potentially very pow-
. central element of an ATTA experiment.
s erful new technique [2, 3]. In a recent experiment one
c The final sensitivity that can be reached in an ATTA
i million year old groundwater from the Nubian Aquifer experiment is limited either by the background of 40Ca
s (Egypt) has been dated using ATTA, by detecting very
y atomsorbytheloadingrateofthetrap. Thebackground
h small traces of 81Kr [4]. Because there are no interfer- of 40Ca atoms can be reduced by improving the isotope
p encesfromotherelementsATTAhasthepotentialtoalso selectivity, the loading rate can be increased by improv-
[ detect the long-lived isotope 41Ca at its natural abun- ing the efficiency. In the ATTA measurements reported
1 dtoanpceerfloervmelroafd1i0o−-c1a4lc[i5u].mTdhaitsinwgouwlidthop41eCnat,hewhpiocshsihbailsitya on in [12] the isotope selectivity was the limiting factor
v for the sensitivity. In this article the isotope selectivity
half-life of 105 years [5, 6]. Furthermore, 41Ca could be
9 hasbeeninvestigatedindetail. This resultsinasetupin
0 used as a tracer to directly monitor the bone loss and which the search for 41Ca atoms is no longer limited by
0 retention rates of human subjects in both research and
the isotope selectivity but by the loading efficiency. The
1 diagnosis of osteoporosis [7]. As an alternative to Accel-
loading efficiency is limited at the moment by the laser
0 erator Mass Spectrometry (AMS), ATTA may provide
power available for the experiment.
5
a small-scale and cost-effective detection method of rare
0 isotopes, such as the example of 81Kr showed. Recently In section II of this article the various parts of our ex-
/ perimental setup will be presented. In section III three
s ATTAhasbeencomparedwiththeestablishedtechnique
differentloadingschemesfortheMOTarecomparedwith
c
of Low Level Counting (LLC)[8]. A competing compact
i the purpose of improving the isotope selectivity. Monte
s laser-based method is Resonance Ionization Mass Spec-
y Carlosimulationswere made to help understandthe iso-
trometry(RIMS),whichhasbeensuccessfullydeveloped
h tope selectivity of the Zeeman slower and the deflection
in recent years [9, 10, 11]. RIMS combines the selec-
p stage. Finally, experimental data of the detection of sin-
: tivity of laser spectrometry with the technique of mass gle calcium atoms in the MOT are presented.
v
separation. Recently it has been shown that ATTA is
i
X already sufficiently sensitive to detect 41Ca in enriched
r (10−8) calcium samples for biomedical applications [12]. II. EXPERIMENTAL SETUP
a We have set up an ATTA experiment with the ultimate
goal of detecting 41Ca at the natural abundance level.
Our experimentalmethod is schematically depicted in
ATTA experiments combine various optical tech- figure 1. The metallic calcium sample is placed in oven
niques,eachofwhichisisotopeselective. Themechanism 1 from which atoms are evaporated to create an atomic
ofisotopeselectionistherepeatedexcitation(byalaser) beam. The divergence of the atomic beam of a selected
ofanopticallyaccessibleelectronictransitioninthe neu- isotope can be reduced using optical compression with
tral atom. Because of the isotope shift the scattering laser beams perpendicular to the atomic beam [14]. The
forceinduced by lightofa fixedfrequency is differentfor other isotopes are not affected or even pushed out of
the differentisotopes. It is the ratiobetween the natural the atomic beam. The second step in the selection of
linewidthandtheisotopeshiftofthepumpingtransition the isotopes, and essential for the efficient loading of
that determines the selectivity that can be reached be- the magneto-optical trap, is a Zeeman slower. It slows
2
Compression of opticalmodulators(AOM).Thelaserfrequencyislocked
the atom beam Oven2 tothecoolingtransitionofcalciumbymeansofpolariza-
tion spectroscopy[16], which is done on an atomic beam
Isotope-selective
from oven 2. The average trapping time of calcium in a
deflection MOT is limited to ∼ 20 ms due to a weak leak (10−5)
Valve
Oven 1 from the 4s4p 1P1 to the 1D2 state. From the 1D2 state
roughly75%decaystothegroundstatewithin3ms,and
can be recaptured if the diameters of the trapping laser
MOT beams are large enough. The rest of the atoms are lost
Zeeman-slower fromthetrap,andlimitthetrappingtime. Thetrapping
time can be increased by repumping the atoms from the
1D2 to the 5s 1P1 state, from which they quickly decay
back to the ground state [17]. The laser light required
FIG. 1: A schematic overview of theexperimental setup. for the repumping is generated by a home built diode
laser operating at 672 nm, of which typically 5 mW is
available for the MOT. Only for the measurements with
single atoms presented here the repump laser has been
the atoms down by the absorption of photons from a
used.
counter-propagating laser beam [15]. The Doppler shift
The calcium atoms are placed in an oven from which
resulting from the longitudinal velocity of the atoms is
the atoms are evaporated. The ovens have 10 exit chan-
continuously compensated by a Zeeman shift, induced
nels each with a diameter of 1 mm and a length of 10
by the magnetic field along the axis. The resulting slow
◦ mm. A ceramic tube around the oven holds tantalum
atom beam leaving from the oven is deflected over 30
wires which are used to heat the oven to temperatures
in the direction of the Magneto-OpticalTrap (MOT) by
◦
in the range of 400 to 600 C. The Maxwellian velocity
a standing wave field tilted at the proper angle. This
distributionforcalciumatomswithatemperatureof600
deflection stage is an essential step in the isotope selec-
◦
C peaks at a velocity of 600 m/s.
tivity and the total sensitivity that can be reached. As
The transverse velocity is less than one tenth of the
will be shown in this paper only the selected isotope is
longitudinal velocity,provided the mean free path of the
effectively deflected and guided into the trap. This im-
atoms is larger than the length of the exit channel of
provesthesignal-to-noiseratiointhedetectionoftherare
the oven. Directly after the atoms leave the oven we
isotopes, and thereby enables the use of a higher atom
have the possibility to apply transverse compression of
flux. The detection of the rare isotopes takes place in
the atom beam. The Doppler shift ω of the moving
the MOT. Only atoms of one isotope can be trapped for D
atom, the isotope shift I and the natural linewidth Γ of
a given laser frequency. By scanning the laser frequency s
the transitiontogetherdetermine the effective scattering
and observing the fluorescence of the trapped atoms we
rate of a specific isotope. For a specific laser detuning δ
detectedallstableisotopesofcalciumdowntothe single
atom level. The trap can also be loaded from a second and power s0 the scattering rate γp [18] is given by
oven; it is connected to the deflection chamber with a
s0Γ/2
valve as indicated in figure 1. This second atom beam γ = (1)
enables us to make a direct comparisonbetween the dif- p 1+s0+(2(δ+ωD+Is)/Γ)2
ferent methods by which the trap can be loaded. This As can be seen from table I the typical isotope shift be-
will be presented in section III. The various parts of the tweentwoadjacentisotopesofcalciumisabout160-200
experiment will be presented here in some more detail. MHz. The natural linewidth of the cooling transition is
At 423 nm, calcium has a strong resonance transition 34 MHz, and the Doppler shift for the calcium atoms is
fromtheground4s21S0statetothe4s4p1P1statewhich 2.1 MHz/(m/s).
is rather well suited for laser cooling. The required 423 Because the transverse Doppler broadening is limited
nm laser light for the cooling is generated by frequency the compression is isotope selective: when tuning the
doublingoftheoutputofan846nmdiodelaser(Toptica laser frequency in between two adjacent isotopes there
Photonics AG). By amplification in a tapered amplifier will be a force on both isotopes, opposite in sign. The
up to 500mW of 846nmlight is produced; after the fre- result is that the lighter isotope of the two will be
quency doubling with an LBO crystal we typically have pushed awayfrom the beam axis while at the same time
55 mW of 423 nm light available for the locking of the the transverse velocity component of the heavier isotope
laser (5 mW), the compression stage (10 mW), the Zee- can be reduced, resulting in an improved transmission
man slower (20 mW), the deflection stage (5 mW) and through the Zeeman slower. We have done Monte Carlo
the MOT(15mW). Theamountoflaserpoweravailable simulations to investigate this effect in more detail: a
is the limiting factorfor the efficiency ofthe experiment, detailedcomparisonwithexperimentalresultswillbere-
and could be increased by investing in a more intense ported on in the near future.
source of light at 846 nm. The main laser beam is split The Zeeman slower is designed to decelerate atoms
and frequency shifted using beam-splitters and acousto- with initial velocities up to 1000 m/s (corresponding to
3
85% of the atoms) down to 50 m/s. The total length is backgroundlight. For a largetotal dynamic rangeofthe
0.86 meter. The magnetic field has a maximum of 0.16 detection system also a CCD camera and a photo-diode
TeslaattheentranceoftheZeemanslower,anddecreases are used. The windows of the MOT have been mounted
towards the exit. The laser beam counter-propagating on extension tubes and are anti-reflection coated. In or-
the atoms has a σ+ polarization and a typical power of der to further reduce the amount of scattered light the
20 mW. To avoid an extra velocity spread of the atoms, inside of the vacuum chamber is coated black. The typi-
the slowingprocesshas to be terminatedquickly,cf. ref- cal pressure in the MOT is 10−9 mbar which can rise to
erence [20]. Therefore,the magnetic fieldhasa negative 10−8 mbar depending on the oven temperature.
offset (as a result the slowing laser is detuned by -320 The abundance of very rare isotopes can no longer be
MHz) and is terminated with a strong positive magnetic determineddirectlyfromtheintensityofthefluorescence
field. The laser beam is focused on the exit channels of from the trapped atoms if the average population of the
the oven. As a result there is a gradient of the laser in- trap falls below one atom. In this case we have to be
tensity along the Zeeman slower, for which the shape of able to count the number of atoms arriving and leaving
themagneticfieldslopehasbeenadjusted. Thecoilgen- thetrapoveracertainperiodoftime, anddeterminethe
erating the magnetic field is divided in 8 independently abundancefromacomparisonwiththeknownabundance
adjustable sections so that the field can be optimized. ofanotherisotope. Experimentalresultsonthedetection
In the deflection chamber the desired isotope is de- ofthesingleatomsarepresentedanddiscussedinsection
flectedoutofthe slowedatombeambya combinationof IIIC.
two counter-propagating red-detuned laser beams which The presentsensitivity of41Ca detectionby ATTA, as
crosstheatombeamunderanangleof30◦. Atthispoint reportedbyMooreetal[12],islimitedbythebackground
theDopplerbroadeningissufficientlyreducedsothatdi- of 40Ca atoms present in the trap, and by the trapping
rect isotope selection is possible, even when probing the time of the atoms. Even though the 40Ca atoms are
beam under 30 degrees. At this point the laser beam nottrappedwhile detecting 41Ca, they contribute to the
has a diameter of only 0.5 cm, the same detuning as the fluorescence signal from the trap, obscuring the signal
trapping beams, and has a typical power of 5 mW. Only fromthelessabundantisotopes. Itisthereforeakeyissue
the selected isotope will be deflected so that it can reach to further increase the isotope selectivity. Besides the
the trap, which is located 40 cm further downstream. fluorescence background from these 40Ca atoms, there
is the fluorescence background due to scattering of the
TheatomsaretrappedbyastandardMagneto-Optical
trapping laser beams from the windows and walls of the
Trap. Typically15mWoflaserpowerissplitover3laser
trappingchamber. For anymeasurementofsingle atoms
beams which are retro-reflected to make the 6 required
in a MOT this source of background has to be made as
trappingbeams. Themagneticquadrupolefieldisgener-
small as possible.
ated by two coils in anti-Helmholtz configuration placed
We have compared the isotope selectivity of three dif-
outside the vacuum (902 windings each, typical current
ferent trap loading schemes. As an indication of the iso-
3 A) resulting in a magnetic field gradient of 8 mT/cm.
tope selectivityofoursystemthe amountoffluorescence
Thefluorescenceoftheatomsinthetrapismeasuredbya
due to the hot 40Ca atoms is measured while trapping
photo-multiplier tube (PMT) in photon-counting mode.
the calcium isotope 43Ca. The experimental results are
A lens system of 2.54 cm diameter is placed inside the
presented in the next section.
chamber at a focal distance of 3 cm from the trapped
atoms to efficiently collect the fluorescence. This lens
system is adapted from reference [21]. Outside the vac-
uumtrapping chamberthe lightfromthe trapis focused III. RESULTS
throughapinholebeforedetectionbythePMTtoreduce
The starting point of the experiment is the atomic
beam as it leaves the oven. The natural abundance of
the variousisotopes in this beamcan be seenin figure 2.
TABLE I: The abundances of the stable isotopes of calcium
In this figure the fluorescence of the atomic beam com-
andtheisotopeshifts[19]ofthe4s21S0-4s4p1P1transition.
Also indicated is 41Ca. The shifts given for 41Ca and 43Ca ing from oven 2 is shown, excited only by the vertical
trapping laser beam in the MOT. The fluorescence is
are for the9/2 hyperfinecomponent.
measured by a PMT under right angles with both the
Isotope Natural abundance(%) Isotope Shift (MHz) atom beam and the laser beam. The peaks have been
fittedwithLorentzianprofiles,allhavingthesamewidth
40 96.94 0
41 1·10−12 166 (38 MHz) and an amplitude corresponding to the nat-
42 0.65 393 ural abundance as given in table I. The fit curve is in
43 0.14 554 good agreement with the measured spectrum. The mea-
44 2.09 774 suredwidthof38MHz isslightlylargerthanthe natural
46 4·10−3 1160 linewidth of 34 MHz: this corresponds to a transverse
48 0.19 1513 velocitycomponent of1.9 m/sin the atomic beam. This
figure gives an indication of the limited maximum selec-
4

6
10
40 5
Ca 42
5 Ca
s)10
nce (# counts / 110034 42Ca 43Ca 44Ca 46Ca 48Ca ce (arb.units)34 43Ca 44Ca 48Ca
ce 2 en2
es10 sc 46
r e Ca
o r
Flu101 Fluo1
0
-200 0 200 400 600 800 1000 1200 1400 1600
400 600 800 1000 1200 1400 1600
40 40
Laser Detuning (relative to Ca, MHz) Laser Detuning (relative to Ca, MHz)
FIG. 2: The fluorescence of calcium isotopes in an atomic FIG. 4: Fluorescence in the trap loaded from a slowed but
beam after a single excitation step. not deflected atom beam. This spectrum was taken before
thedeflection stage was installed (cf. fig. 1)

3.0 can excite the fast 40Ca atoms in the atom beam as the
44
Ca frequency of the trapping laser beams is scanned over
2.5
the various isotopes. The broad velocity distribution of
nits)2.0 these hot 40Ca atoms can be seen in figure 3 as it dom-
u inates the fluorescence at frequencies where for example
b.
ar 42 trapped 46Ca atoms should be visible. To enable com-
e (1.5 Ca 48Ca parison with figures 4 and 5, the fluorescence is set to 1
c
cen 43Ca attheresonancefrequencyof46Ca(1160MHz). Thehot
es1.0 atoms not only scatter the laser-light, thereby obscur-
r
o
u ing the signal from the trapped atoms, but also shorten
Fl0.5 the trappingtime ofotherisotopesbycollisionswiththe
trappedatoms. Theratiobetweenthefluorescenceofthe
0.0 trapped 43Ca and the background 40Ca is ∼0.15.
400 600 800 1000 1200 1400 1600
40 When the trap is loaded from a slowed atom beam
Laser Detuning (relative to Ca, MHz)
the amount of trapped atoms increases because a larger
FIG. 3: Fluorescence in the trap loaded from oven 2. The
fraction of the atoms falls within the capture range of
backgroundsignaliscausedby40Capassingthroughthetrap
the trap. Figure 4 shows the fluorescence detected in
withitsMaxwell-Boltzmannvelocitydistributionandexcited
the MOT, while simultaneously scanning the frequency
by thehorizontal trappinglaser beams.
of the trapping laser and the Zeeman slowerlaser beams
over the range of isotopes. This measurement was done
before the deflection stage was installed. It can be seen
tivitythatcanbereachedinasingleexcitationstep: the
that the relative contribution of the hot 40Ca atoms is
power of ATTA lies in the fact that the same transition
greatlyreduced. Comparingfigure3tofigure4,theratio
is excited very often.
offorexamplethe trapped44Ca tothe 40Ca-background
increases from 2.5 to 5000. The reduction of the 40Ca-
backgroundenablesthe detectionoftrapped46Caatoms
A. Comparing different loading schemes withanaturalabundanceofonly0.004%,whichwasnot
possiblewhenloadingthe trapdirectlyfromthe thermal
Inthissectionthreedifferentloadingschemesarecom- beam. The figure is normalized to the intensity of the
pared with respect to isotope selectivity. The simplest 46Ca peak. The ratio between the trapped 46Ca and the
configurationistoloadtheMOTdirectlyfromathermal background 40Ca is ∼ 3, for 43Ca the ratio to the 40Ca
beam. Since the capture velocityofthe trapis ∼50m/s background is ∼ 15. The increase of isotope selectivity
onlythelowvelocitytailoftheBoltzmanndistributionis is the result of both the increasedfraction of slow atoms
trapped. WhentheMOTisoperatedononeoftheheav- andtheisotopeselectivityoftheZeemansloweritself. In
ierisotopes,thelargeamountof40Calimitsthedetection section IIIB we will look at this in some more detail.
oftheseless abundantisotopesinthe trap. The horizon- We find that the background signal from fast 40Ca
◦
taltrappingbeamswhichintersecttheatombeamat45 atoms disappears almost completely when loading the
5

0
2.0 519 C
4000
42Ca 44Ca 48Ca 450 0C
)
s
nit 1.5 ms
b.u 10 3000
nce (ar 1.0 43Ca 46Ca counts / 2000
ce n
s o
uore 0.5 Phot
l 1000
F
0.0
0
400 600 800 1000 1200 1400 -1000 -500 0 500 1000
40
Frequency detuning relative to Ca (MHz) Frequency (arb.units)
FIG. 5: Fluorescence in the trap loaded from a slowed and FIG. 6: Fluorescence intensity of 43Ca and background level
deflected beam. intensityfortwodifferentoventemperatures. The43Capeak
intensity increases by a factor of 6.6, while the fluorescence
background level remains almost constant.
trap from a deflected, slow beam. In the measurement
presented in figure 5 the background in between all the
trappedisotopes is foundto be mostly dependent onthe
intensity of the laser trapping beams, and only slightly
Initial velocity distribution
on the oven temperature (atom flux). This is further il- 50
lustratedbyfigure6. Herethefluorescencefromthetrap
isshownwhilescanningoverthe43Catrappingfrequency ms 0
for two different oven temperatures. While the 43Ca o 800
peak intensity increases by a factor of 6.6 (from ∼ 500 f at Final velocity distribu4t0ion
to ∼ 3300 counts/10 ms), the average background level er o 600 41Ca
changes only from 475.9±0.7 to 492.5±0.5 counts/10 mb 42Ca
ms. This insignificant background increase of less then Nu 400 Ca
4 %, corresponding to 16.6±0.6, is due to extra 40Ca
atoms. The purely 40Ca dependent background compo- 200
nent shouldalsohaveincreasedby a factor of6.6: there-
◦
forewecanconcludethatat450 Cthebackgroundcon- 0
tribution due to 40Ca is 2.5 ± 0.1 counts/10 ms. The -200 0 200 400 600 800 1000 1200
43Ca signal relative to the 40Ca background is therefore Velocity (m/s)
∼200. When comparing this to a directly trapped ther- FIG.7: Acalculation ofthefinallongitudinalvelocity distri-
mal beam (figure 3) the ratio of the 43Ca signal to the bution(1000atomseach)oftheisotopes40Ca,41Caand42Ca
40Ca backgroundis increasedby a factorof∼1300. The travelling through the Zeeman slower. The laser detuning is
set for 41Ca. An example of a Monte Carlo sampling of the
restofthebackgroundisduetolaserlightscatteredfrom
initial velocity distribution upon entering the Zeeman slower
the walls and the windows of the trapping chamber, and
is shown in thetop panel.
can be further reduced to 125 counts / 10 ms as shown
by the data on single atoms, presented in section IIIC.
Itisnotedthatthemeasured43Cato46Caratiochanges, laser frequency optimized for 41Ca. Most of the 41Ca
when comparingfigure 4 to figure 5. This is discussedin
atomsaredeceleratedto the desiredvelocityofabout50
section IIID.
m/s; for both the other isotopes this is different. This
can be understood as follows: for a given laser detun-
ing all the isotopes of calcium will be resonant in the
B. Monte Carlo simulations Zeeman slower, but at different locations because of the
isotope shifts. These isotope shifts translate into dif-
The isotope selectivity of the Zeeman slower can be ferent scattering rates in the Zeeman slower, according
understood on basis of the results of Monte Carlo sim- to equation 1. Therefore the final velocity of the differ-
ulations. In the simulation results depicted in figure 7, ent isotopes leaving the Zeeman slower will be different.
the final velocity distributions for 40Ca, 41Ca and 42Ca The magnetic field slope of the Zeemanslower is steeper
atoms were calculated for our Zeeman slower with the at the end, where the average velocity of the atoms is
6
for. Plotted in figure 8 are the deflection angles as a
2
function of the initial velocity for 40Ca, 41Ca, and 42Ca
atoms. In the inset the geometry of the atomic beam
1 and the deflection laser beams is shown. As in the ex-
periment,the laserpoweris5 mWdistributeduniformly
over a beam diameter of 0.5 cm. The deflection laser is
tuned 40 MHz below the resonance frequency of 41Ca.
While the 41Ca atoms aredeflected well for velocities up
to 90 m/s, the 40Ca are pushed away from the atomic
beamaxis. Thisisthemainreasonthatthecombination
of a Zeeman slower and the large-angle deflection is so
effective in selectivelydeflecting only one desiredisotope
out of the atom beam. Due to the large additional de-
tuning caused by the isotope shift, 42Ca is not affected
at all. Similar simulations have been done for different
laserpower,anditfollowsthatboththeisotopeselectiv-
FIG. 8: A simulation of the large-angle atomic beam deflec- ityandtheefficiencyofthedeflectionstageincreasewith
tion for the different isotopes. Shown is the deflection angle increasing laser power.
asafunctionoftheinitialvelocityforthreedifferentisotopes: For 40Ca we can analyze the deflection behavior in
40Ca, 41Ca and 42Ca. The inset shows the geometry of the
somemoredetail. Onlythevelocitycomponentalongthe
atomicbeamandthedeflectionlaserbeams. Thelaserdetun-
axis of the molasses laser beams (called v ) is affected
ingis40MHzreddetunedwithrespecttothe41Caresonance by the deflection molasses. The 40Ca atmoomls are much
frequency. Furtherdetails are given in thetext.
closer to resonance to the molasses laser beam pushing
them away from the trap (laser 2, cf. fig 8). The num-
lower. If the laseris tuned to 41Ca atoms,then the 42Ca ber of scattered photons depends on the scattering rate
as given in formula 1, and on the time the atoms spend
atoms will initially also be decelerated, but the slope of
in the optical molasses. For the 40Ca atoms at the given
the magnetic field is too steep: the change in velocity is
detuningthisscatteringrateisaLorentzianwithitsmax-
notenoughtokeepupwiththechangeinmagneticfield.
imum at v = 50 m/s. This corresponds to an atom
Therefore this isotope will be lost from the slowing pro- mol
cess. On the other hand, a 40Ca atom is nicely slowed with a longitudinal velocity (called vlong) of 100 m/s.
During the time that the atoms are in the optical mo-
downuntiltheend,buttheslowingprocesscontinuestoo
lasses v will change due to the scattering. The atoms
long. In the simulation the far majority of these atoms mol
can be accelerated to a final v which depends on the
undergo a reversal of their longitudinal velocity. They mol
time spentinthemolassesandthe linewidthofthe tran-
will thus be lost even due to their small transversal ve-
sition. The deflection angle is determined by the ratio
locity component and do not reach the MOT.
between v and v . The minimum in the deflec-
Ascanbeseenfromfigure4asignificantlylowerback- mol long
tion angle for 40Ca atoms around 20 m/s is the region
groundfrom40Ca is detected inthe MOT fora trapping
where v is limited by the time the atom spent in the
detuning smallerthanabout450MHz. With this detun- mol
molasses. For v < 5 m/s the deflection reaches the
ingweprobe40Caatomswithavelocityrangebelow200 long
◦
maximum possible deflection angle of 60 , i.e. parallel
m/s. Since there is at the moment no collimation of the
to the molasses laser beams. For v > 30 m/s v
atombeamatthe exitofthe Zeemanslowerthese atoms long mol
reachesamaximumvaluelimitedbythe linewidthofthe
probably do not reach the trap due to the divergence of
transition. The deflection angle is then just determined
theatomicbeam. TheZeemanslowerisdesignedtoslow
bytheratioofthismaximumvalueofv andtheinitial
the desiredisotope to50m/s;fromthe factthatwetrap mol
longitudinal velocity.
these isotopes we conclude that for these isotopes the
gain due to the larger number of slow atoms outweighs
the loss due to the transverse velocity spread. However,
many more of these slow atoms could reach the trap if C. Single atoms
we implement a second transversal cooling stage at the
exit of the Zeeman slower. Single atoms can be detected in a magneto-optical
Toassessthefunctionalityofthelarge-angledeflection trap because the trapped atoms are continuously scat-
byopticalmolasseswehaveperformedMonte-Carlosim- tering photons from the trapping laser beams. Provided
ulations. 40Ca, 41Ca and 42Ca atoms with a range of the amountofdetectedphotonsnotoriginatingfromthe
longitudinal velocities have been traced through the de- trapped atom is low enough, a single trapped atom can
flection molasses. Absorption and emission probabilities be detected as a temporal burst of light. In order to
are calculated along the way,and every time a photon is test the sensitivity of the detection system, we have de-
absorbedandemittedthevelocityoftheatomisadjusted tected the fluorescence of trapped calcium atoms for low
correspondingly. Stimulated emission is also accounted oven temperatures. With decreasing oven temperature
7
180 TABLE II: The measured abundance of the stable calcium
ms 160 isotopescomparedtoliteraturevaluesfrom[22]. 44Caistaken
s / 4 140 tawsoadriefffeerreenntcelapseorinpt,owaenrdsf(o5r04m3CWa/tw7o0vmaWlue)s. are shown for
nt 120
u
o
c 100 Isotope Measured(%) Literature(%)
n
oto 80 40 − 96.94(16)
h 60 42 0.68 0.65(2)
P
40 43 0.006/0.06 0.14(1)
44 [2.09] 2.09(11)
20
0 1 2 3 4 5 6 7 8 9 10 46 0.005 0.004(3)
48 0.15 0.19(2)
Time (s)
FIG. 9: Fluorescence of individual atoms detected in the
MOT.Thedottedlinesindicatethefluorescencelevelfor1,2
and3atomsinthetrap. Theintegration timeofthephoton-
detector is 4 ms.
the atomic beam becomes less and less intense, down
to a loading rate of only a few atoms per minute. At 0.006% for the typically used laser power of ∼ 40 mW.
some point the fluorescence from the trap displays dis- This corresponds to only ∼ 4 % of the literature value.
crete steps: we can count the number of atoms in the
This large discrepancy is due to differences in the cool-
trap. Shown in figure 9 is the fluorescence of single 40Ca
ing and trapping efficiency of the odd isotopes of cal-
atoms detected in the trap for a period of 10 seconds. cium: the odd isotopes 41Ca and 43Ca have a nuclear
We have also detected single atoms from all other sta-
spinofI=7/2. Theresultingmagneticsubstructureofthe
ble calcium isotopes. During the time that an atom is
groundandtheexcitedstateinfluencestheDopplercool-
trapped it can scatter photons at an estimated rate (de-
ing force. Comparable observations have been reported
pending on laser detuning and intensity) of 1.3·106 s−1.
for the case if the odd strontium isotopes [23]. We have
We detect 35±3 photons per 4 ms per atom, which re-
adapted the theoretical model developed for strontium
sults in a totalphoton detection efficiency of 0.7 %. The
and have solved the generalized optical Bloch equations
background level is 50 photons per 4 ms. This should
for the odd calcium isotopes taking into account all the
not be confused with the noise level, which is limited by
hyperfine states and their magnetic sub-states. We find
statistics. Trapping the atoms longerenables us to use a
thatthemaximumdecelerationforceontheoddisotopes
larger integration time which reduces the statistical er- for a one-dimensional σ+-σ− optical molasses configura-
ror on the signal. During the measurement of figure 9
tion is only half as strong as that on the even isotopes.
the repump laser was used: we concluded from trap de-
This indicates that the number of photons emitted per
cay time measurements that the average trapping time
trappedatominacertainperiodoftimeisonlyhalfthat
improved from ∼ 20 ms to ∼ 200 ms. It is important to
of the even isotopes. This alone cannot explain the re-
note that the background contribution due to hot 40Ca duction of a factor of 25 in the detection of 43Ca. Since
atomssuchasreportedinsectionIIIA,evenathighoven
the coolingforce isweakerthis effectcouldalsolimit the
temperatures, is much lower then the fluorescence signal
efficiency of the deflection and slowing of the odd iso-
of a single trapped atom.
topes. In order to investigate this issue, we have done a
recentexperimentwherewefindthatthemeasured43Ca
abundance depends significantly on the laser-power. In-
D. Isotope fractionation
creasing the total laser-power from 50 mW to 70 mW
the ratio between 43Ca and 46Ca increases from 1.2 to
The final issue we will address in this article is that 15. This ratio can be more accurately measured than
of isotope fractionation effects in the experiment. The the relative abundances, due to non-linear effects in the
maximumfluorescenceofthe varioustrappedisotopesin detectionsystemfortheveryhighcountrateswhenmea-
figure 5 is compared to literature values [22] in table II. suring 44Ca. A ratio of 15 corresponds to a measured
The absolute amount of 40Ca could not be measuredac- abundance for 43Ca of 0.06%: this is roughlyhalf of the
curatelyinthesameexperimentduetothehighintensity literature value. This observation indicates clearly that
of the fluorescence: therefore the relative abundance of the efficiency of the deflection and the Zeeman slower is
the heavier isotopes was compared to 44Ca. The abun- differentfortheoddandevenisotopes,anddependscrit-
dance of 44Ca was set to the literature value of 2.09. ically on the laser power available. Thus for the planned
For all isotopes except 43Ca the agreement is reason- investigations on 41Ca, the isotope 43Ca should be cho-
able. In the case of 43Ca we detect an amount of flu- sen as reference, due to its expected similar behavior in
orescence which would indicate an abundance of only the experimental scheme.
8
IV. CONCLUSION pression, Zeeman slower and deflection stage. Adding
a second isotope selective compression stage directly af-
We have demonstrated the trapping of all stable iso- terthe Zeemanslowerisanotherpotentialimprovement.
topesofcalciuminvolvingcoolinginaZeemanslowerand With these changes the system will be ready to start
deflection of the cooled beam by 30◦ in a tilted optical searchingfor41Caatomsatthenaturalabundancelevel.
molasses. Acorrespondingexperimentalsystemhasbeen
builtwithasensitivitythatenablesustodetectevensin-
gle trapped atoms of all these isotopes. To suppress the
interfering40Cafluorescencebackgroundwhendetecting Acknowledgments
the less abundant isotopes the deflection of the slowed
◦
loading beam over 30 was found to be very effective. TheauthorswouldliketothanktheKVItechnicalstaff
The background due to 40Ca decreased by three orders (J. Mulder and J. Sa) for their support, C. van Ditzhui-
of magnitude comparedto direct loadingfrom a thermal jzen for her work on the Monte-Carlosimulations, J. W.
atomicbeam. Wefindthatfinallythe backgroundsignal Dunn for providing the code to take into account the
for singleatomdetectionofthe lessabundantisotopes is multilevel structure of 43Ca and Toptica Photonics for
no longer limited by the 40Ca atoms but dominated by prompt assistance. This project (00PR1887) is part of
laserstraylight. Thisenablessingleatomdetectionofall theresearchprogramoftheStichtingvoorFundamenteel
stableisotopes. Improvementswillbemadetothesetup: OnderzoekderMaterie(FOM)whichissupportedbythe
increasingthelaserpowerwillincreasetheefficiencyand Nederlandse Organisatie voor Wetenschappelijk Onder-
furtherimprovetheperformanceandtheisotopeselectiv- zoek(NWO).AdditionalsupportisfromtheEUcontract
ity ofthe individualcomponents: transversalbeamcom- NIPNET (HPRI-CT-2001-50034).
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