A compact high-flux source of cold sodium atoms

1.8 MB·English

by  G. Lamporesi

A compact high-flux source of cold sodium atoms
G. Lamporesi, S. Donadello, S. Serafini, and G. Ferrari∗
Dipartimento di Fisica, Università di Trento and
INO-CNR BEC Center – I-38123 Povo, Italy, EU
(Dated: January 29, 2013)
Wepresentacompactsourceofcoldsodiumatomssuitablefortheproductionofquantumdegen-
erategasesandversatileforamulti-speciesexperiment. Themagneticfieldproducedbypermanent
magnets allows to simultaneously realize a Zeeman slower and a two-dimensional MOT within an
order of magnitude smaller length than standard sodium sources. We achieve an atomic flux ex-
ceeding 4×109 atoms/s loaded in a MOT, with a most probable longitudinal velocity of 20 m/s,
3 andabrightnesslargerthan2.5×1012 atoms/s/sr. Thisatomicsourceallowedustoproduceapure
1 BEC with more than 107 atoms and a background pressure limited lifetime of 5 minutes.
0
2
PACSnumbers: 37.10.De,32.60.+i

n
a
J I. INTRODUCTION pactness and simplicity of the experimental setup. It

8 is based on a thermal sodium atomic beam coming out
2 from an oven that is slowed down and two-dimensionally
Laser cooling techniques developed in the last thirty
trapped. Anadditionallaserbeamalignedalongthenon-
yearsrevolutionizedatomicphysicsallowingtocoolneu-
]
trapped direction pushes the atoms hence obtaining a
s tral atoms down to micro and nanokelvin temperatures,
a collimated and slow atomic beam that is finally recap-
at which ultimate control of each atomic degree of free-
g
tured and cooled in a three-dimensional magneto-optical
t- dpolomyedbercooumtienselpyosinsibmlee.troNloogwicaadlayasppcloicldatiaotnosm[s1]a,rienetmhe- trap (3D MOT) in a nearby ultra-high vacuum (UHV)
n
region.
a realization of inertial sensors ([2] and Refs. therein) and
u to operate state-of-the-art atomic clocks [3]. At these Sodium is a valuable option if one needs to produce
q temperatures dilute gases can also reach quantum de- verylargeBose-Einsteincondensates, thankstoitssmall
t. generacy offering the possibility to directly manipulate three-bodyrecombinationrateandconvenientscattering
a quantumdegeneratesystemswithextremeprecisionand length. In the last years interest in producing cold sam-
m
control (see [4] and Refs. therein). ples of sodium comes also from the ultra-cold molecules
- fieldcommunity[10];togetherwithKCs,NaKseems[11]
d The growing interest in cold atoms led to the devel-
infacttobeanexcellentpairofalkaliatomsforthepro-
n opment of specific atomic sources. Sources capable of
duction of stable systems [12] of ground state molecules
o high fluxes have been developed for many atomic species
c addressing issues of compactness, atomic yield, and ease with a dipole moment of a few debyes [13] that therefore
[ representsapromisingsystemforaccessinganewdomain
of use. In fact the availability of essential experimen-
ofcoldatomic/molecularphysicspassingfromcontactin-
1 tal tools as the atomic source, in many circumstances
teraction to long-range, anisotropic interactions.
v proved to drive the choice of the atomic species to study
6 and, eventually, the physical domain to address. So far With the exception of a few experiments in which a
6 high fluxes of cold atoms are obtained mainly with two small number of atoms is needed [14], standard cold
5 classes of atomic sources. In the first one a flux of hot sodium experiments employ a long Zeeman slower (ZS)
6
atoms from an oven is slowed down by means of dis- [9]toefficientlyslowdownalargenumberofatomscom-
.
1 sipative light forces and inhomogeneous magnetic fields ing out from an oven. Sodium 2D MOTs were already
0 [5]. This technique is applied to a wide class of atomic demonstratedasatomfunnels[15]toincreasethebright-
3 species, such as alkali metals, alkali earths, rare earth ness of traditional ZS.
1
: elements and noble gases. The second class of atomic Theworkreportedin[16]introducedaninnovativeap-
v sources is based on the trapping and cooling of atoms proachinthecaptureoflightatoms(lithiuminthatcase)
Xi directly from vapor pressure. This simplifies the experi- fromathermaldistributiondirectlyina2DMOTplaced
mental setup, but the performances are significant only in the vicinity of the oven. We demonstrated this ap-
r
a for some medium-heavy alkali atoms such as potassium proach for sodium atoms and we showed how a shrewd
[6], rubidium [7] and cesium [8]. choice of magnetic fields and the addition of a further
In this article we present a novel type of compact laser beam results in higher yields of the atomic source.
atomic source delivering cold sodium atoms with state- The cold sodium atom source thus realized represents a
of-the-art fluxes [9]. This sodium source has a novel de- compactandconvenientalternativetotheclassiconefor
signthatcombineshigh-fluxperformanceswiththecom- loading a large number of atoms in a 3D MOT.
In the following sections the reader will find a de-
scription of the atomic source working principle with
details of the the vacuum, optical and magnetic setup
∗Electronicaddress: [email protected] (Sec. II), a set of the most meaningful characterization
2
(a) (b) (c)
Zeeman slower TSP
beam magnets differential
TSP pumping εy
channel
ε− ε+
UHV ion
HV ion pump
pump 3D MOT
K
push Sr
beam
ε+ Na ε−
m
m
magnets 126
Na oven
2D MOT
laser beams
2D-MOT plane
FIG.1: (Coloronline)(a)3Dviewofthevacuumsystem. HVregionontheleftsidecontainstheatomicsourceandtheoptical
access for the pre-cooling stage. The differential pumping channel connects this to the UHV region where the experiment is
performed in a clean environment. Light beams (yellow) and magnets (red-blue) are shown. (b) Magnification of the compact
slowing/cooling region. (c) 2D view of the pre-cooling plane showing atomic sources and beams configuration.
curves(Sec.III)thatwereexperimentallyrecordedonthe one on the right is designed for trapping cold atoms and
apparatus, and a simulation (Sec. IV) of the atomic tra- studying them in UHV conditions.
jectory compared with the final performances obtained. The differential pumping channel, with diameter
d=2.0 mm and length l=22.8 mm, in the long tube ap-
proximationhasaconductanceof4.3×10−2 l/s. Assum-
II. APPARATUS DESCRIPTION ing the nominal pumping velocity of the pump in the
UHV region, from the conservation of the mass flow we
A sketch of the experimental setup is given in Fig. 1. can obtain a differential pressure between the HV and
Sodiumatomsevaporatedfromanoven,heatedto210◦C, UHV chambers up to 103.
propagateintheverticaldirectiontowardsthe2D MOT The geometry of the 2D MOT chamber is inspired to
region. Along their trajectory a red-detuned counter- theonedescribedin[16]. InaverticalplaneseveralAISI
propagating beam, in combination with a magnetic field 316L stainless steel tubes cross allowing for atomic and
increasing with z, slows a large velocity class of atoms opticalaccessforpre-cooling. 5gramsofmetallicsodium
belowthecapturevelocityofa2D MOTlocatedjust12 areheldinacruciblepositionedintheplane126mmbe-
cm above the oven. The 2D MOT is in a vertical plane low the 2D MOT region and connected through a CF16
and atoms are free to move along a horizontal transfer flange. The oven is heated up to temperatures of the or-
axis. A beam aligned on that axis pushes the cold cap- der of 210◦C, higher than the melting temperature of
tured atoms through a differential pumping channel to- sodium (T =97.8◦C), obtaining a flux of fast moving
m
wards a cleaner environment where a 3D MOT collects atoms. Our oven operating temperature is 100◦C less
the incoming atomic flux. than thetypical temperatures ofsodium ovens employed
Themainfeaturesandsometechnicaldetailsoftheex- in combination with a ZS [9]. This is a good point for
perimental apparatus will be provided in the following. the reliable operation on the long term and for ensuring
a high quality of vacuum already in the HV region.
Atoms collected in the 2D MOT and pushed with an
A. Vacuum system on-axis quasi-resonant beam cross the differential pump-
ing channel and enter the UHV chamber at the end of
Standard cold atoms experiments typically need to which a quartz cell hosts a 3D MOT and other atomic
suppress background vapor pressure to extend the life- traps for future experiments.
timeofthesampleontheminutetimescale. Atthesame There are many advantages in using a transversely
time large number of cold atoms collectable in the final loaded2DMOTinsteadofatomicsourceswithacoaxial
trap is desirable. These two requirements are difficult to loading. Atomsfromtheovencannotpassdirectlytothe
be simultaneously achieved in the same vacuum cham- UHVchamberthroughthedifferentialpumpingchannel,
ber, hence in our design the vacuum system is divided therefore no extra stages, such as mechanical shutters,
in two regions (HV and UHV chambers) connected by a areneededinthevacuumchambertoreducebackground
narrow channel which ensures differential pumping. The hotatomsintherecaptureregion. Thetransferofatoms
chamber on the left side of Fig. 1(a) is mainly devoted tothe3DMOTcanbeopticallymodulatedbyswitching
to the atomic source with a pre-cooling stage, while the off the push and 2D MOT beams; in our case no atoms
3
are detected in the 3D MOT in absence of these beams. series) pumped with an Ytterbium fiber laser provides
In addition to the simplification of the apparatus, our up to 8 W output power on a single transverse mode,
approach offers the possibility to simultaneously deal when injected with 9 mW, while maintaining polariza-
withmoreatomicspecies. Thankstoitsradialsymmetry tion and spectral properties of the incoming beam.
the 2D MOT can be transversely loaded from different The frequency of the amplified infrared light is dou-
sources (see Fig. 1(c)). Our setup is already set for cool- bled through a resonant frequency doubling unit, based
ing also potassium from a vapor-cell 2D MOT. Also a ona15mmlongLiB O non-linearcrystal. Thebirefrin-
3 5
strontium oven is present for future developments. The gentphasematchingisachievedwithtemperaturetuning
coolinglightsfortheoperationofdifferentatomicspecies at 45◦C. The resonant bow-tie cavity has a round-trip
2D MOTs are mixed with dichroic mirrors. length of 300 mm, a finesse of 150, and it is stabilized by
means of polarization spectroscopy [18].
When operating the RFA at 7 W we obtain 3.5 W of
B. Laser system light, stabilized at 589 nm. The emission linewidth is
about 20 times narrower than the natural linewidth for
Lasercoolingofsodiumcanbeachievedbyusingcool- the D2 transition of sodium. A stable and reliable fre-
inglightslightlyred-detunedfromits|F =2(cid:105)→|F(cid:48) =3(cid:105) quency reference is obtained directly from the D2 tran-
transitionontheD lineandrepumpinglighttunedclose sition of sodium, with FM saturated absorption spec-
2
tothe|F =1(cid:105)→|F(cid:48) =2(cid:105). D lineforsodiumliesat589 troscopy performed on a sodium heat pipe.
2
nm, hence not directly accessible with diode lasers. Dye As sketched in Fig. 2, repumping light is produced in
laserscanbeemployedatthiswavelength,butareusually two ways: an EOM tuned at 1.713 GHz provides two
large, expensive, and involved to operate on a long pe- frequency sidebands, one of which is resonant with the
riod. On the other hand, the infrared region of the spec- repumpingtransition,andweemployitfortheoperation
trum around 1200 nm, twice the wavelength of sodium of ZS and 2D MOT. In addition a series of two 350
D line, has recently become accessible with quantum MHzAOMsindoublepassandasinglepassoneshiftthe
2
dots technology [17]. coolinglightfrequencyagainby1.713GHz. Thissolution
Fig. 2 illustrates our approach that consists in fre- instead,isusedtoindependentlycontrolrepumpinglight
quency doubling a MOPA system delivering 1178 nm in the final 3D MOT region and for a state selective
light. The master oscillator is a diode laser based on imaging.
InAs quantum dots on GaAs substrate (Innolume GC- Polarization maintaining optical fibers are used to de-
1178-TO-200),withsingletransversemodeandananti- liverlightontheexperimentalapparatusprovidinggood
reflection coating on the output facet and it delivers quality TEM mode and decoupling the laser sources
00
about20mW.ARamanfiberamplifier(MPB RFA-SF- from the optical table hosting the vacuum system. All
the beams have a diameter of 25 mm with the exception
ofthepushbeamthatisfocussedtoawaistof320µmin
the differential pumping channel. The total power after
/4
the optical fibers is around 600 mW.
AOM-~80 lock on the
F=2 F'=3 line
/2 /2
AOM+80 Na heatpipe
3.5 W /2
SHG C. Magnetic field sources
1178-589nm AOM+98 AOM-121 cooler 3D MOT
7 W /2 Neodymium bar magnets (Eclipse N750-RB) gen-
RFA
1178nm AOM+116 AOM-104 probe/push erate the permanent field that, at the same time, is
/2 used for slowing down hot atoms coming from the oven
20 mW EOM1715 /2 AOM-115 AOM+105 2D MOT in a ZS-like configuration and for trapping and cooling
ECDL
1178nm /2 themina2D MOT.Thesemagnetsarerelativelysmall,
/4
AOM-152 Zeeman slower (10×25×3) mm3, favoring the development of compact
/2
/4 /4 atomicsources,andprovideastablemagneticfieldwhen
AOM+400 AOM+400 operatedbelow100◦C.Themagnetizationandthecorre-
/2
sponding point-like dipole for a single magnet, resulting
AOM+113 repump 3D MOT
from our measurements, are M=(8.7±0.1)×105 Am−1
AOM+11a3 repump dark spot and m=(0.65±0.01) Am2, in good agreement with the
value reported in [16] for the same magnets used for a
FIG. 2: (Color online) Sketch of the optical setup used for lithium 2D MOT.
producing all the light beams needed to cool sodium atoms. Given the spatial constraints of the vacuum appara-
Reported power values indicate the power output of the de- tus, we found that the optimal magnets arrangement is
vices, without considering further power losses. Signed num- achieved by placing four equal stacks of nine magnets
bers in the blue AOM boxes report the chosen AOM order each at the corners of a hypothetical vertical rectangle
(±1) and its driving frequency in MHz. centered on the 2D MOT axis (see Fig. 1). To get a
4
∇zBx [T/m] x [m] No field is present along the 2D MOT axis (y).
5 0 5
0. 0. 0. -0.10 -0.05 0.00 0.05 0.10 Since we cannot turn off the magnets field once the
-
3D MOTloadingiscompleted,weevaluatedthemagni-
0 tude of the field in the 3D MOT region. It results being
1
0. atmost2×10−7 Twithamaximumgradientof3×10−5
Tm−1, both much smaller than the typical values for
5 MOT operation.
0
0. Themaindrawbackofourmagneticconfigurationcon-
sists in the fact that at most only half of the power of
m] 00 the ZS beam has a well-defined circular polarization, as
z [ 0. desired foran optimaloperation. Given thefield along x
and the ZS beam propagating along z, in fact, one can
5 maximize the amount of circular polarization by polariz-
0
-0. ing the ZS slower beam along y.
0
1
-0. III. SYSTEM CHARACTERIZATION
2 0 2
0.0 0.0 0.0 The atomic source was optimized by measuring the
Bx [T] - loading rate of the 3D MOT as a function of several pa-
Bx(x=0) 0.000 0.005 0.010 0.015 0.020 rametersof 2DMOT,ZS,pushbeamsandtheoventem-
∇zBx(x=0) B [T] perature. For very large atom number in the 3D MOT
rescattered light from cold atoms and excited state col-
FIG. 3: (Color online) Representation of the field generated
lisions limit the maximum atomic density achievable.
bythemagnetsinthe2D MOTcentralverticalplane(y=0)
We circumvented this issue by using a dark-spot MOT
orthogonal to the chamber axis. The color scale is a func-
scheme [19].
tion of the magnitude of the field, while the vectors repre-
sent its direction. The four magnet stacks are located in Intensity and detuning of each beam are respectively
(x,y,z)=(0,±37,±49) mm, the two on top being oriented reported in sodium units of saturation intensity for σ±
along −x and oppositely the other two. The plot on the left polarizedlightI =6.26mW/cm2 andnaturallinewidth
sat
showsmagneticfieldandgradientalongthecentral(x=y=0) for the D line Γ=2π·9.79 MHz.
2
vertical axis of the 2D MOT, along which the ZS acts. The Table I summarizes the system parameters, experi-
field along y axis is zero. mentally found, that provide the best performances of
the apparatus. Reported intensity values for MOTs are
meantastotalintensitiessummingoverallMOTbeams,
quadrupolar field the upper dipoles are aligned perpen- whereas ZS intensity corresponds to the σ+ component
dicularly to the plane and the lower ones in the opposite at the cooling frequency (the beam contains 50% power
direction. In comparison with [16] we replaced each in- on the cooling, 25% on the repumping sideband and has
plane magnetic stack with a pair of two stacks equally a linear polarization along y).
distant from the cooling plane in order to leave access to
the main axis of the vacuum system allowing for multi-
speciesatomicin-flowandfortheZSbeamopticalaccess. TABLE I: Set of frequency detuning (from the |F =2(cid:105) →
Furthermore the plane of the magnets is rotated by 90◦ |F(cid:48) =3(cid:105)transition)andintensityforeachbeamintheatomic
with respect to the 2D MOT plane, leaving the oper- source.
ation of the 2D MOT unaltered, but ensuring about a 2D MOTcool −10MHz (−Γ) 3.6Isat
3-fold increase of the peak magnetic field along the ZS 2D MOTrep +1713MHz 1.8Isat
trajectory. Z3DS MOTcool −−33034MMHHzz ((−−33.14ΓΓ)) 62..52IIssaatt
The magnet stacks are fixed along the chamber axis 3D MOTrep +1718MHz 0.5Isat
neartheverticaltubesoftheZSandtheoven, withcen- push +12MHz (+1.2Γ) 11Isat
ters at a vertical distance of 98 mm and a horizontal one
of 75 mm. The sensitivity of the system performances to any pa-
Thetotalcalculatedmagneticfieldforthefinalconfig- rameter was explored by varying one of them at a time
uration of the 2D MOT in the xz plane (see notation in and the most significant are reported in the following.
Fig. 1) is reported in Fig. 3. On the central vertical axis Fig. 4(a) shows the atomic flux as a function of the
the field is directed along x. Its magnitude as a function 2D MOT cooling frequency. One can see that the best
of z is also reported in Fig. 3. The expected vertical and detuningisaround−1Γandthat±0.5Γawayfromthat
horizontal gradient in the middle is 0.36 Tm, while the detuning the efficiency drops by 10%. This result can
largest magnitude of the field is 1.71×10−2 T along the be compared with 2D MOT systems of other atomic
vertical axis and 6.6×10−3 T along the horizontal one. species. An optimal detuning of −1.7Γ was found for
5
5 best ZS frequency 5 vapor pressure 101
peak atomic flux atomic flux
305 10-3
4 4
9s]flux [10 atoms/ 123 ZS frequency [MHz] 222389905050 9ux [10 atoms/s] 123 240ZS fre 2q8u0ency [M 3H2z0] 1239flux [10 atoms/s] pressure [torr]1100--54 111000--021 9flux [10 atoms/s]
fl
0
0 0 10-6
-25 -20 -15 -10 -5 0 3 4 5 6 7 150 200 250
(a) 2D MOT frequency [MHz] (b) ZS beam intensity [I/Isat] (c) T oven [°C]
FIG. 4: (Color online) (a) Measured flux of atoms (green circles) captured in the 3D MOT as a function of the frequency
detuning of the 2D MOT beams. Central data are fit to a Gaussian (black line) to find the best frequency. (b) Best ZS
frequency (red) and maximum flux recorded (yellow) for different ZS intensities. The inset shows a typical dependence of
atomic flux on the ZS frequency at fixed intensity. (c) Comparison between the vapor pressure of sodium (blue line) and the
3D MOT loading rate (red circles) as a function of the oven temperature. For this dataset about 8 times smaller repumping
power was used in 2D MOT and ZS, explaining the smaller maximum flux achieved.
87Rb [7], that is characterized by a much better defined of-flight (TOF) method. The population of a specific
hyperfine structure; larger detunings were used for 39K velocity class of the source can be measured with the
and 41K where the repumping light also has a cooling following procedure. Starting from an empty 3D MOT
effect [6]; optimum detuning was even larger (−8Γ) in without the push beam, a 1 ms long pulse of the push
[16]for6Liwhosehyperfinestructureisnotonlynarrow, beamlaunchesanatomicpacketfromthe2DMOTwhile
but also inverted. the 3D MOT repumping light is switched off. After a
The optimization of the ZS parameters is reported in given time tTOF the repumping light is switched back on
Fig. 4(b). ZS frequency was scanned for a few given in- for 3 ms time, so that only atoms traveling with a veloc-
tmenaxsiitmyizvianlguetsh.eWaetonmoitcicfleduxt,hachtatnhgeeospwtiimthumZSfrienqtueennsictyy, 2itDyvMlonOgT=adtTnTOOdFF3(DdTMOFO=T42c±e1ntcemrs)isatrheerdeicsatpatnucreebdeitnwethene
and also that the maximum flux detected for each inten- 3D MOT. In order to increase the signal-to-noise ratio
sity value varies as power is increased, starting to show this procedure is repeated 450 times every 34 ms, accu-
a saturating behavior. mulating atoms in the trap, before acquiring the signal
Atoms trapped in the 2D MOT are pushed towards reported in Fig. 5.
the3DMOTbyusingabeamfocussedinthedifferential ThedistributionoftTOF wasfittedtoaGaussianfunc-
pumpingchannel(waistw=320µm)with110µWpower. tion finding a mean value of t0=(21.0±0.1) ms and a
We observe best transfer efficiency when using a blue-
detuning of 12 MHz. No repumping light is present on
this beam. 0.12
The optimization of the sodium oven temperature
keepingallotherparametersfixedisreportedinFig.4(c). u.]
We see that for oven temperatures lower than 160◦C the e [a. 0.08
atomic flux is negligible. Then the loading rate increases nc
e
withtheoventemperatureuptoabout240◦C.Forhigher sc
e
temperatures the loading rate decreases. The loading uor 0.04
fl
rateiscomparedwiththetheoreticalvaporpressurepre- T
O
dictedforliquidsodium[20]. Weobservethatthetwopa- M
D
rametersaredirectlyproportionalfortemperatureslower 3
0.00
than 200◦C: the initial growth of the atomic flux can be
explained with the rise of the oven yield, proportional to
the sodium vapor pressure until it reaches 2×10−4 torr. 10 20 30 10 20 30 40 50
At higher temperatures the loading rate flattens and de- tTOF [ms] vlong [m/s]
creases,likelybecauseofcollisionallossesinducedbythe
FIG.5: (Coloronline)Measuredtimeofflightdistributionof
hot beam hitting the trapped atoms in the 2D MOT.
the atomic beam (left). Velocity distribution (right) of the
The longitudinal velocity distribution of the atomic atomic beam deduced from the time of flight and the known
beam from the 2D MOT was measured with a time- distance between the MOTs.
6
standard deviation ∆t=(3.4±0.1) ms (Fig. 5 left). The axis and treat separately two regions: the ZS stage
velocity distribution (Fig. 5 right) is therefore centered (−126 mm<z <−17.7 mm), and the 2D MOT region
atv =(20.0±0.5)m/sandhasahalf-width∆v ofthe (−17.7 mm < z < 17.7 mm), the latter being delimited
0 long
order of 3 m/s. This measurement of the peak velocity by the overlapping region between the 2D MOT light
isnotlimitedbytherecapturevelocityofthe3D MOT, beams. Since the ZS and the 2D MOT beams have fre-
expected to be much larger, nor by the gravity fall dur- quencyoffsetsofseveralnaturallinewidths,wecanargue
ingthetransfer,thatintroducesalowercut-offat2m/s, that the two forces cannot be simultaneously active on
considering our geometry. atoms, thusjustifyingourseparatetreatment. Themag-
The residual longitudinal temperature of the atomic netic field is numerically calculated for the permanent
beam can be estimated from the width of the veloc- magnets configuration described in Sec. IIC.
ity distribution as T =m∆v2 /k ∼ 30 mK. In the The starting conditions are the oven vertical position
long long B
transversedirection,onecanconsiderthesolidanglecov- z =−126 mm and the initial velocity v , whereas v rep-
0 0 1
ered by the 3D MOT capture area and the distance resents the velocity at the end of the ZS region. For the
d , obtaining 1.8 × 10−3 sr. The measured atomic simulationsweusetheparametersthathavebeenexper-
TOF
flux of 4.5×109 atoms/s implies then a source bright- imentally optimized (see Tab. I).
ness larger than 2.5×1012 atoms/s/sr. The differential Under the above conditions the atoms in the simula-
pumping channel sets a geometrical upper limit on the tions are either bounced back by radiation pressure be-
velocity dispersion ∆v =0.9 m/s. This corresponds fore reaching the 2D MOT or not decelerated at all,
trans
toatransversetemperatureoftheorderofT =2mK, dependingonv . Thisisincontrastwiththeexperimen-
trans 0
which amounts to a few times the Doppler tempera- tal evidence of gain when using the ZS. This simplified
ture T =235 µK. The divergence set by the channel model serves as a demonstration of the system working
D
(5.9×10−3 sr)islargerthanthemeasuredone,therefore principle, not as a quantitative calculation. We verified,
not limiting the atom transfer. though,thatbyconsideringa20%smallermagneticfield
The best performances of the atomic source are sum- the simulation provides reasonable numbers in terms of
marized in Table II. From the values reported in that efficiency of the cooling system, of the same order of the
table we can see that the ZS beam increases the load- magnitude of the one experimentally observed. More-
ing rate by a factor 12. This value is of the same order over, efficiencyandtypicalvelocityclassesinvolvedseem
of magnitude of the factor estimated in the simulation not to change significantly as field or intensity param-
described in the following section. eters are slightly changed. Here we present the results
weobtainedbyconsideringa20%smallermagneticfield,
without further corrections on beams intensity.
TABLE II: Atomic source performances.
loading rate without ZS (3.7±0.5)×108 atoms/s
loading rate with ZS (4.5±0.5)×109 atoms/s 1.02
250
total trapped atoms
in the 3D dark spot MOT (1.2±0.1)×1010 atoms 1.00 200
most probable s]150
m/
longitudinal velocity (20.0±0.5) m/s a.u.] 0.98 v [1100
source brightness >2.5×1012 atoms/s/sr ution [ 50
b
stri 0
di 0 50 100 150 200 250
flux 0.04 v0 [m/s]
IV. SIMULATION OF ZS AND 2D MOT vc
OPERATION without ZS
with ZS
0.02
Slowingandcoolingeffectsduetoradiationpressurein
presence of the magnetic field generated by the perma-
nent magnets were simulated both for the first slowing 0.00
0 50 100 150 200 250
stage and for the 2D MOT.
v [m/s]
The numerical model is based on several simplifica-
tions: we restrict the simulation to a single two-level- FIG.6: (Coloronline)Fluxdistributionφ(v)ofatomsemitted
atom trajectory in a 1D geometry, subject to classical bytheovenwith(red)andwithout(blue)theZSeffectfora
radiation pressure. sampleat210◦C.Inset: ZSoutputvelocity,v ,asafunction
1
The goal is to slow down the largest amount of atoms ofthestartingvelocityattheoven,v . Alargevelocityclassis
0
coming from the oven, below the 2D MOT capture ve- sloweddownto19m/s,belowthe2D MOTcapturevelocity
locity vc. We set the origin z=0 on the 2D MOT vc.
7
Atoms with v ranging between 51 m/s and 187 m/s V. CONCLUSION
0
are decelerated to v =19 m/s, as shown in the inset of
1
Fig. 6. For lower velocities the atoms are bounced back,
Inconclusionwereportedonanewreliableschemefor
while for higher velocities the ZS does not significantly
producing a cold beam of sodium atoms which is char-
affect the atomic trajectories.
acterized by compactness and high-flux performances at
With similar methods we simulated the atomic trajec-
the same time. We demonstrated the possibility to effi-
tory in the 2D MOT, taking into account the proper
ciently trap sodium atoms in a 2D MOT from a nearby,
beams geometry and the magnetic field. The initial po-
in-plane oven by first slowing them down within a short
sition is now z =−17.7 mm. The atoms are trapped on
1 length in a ZS-like configuration. The design allows to
a ms timescale if their initial velocity is smaller than the
introduce additional atomic species to cool with analo-
capture velocity, that is found to be v =76 m/s. This
c gous procedure in the same system for the realization of
velocity is larger than the velocity of the atoms slowed
multi-species experiments.
down by the ZS stage. All the atoms involved in the ZS
are thus captured in the 2D MOT. Thebestloadingrateina3Ddark-spotMOT,located
The compact ZS stage is essential to change the ve- about 42 cm away from the source, of more than 4 ×
locity range of atoms involved in the full cooling process 109 atoms/s, allowed us to readily create a 3D MOT
from 0-76 m/s to 51-187 m/s. This means more than containing more than 1010 atoms. We observed that a
just a 2 times larger velocity class because the atomic few ms optical molasses stage [22, 23] after loading a
flux, considering the Maxwell-Boltzmann distribution, is dark-spot MOT, consistently enhanced the phase space
notlinearinv. ConsideringtheMaxwell-Boltzmanndis- densityevenintheregimeofhighopticaldepth,similarly
tribution of a 1D thermal beam modified by the ZS (in- to what has been observed on 39K [24]. A large amount
set of Fig. 6), we calculate the atomic flux distribution of atoms was thus transferred in a Ioffe-Pritchard [25]
φ(v) at the entrance of the 2D MOT region (Fig. 6), magnetic trap with axial and radial frequencies of 12 Hz
whichissubstantiallyincreasedinthe2D MOTcapture and128Hzandperformedevaporativecoolingachieving
range. The atomic flux distribution over an area σ is a pure BEC with more than 107 sodium atoms.
φ(v)dv =nσvf(v)dv, where n is the atomic density. Webelievethisnovelandcompactatomicsourcerepre-
We can integrate φ(v) from 0 to vc with and without sents a valid alternative for the realization of a high-flux
the ZS. The ratio between the two integrals gives 35. sourceofsodiumatoms,especiallyincaseofmulti-species
This represents the gain factor given by the compact ZS experiments where complexity and encumbrance are im-
stage to be compared with the experimentally measured portant issues.
flux ratio of 12.
We are aware that the model is oversimplified and, in
order to get an accurate quantitative result, one should
haveabetterknowledgeoftheactualmagneticfield[21],
ACKNOWLEDGMENTS
properly consider the multi-level atomic structure inter-
acting with σ+ and σ− light and extend the single axis
model to a 3D trajectory. This goes beyond our goals. The authors thank R. Graziola, M. Tomasi and
The numerical model can be adapted also for differ- the Electronic&Engineering Service of the University of
ent simulations. In particular it was useful to predict Trento for the valuable and effective support provided
whether with our setup the 2D MOT would work cor- during the activation of our laboratory. We also ac-
rectly also for potassium, when the experiment will pro- knowledge fruitful discussions with M. Prevedelli and F.
ceed towards the production of atomic mixtures. Try- Schreck, the support of the whole BEC Center in Trento
ing different plausible parameters we found that the andthecollaborativeexchangewiththeQuantumDegen-
2D MOT can also trap all the stable isotopes of potas- erate Gases group at LENS in Florence. This work was
sium. financially supported by Provincia Autonoma di Trento.
[1] S. Chu, Nature 416, 206 (2002). guscio, Phys. Rev. A 73, 033415 (2006).
[2] M. de Angelis, A. Bertoldi, L. Cacciapuoti, A. Giorgini, [7] K. Dieckmann, R. J. C. Spreeuw, M. Weidemüller, and
G. Lamporesi, M. Prevedelli, G. Saccorotti, F. Sor- J. T. M. Walraven, Phys. Rev. A 58, 3891 (1998).
rentino,andG.M.Tino,MeasurementScienceandTech- [8] J.Yu,J.Djemaa,P.Nosbaum,andP.Pillet,OpticsCom-
nology 20, 022001 (2009). munications 112, 136 (1994), ISSN 0030-4018.
[3] H. Katori, Nature Photonics 5, 203 (2011). [9] K.M.R.vanderStam,E.D.vanOoijen,R.Meppelink,
[4] J. R. Anglin and W. Ketterle, Nature 416, 211 (2002). J.M.Vogels,andP.vanderStraten,ReviewofScientific
[5] W. D. Phillips and H. Metcalf, Phys. Rev. Lett. 48, 596 Instruments 78, 013102 (pages 10) (2007).
(1982). [10] K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er,
[6] J.Catani,P.Maioli,L.DeSarlo,F.Minardi,andM.In- B.Neyenhuis,J.J.Zirbel,S.Kotochigova,P.S.Julienne,
8
D. S. Jin, and J. Ye, Science 322, 231 (2008). [21] We believe that the main source of error in the simpli-
[11] C.-H. Wu, J. W. Park, P. Ahmadi, S. Will, and M. W. fied model comes from the computed magnetic field. In
Zwierlein, Phys. Rev. Lett. 109, 085301 (2012). fact the vacuum system weldings show some finite mag-
[12] P. S. Zuchowski and J. M. Hutson, Phys. Rev. A 81, netizationandbeingaroundthecoolingareatheymight
060703 (2010). modify the actual field. In addition the model considers
[13] A.Gerdes,O.Dulieu,H.Knöckel,andE.Tiemann,The only the field along the central vertical axis, but atoms
European Physical Journal D 65, 105 (2011). feel the slowing force on a circle of 8 mm radius, where
[14] E. Mimoun, L. De Sarlo, D. Jacob, J. Dalibard, and themaximumfieldalongaverticallinecanvarybymore
F. Gerbier, Phys. Rev. A 81, 023631 (2010). than 10%.
[15] E.Riis,D.S.Weiss,K.A.Moler,andS.Chu,Phys.Rev. [22] P.D.Lett,R.N.Watts,C.I.Westbrook,W.D.Phillips,
Lett. 64, 1658 (1990). P.L.Gould,andH.J.Metcalf,Phys.Rev.Lett.61,169
[16] T. G. Tiecke, S. D. Gensemer, A. Ludewig, and (1988).
J.T.M.Walraven,PhysicalReviewA80,013409(2009). [23] After loading in the dark-spot MOT we keep atoms for
[17] A. Nevsky, U. Bressel, I. Ernsting, C. Eisele, M. Okhap- 5msinanopticalmolassestoreducetemperature.Mag-
kin, S. Schiller, A. Gubenko, D. Livshits, S. Mikhrin, neticfieldsareswitchedoff,coolinglightdetuningislin-
I. Krestnikov, et al., Applied Physics B 92, 501 (2008). earlyrampedfrom−Γto−3Γanditsintensitydecreased
[18] T.W.HanschandB.Couillaud,OpticsCommunications by 20%.
35, 441 (1980). [24] M. Landini, S. Roy, L. Carcagní, D. Trypogeorgos,
[19] W. Ketterle, K. Davis, M. Joffe, A. Martin, and M. Fattori, M. Inguscio, and G. Modugno, Phys. Rev.
D. Pritchard, Physical review letters 70, 2253 (1993). A 84, 043432 (2011).
[20] C. B. Alcock, V. P. Itkin, and M. K. Horrigan, Vapor [25] D. E. Pritchard, Phys. Rev. Lett. 51, 1336 (1983).
Pressure Equations for the Metallic Elements: 298-2500
K, vol. 23 (Canadian Metallurgical Quarterly, 1984).