Heteronuclear ionizing collisions between laser-cooled metastable helium atoms

0.24 MB·English

by  J. M. McNamara

Heteronuclear ionizing collisions between laser-cooled metastable helium atoms
J. M. McNamara, R. J. W. Stas, W. Hogervorst, and W. Vassen
Department of Physics and Astronomy, Laser Centre Vrije Universiteit,
De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
(Dated: February 2, 2008)
We have investigated cold ionizing heteronuclear collisions in dilute mixtures of metastable
7 (23S1) 3He and 4He atoms, extending our previous work on the analogous homonuclear collisions
0 [R.J.W.Staset al.,PRA73,032713 (2006)]. Asimpletheoreticalmodelofsuchcollisions enables
0 us to calculate the heteronuclear ionization rate coefficient, for our quasi-unpolarized gas, in the
2 absenceof resonant light (T =1.2mK): K(th)=2.4×10−10cm3/s. This calculation issupportedby
34
ameasurement of K usingmagneto-optically trapped mixturescontaining about 1×108 atoms of
n 34
a each species, K3(e4xp)=2.5(8)×10−10cm3/s. Theory and experiment show good agreement.
J
7 PACSnumbers: 32.80.Pj,34.50.Fa,34.50.Rk
1

] I. INTRODUCTION the dark”, between isotopes of a single element are both
h mediatedatlong-rangeby the van-der-Waalsinteraction
p (∝ 1/R6) and any differences are due, in the main, to
- The importance of cold collisions with regard to the
m differing atomic structures and quantum statistical sym-
dynamicsofdiluteneutralatomcloudswasrealizedsoon
metries.
o aftertheadventoflaser-cooledandtrappedatomicsam-
t ples [1]. Since then, numerous investigations, both ex- Duetothehighinternalenergy(19.8eV)ofmetastable
a
. perimentalandtheoretical,havebeen made into the col- (23S1) helium atoms (He*), the spherical symmetry of
s
c lisional properties of many different homonuclear [2, 3, this atomic state, and the inverted (hyper)fine structure
i 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] and (later) heteronuclear of the atoms; ionizing collisions (Penning (PI) and asso-
s
y [14, 15, 16, 17, 18, 19] systems. Collisional studies are ciative (AI)):
h in themselves interesting, leading to an in-depth under-
p standingofthe variousscatteringmechanismspresentat
[ such low kinetic energies and methods by which we can He*+He*→He+He++e− (PI),

1 have some measure of control over elastic and inelastic He*+He*→He++e− (AI),
v collisions. 2
4
As opposed to collisions between thermal atoms, col-
9
lisions between cold atoms are sensitive to the long- dominate losses in trapped samples of laser-cooled He*.
1
1 range part of the interatomic interaction potential. The This has provided a unique setting for the study of cold
0 de Broglie wavelength may become comparable to the ionizingcollisionsinwhichthe highlyefficient, directde-
7 characteristicrange of the interatomic potential, and (in tection ofcollisionalloss products using charged-particle
0 the presence of a light field) the possibility of exciting a detectors is possible. In the past, several experiments
s/ quasi-molecular state, and the subsequent decay of that havemadeuseofmicrochannelplate(MCP)detectorsto
c stateduringacollision,becomesimportant. Theseeffects measure ion production rates and investigate collisional
si lead to phenomena such as scattering resonances, inter- losses in 3He* [20] and 4He* [20, 21, 22, 23]. Having re-
y action retardation, optically assisted collisions, photoas- alized the ability to trap large numbers (>108) of both
h sociation, opticalshielding and the formation of ground- isotopes (either individually or simultaneously) [19], we
p
state molecules. have previously reported on the isotopic differences be-
:
v tween binary homonuclear collisions of 3He and 4He [13]
Optically assisted collisions lead to large losses in
i inthe absenceofresonantlight,resolvinginconsistencies
X magneto-opticaltraps(MOTs)andareclearlydependant
in prior experimental and theoretical results.
r upon experimental parameters such as the intensity and
a detuning of the light frequencies present. A full theoret- In this article we describe what we believe to be the
ical treatment of these collisions is often hampered by first study of heteronuclear binary collisions between
the complexity of the molecular hyperfine structure [1], metastable atoms. Adapting our transparent theoretical
thusMOTsareusuallyempiricallyoptimizedfortheirin- model [13] slightly, we first derive a value for K (Sec.
34
tendedapplication,andcomparisonswiththeoryorother II), the heteronuclear ionization rate coefficient in the
experiments are difficult. Collisions in the absence of a absence of a resonant light field. This is complemented
resonantlightfieldare,ontheotherhand,atheoretically by trap loss measurements performed on a two-isotope
moretractableproblemandtheirassociatedlossrateco- magneto-optical trap (TIMOT) of 3He* and 4He* [19],
efficients are fundamental properties of a given system, fromwhich we also extracta value for K (Sec. IV). In
34
allowingdirectcomparisonswiththeoryandbetweenex- Section V we compare both results and briefly comment
periments. Homonuclearandheteronuclearcollisions,”in uponlossratesinthepresenceofthetrappinglightfields.
2
II. SINGLE CHANNEL MODEL OF THE
HETERONUCLEAR IONIZING LOSS RATE
The following model has been described in depth else-
where in its successful application to the description of
homonuclear ionizing collisions [13, 24], where it com-
pares well with the more comprehensive close coupling
theories developed by Venturi et al. [25, 26] and Leo et
al. [27]. Here we extend its applicability to include the
description of heteronuclear He* collisions for which no
calculations have previously been made. In the interests
ofbrevityweonlydescribethe modelssalientpoints and
its adaption to the heteronuclear case.
FIG. 1: He* potentials (labeled in Hund’s case (a) notation)
constructed as described in [27] (solid), together with the
modifications made (dashed). Atoms reaching the region of
A. Ionization rate coefficients
smallRionize;thecorrespondingrelativeparticlepropagates
freely to R=−∞ in our model, and ionization is accounted
At mK temperatures, collisional processes are domi- for by the loss of probability flux from the region of the po-
nated by only a few partial waves, ℓ, and the ionization tential well.
cross section may be written as a sum over the partial
wave contributions:
σ(ion) = σ(ion). (1)
ℓ
ℓ
X
Fromasemi-classicalviewpointwemayfurthertreatthe
inelastic scattering as a two-stage process in which (at
low energies) elastic scattering from the interaction po-
tential V(R) occurs at relatively large internuclear dis-
tance(R≥100a ),whilstionizationoccursonlyatsmall
0
internuclear distance (R ≈ 5a ) [28]. The assumption
0
thattheprocessesofelasticscatteringandionizationare
uncoupled allows us to factorize the probability of ion-
ization occurring in a collision, and write the ionization FIG. 2: Partial wave ionization cross sections (S = 0)
cross section for collisions with total electronic spin S as for 3He*-4He* (solid lines), 3He*-3He* (dotted lines) and
4He*-4He* (dashed lines). The familiar quantum threshold
(2S+1)σ(ion) = π (2ℓ+1)(2S+1)P(tun)(2S+1)P(ion), behavior (σ(ion)∝k2ℓ−1 (k→0)) is displayed.
k2 ℓ ℓ
ℓ
X
(2)
where k is the wave vector of the relative motion of the lated partial wave ionization cross sections are shown in
two atoms, (2S+1)P(tun) is the probability of the atoms Fig. 2.
reaching small interℓnuclear distance (i.e., not elastically The ionization rate coefficient K (particle−1cm3/s)
scattering) and (2S+1)P(ion) is the probability of ioniza- (determined in experiments) is temperature dependant,
tion occurring at short internucleardistance. In the He* and may be written in terms of the ionization cross sec-
system the quantum number S is well conserved during tion σ(ion)(E) [1, 32, 33]:
ionization and the application of Wigner’s spin conser-
∞
vation rule [29] tells us that 5P(ion) is very small [30], K(T)= σ(ion)(E)P(MB)(v )v dv , (3)
while Mu¨ller et al. [31] report ionization probabilities T r r r
Z0
of 0.975 for other spin states; we thus set 5P(ion) = 0
and 1P(ion)=3P(ion)=1 in Eq. (2). Having constructed whereP(MB)(v )istheMaxwell-Boltzmanndistribution,
T r
the1Σ+,3Σ+ and5Σ+ molecularpotentialsasdescribed for a given temperature, of the relative velocities in the
g u g
in [27] (to which we may add rotational barriers as re- atomic sample. Similarly, we may calculate the partial
quired) we modify them to simulate the losses due to wave ionization rate coefficients (2S+1)Kℓ(T) associated
ionization (Fig. 1) [32]. By numerically solving the ra- with a given molecular state (ignoring the radial contri-
dialwaveequationandfindingthestationarystatesusing butions: |s1i1,s2,S,FMF,ℓmℓi) [32].
thesepotentials,wemaycalculatetheincidentandtrans- Althoughthe calculatedvaluesof(2S+1)σ(ion) (Fig.2),
ℓ
mitted probability currents, Jin and Jtr respectively, the and (2S+1)Kℓ(T), are very similar for all isotopic combi-
ratioofwhich(J /J )givesus (2S+1)P(tun). The calcu- nations,thedescriptionofthecollisionalprocessinterms
tr in ℓ
3
TABLE I: Expansion coefficients a (F) =
SI
hs i ,s ,S,FM ,ℓm |s i f ,s j ,FM ,ℓm i. The scatter-
1 1 2 F ℓ 1 1 1 2 2 F ℓ
ing states |s i f ,s j ,FM ,ℓm i are indicated by their
1 1 1 2 2 F ℓ
valuesofF,whilethemolecularstates|s i ,s ,S,FM ,ℓm i
1 1 2 F ℓ
are given in Hund’scase (a) notation, 2S+1Σ+ .
g/u
F 1Σ+ 3Σ+ 5Σ+
g u g
1/2 p2/3 −p1/3
3/2 p5/6 −p1/6
5/2 1
FIG. 3: Theoretical unpolarized loss rate coefficient curves:
3He–3He(dashed),4He–4He(dotted)and,3He–4He(solid),
ofpartialwavesforeachcombinationisverydifferentdue together with our experimental data points and their error
to the differing quantum statistics involved. In the case bars: 3He–3He(diamond),4He–4He(triangle)and3He–4He
of homonuclear collisions the symmetrization postulate (square). For the purposes of this figure, the experimental
limits the number of physical scattering states describ- points have been corrected for the inhomogeneous distribu-
ing a colliding pair. However, in the heteronuclear case tion over the magnetic substates found in our MOT’s (see
there is no symmetry requirement and all partial wave Sec. IIB).
contributions must be taken into account.
Because the energy gained during a collision
ficients are shown in Fig. 3 (including those rates previ-
is so large, the evolution of an atomic state
ously calculated [13] for 3He* and 4He*) and for a tem-
(|s i f ,s j ,FM ,ℓm i)intheregionwheretheatomic
1 1 1 2 2 F ℓ
perature of T=1mK we obtain
hyperfine interaction is of the same order of magnitude
as the molecular interaction may be described to a good
approximationasbeing diabatic. Thus, to determine the K3(u4npol) =2.9×10−10 cm3/s. (8)
ionization rate associated with a given scattering state
K(F), we simply expand the atomic states onto the
eigenstates of the short-range molecular Hamiltonian, B. Ionization rate coefficient of trapped samples
Optical pumping processes in a MOT cause the dis-
|s i f ,s j ,FM ,ℓm i= a (F)×
1 1 1 2 2 F ℓ SI
tribution over magnetic substates P (where m is the
m
S,I
X azimuthalquantumnumber)ofthetrappedatomstodif-
|s i ,s ,S,FM ,ℓm i, (4)
1 1 2 F ℓ fer from the uniform (unpolarized) distribution assumed
above. Thisisimportantasthecontributionofeachcolli-
determine the fractionof ionizing states (S=0,1)in this
sionchanneltotheionizinglossesdependsuponP ,and
m
expansion (see Table I), and sum over the contributing
can be accounted for in our theoretical model by using
partial waves:
the density operator [34]
K(F)= |aSI(F)|2×(2S+1)Kℓ. (5) ρ(r)= P (r)P (r)|m,nihm,n| (9)
m n
Xℓ XS,I m n≤m
X X
Using the partial wave ionization rates obtained we may to describe a statistical mixture of magnetic substate
thenderivethetotalionizationratecoefficientforanun- pairs |m,ni, where m and n are the azimuthal quan-
polarized sample, i.e., the rate coefficient for which the tum numbers of the colliding atoms. The ionizationrate
magneticsubstatesoftheatomsinoursampleareevenly coefficient of the mixture can then be written as
populated:
1
K = 1b1K +3b3K n (r)n (r)d3r,
K(unpol) = (2f11+1)(2f21+1) K(F), (6) 34 N3N4 ZZZ (cid:16)Xℓ (cid:0) ℓ ℓ(cid:1)(cid:17) 3 4 (10)
XF XMF
where N and N are the number of trapped atoms in
3 4
which in the heteronuclear case gives: each component of the mixture, the coefficients (2S+1)b
are the sums of the expectation values of the density
K(unpol) ≈ 1 4(1K +1K )+4(3K +3K ) . (7) operator for all ionizing molecular states with total spin
34 12 3 0 1 0 1 S, and, n3(r) and n4(r) are the density distributions of
(cid:20) (cid:21)
each component in the sample. Explicit expressions for
The energy dependant unpolarized ionization rate coef- the coefficients (2S+1)b are given in Table II. One may
4
TABLE II: 3He*-4He* (2S+1)b coefficients from Eq. (10). The coefficients are the expectation values of the density operator,
Eq. (9), for all ionizing molecular states of given S and parity.
(2S+1)b 3He*-4He*
1b (1/3)(P−3/2P1+P3/2P−1)+(2/9)(P−1/2P0+P1/2P0)+(1/9)(P−1/2P1+P1/2P−1)
3b (1/2)(P−3/2P1+P−3/2P0+P−1/2P1+P1/2P−1+P3/2P0+P3/2P−1)
+(1/3)(P−1/2P−1+P1/2P1)+(1/6)(P−1/2P0+P1/2P0)
easily check that we recover Eq. (7) from Eq. (10) by
substituting the values P =P =P =P =
−3/2 −1/2 1/2 3/2
1 and P = P = P = 1 into the expressions for the
4 −1 0 1 3
coefficients (2S+1)b (Table II) and evaluating Eq. (10).
In order to later make a comparison between theory
and experiment, we determine the distribution P (r)
m
by obtaining the steady-state solution of a rate equation
model describing the optical pumping in our MOT [23].
AtatemperatureofT=1.2mKtheresultingvalueofthe
theoretical ionization rate coefficient is
K(th) =2.4×10−10 cm3/s (11)
34
III. EXPERIMENTAL SETUP FIG. 4: A schematic overview of the TIMOT experimental
apparatus used in these experiments. Component labels are:
AOM, acousto-optic modulator; QW, quater-wave plate; S,
We investigate cold ionizing collisions in a setup (see
shutter;PBSC,polarizingbeamsplittercube;HW,half-wave
Fig.4)capableoftrappinglargenumbers(>∼108)ofboth plate;CL,cylindricallens;andNPBSC,non-polarizingbeam-
3He* and 4He* atoms simultaneously in a TIMOT [13]. splitter cube. For clarity, all spherical lenses and excess mir-
A collimated and Zeeman slowed He* beam is used to rors havebeen omitted.
loadourTIMOT whichis housedinside a stainlesssteel,
ultra-highvacuum chamber. The beamis producedby a
liquidnitrogen(LN )cooleddcdischargesourcesupplied magneticfield(dB/dz=0.35T/m)fortheTIMOT;these
2
with an isotopically enriched (≈50/50) gaseous mixture are placed in water cooled buckets outside the vacuum
of 3He and 4He held in a helium tight reservoir. During and are brought close to the trapping region by placing
operation the reservoiris connected such that all helium them inside reentrant glass windows situated on either
notenteringthecollimationsection(thevastmajorityof side of the chamber.
it) is pumped back into the reservoir and recycled, con- Both helium isotopes are collimated, slowed, and con-
serving our supply of the relatively expensive 3He gas. finedinthe TIMOT using1083nm lightnearlyresonant
Two LN cooled molecular sieves, ensuring a pure sup- with their 23S → 23P optical transitions (see Fig. 5)
2 1 2
ply of helium to the source, are also contained within (natural linewidth Γ/2π=1.62MHz and saturation in-
this reservoir; the first of these is a type 13X molecu- tensity I =0.166mWcm−2, for the cycling transition).
sat
lar sieve, whilst the second is type 4A (both are sodium As the isotope shift for this transition is ≈34GHz the
zeolites having pore sizes of 10˚A and 4˚A respectively). bichromaticbeams areproducedbyoverlappingthe out-
We then make use of the curved wavefront technique to putfromtwoytterbium-dopedfiber lasers(IPGPhoton-
collimate our atomic beam in two dimensions [35] before ics) on a non-polarizing 50/50 beam splitter. One beam
it enters the Zeeman slower. Due to its lighter mass 3He is sent to the collimation section, whilst the second is
atomsemergefromthesourcewithagreatermeanveloc- coupledintoasinglemodepolarizationmaintainingfiber
itythan4Heatomsandinordertoachievealargefluxof to ensure a perfect overlap of the two frequency compo-
both3He*and4He*atomswehaveincreasedthecapture nents, before being split into the Zeeman slowing beam
velocity of our Zeeman slower [19, 24]. Our ultra-high andthetrappingbeams. Eachfiberlaserislockedtothe
vacuum chamber maintains an operational pressure of respective cooling transition using saturated absorption
7×10−10mbar(withapartialpresureof6.5×10−10mbar, spectroscopyinanrf-dischargecell;acousto-opticmodu-
ground state He atoms from the atomic beam are the latorsarethenusedtogeneratetheslowingandtrapping
majorcontributionto this)andis basedupon the design frequencieswhicharedetunedby-500MHz and-40MHz
of our next-generation BEC chamber [36]. Two coils in respectively (see Fig. 5). The slowing beam is focused
an anti-Helmholtz configurationproduce the quadrupole on the source and has a 1/e2 intensity width of 2.2cm
5
or released from the trap. With an exposed front plate
held at negative high voltage, one MCP mounted above
the trap center attracts all positive ions produced dur-
ing ionizing collisions (Eq. (1)) in the trap. The second
MCP is shieldedby a groundedgrid,mounted below the
trap center, and detects only He∗ atoms.
The shielded MCP is used to perform time-of-flight
(TOF)measurementsfromwhichwedetermine the tem-
perature of the trapped atoms. An absorpton image,
in combinationwith the measuredtemperature, then al-
lows us to determine the density distribution, size, and
TABLE III: Typical experimental values of the 3He* and
4He* components in ourTIMOT (error bars correspond to 1
standard deviation).
3He* 4He*
FIG. 5: Level scheme for the ground and first excited states
in 4He∗ and 3He∗.
Temperature T (mK) 1.2(1) 1.2(1)
Numberof atoms N 1.0(3)×108 1.3(3)×108
atthepositionofthetrappedcloud,witheachfrequency Central density n0 (cm−3) 0.5(1)×109 1.0(2)×109
componenthavingapeakintensityofI =9mWcm−2
peak Axial radius σ (cm) 0.28(4) 0.25(3)
p
(I /I ≈54),whilethetrappingbeamissplitintosix
peak sat
independent Gaussian beams with 1/e2 intensity widths Radial radius σz (cm) 0.16(2) 0.14(1)
of 1.8cm and total peak intensity I =57mWcm−2
peak
(I /I ≈ 335). The outputs of two diode lasers
peak sat
(linewidths < 500kHz), each locked using saturated ab-
sorption spectroscopy to the helium 23S → 23P reso- absolute atom number of the sample. We then use the
1 2
unshieldedMCPtomeasuretheinstantaneousionization
nance of one of the isotopes, are overlapped on a second
rate in the trapped sample, which, in combination with
non-polarizingbeam-splittercubeandcoupledintoasin-
theinformationobtainedfromtheabsorptionimages,al-
glemodepolarizationmaintainingfiber. Thissystemde-
lows us to determine trap loss and ionization rates in
livers two, weak, linearly polarized probe beams (∆=0,
I =0.05I , with I =0.27mWcm−2 assuming equal the sample. Our typical TIMOT parameters and mea-
sat sat
population of all magnetic sublevels of the 23S state in surementshavebeenreportedpreviously[13,19]andare
1
given in Table III. The lower temperatures realized in
the trap) to the chamber for the absorption imaging of
the present experiments are due to the resolution of a
eachcomponentofthetrappedcloud. Absorptionimages
power imbalance in two of the trapping laser beams.
are recorded using an IR-sensitive charge-coupleddevice
(CCD) camera [37]. Unfortunately the imaging of both
trappedcomponentscannotbecarriedoutinasingleex-
perimentalcycle;sequentialrunsmustbe made,imaging
IV. DETERMINATION OF THE
first one component and then the other.
HETERONUCLEAR LOSS RATE
Trapped clouds are further monitored by two mi-
crochannel plate (MCP) detectors mounted inside the
chamber. Operatedatavoltageof-1.5kVandpositioned The time evolution of the total number of atoms
11cmfromthe centerofthetrap,theMCP’sareusedto trapped in our TIMOT, N=N +N , may be described
3 4
independently monitor the ions and He∗ atoms escaping by the following phenomenologicalequation [2]:
dN
=L −α N (t)−β n2(r,t)d3r+L −α N (t)−β n2(r,t)d3r−β n (r,t)n (r,t)d3r, (12)
dt 3 3 3 33 3 4 4 4 44 4 34 3 4
ZZZ ZZZ ZZZ
where t denotes time, L is the rate at which atoms are ficient describing collisions between trapped He* atoms
loaded into the TIMOT, α is the linear loss rate coef- andbackgroundgases,β isthelossrate coefficientresult-
6
ing from binary collisions between trapped He* atoms, sional losses. This is born out in Eq. (12) by the time
and n is the cloud density. Subscripts denote whether a dependance of the atom density distributions and hence
given parameter pertains to either of the 3He* or 4He* our inability to make the simplifying constant density
components of the mixture. approximationin the following experiments.
It should be noted at this point that the ”density lim- Both linear and quadratic losses in Eq. (12) are due
ited” regime, often mentioned with regard to the alkali to a number of different mechanisms, andmay be subdi-
systems,is nota featureofthe metastablenoble gassys- videdintoeitherionizingornon-ionizingcategories. The
tems; in the latter the density is not limited by radi- ion production rate may then be expressed in a manner
ation trapping within the cloud, but by ionizing colli- analogous to Eq. (12):
dN
ion =ǫ α N (t)+ǫ K n2(r,t)d3r+ǫ α N (t)+ǫ K n2(r,t)d3r+ǫ K n (r,t)n (r,t)d3r,
dt a 3 3 b 33 3 c 4 4 d 44 4 e 34 3 4
ZZZ ZZZ ZZZ
(13)
where ǫ ,ǫ ,ǫ ,ǫ and ǫ are the weights of the various From an analysis of the trap loss mechanisms [13, 24] it
a b c d e
ionization mechanisms (and may include a factor to ac- can be seen that to a good approximation ǫ =ǫ =0,
a c
count for a less than unity detection efficiency), and the whilst ǫ =ǫ =ǫ . The current signal measured by the
b d e
collision ratecoefficientK hasbeenintroduced. Theloss MCPisproportionaltotheionizationrate,Eq.(13);and
andcollision ratecoefficientsarerelatedbythe equation for gaussian spatial density distributions (centered with
β =2K,andtheappearanceofK,insteadofβ inEq.13 respect to each other), the voltage measured by the os-
expressesthe factthatduringeachionizingcollision,one cilloscope may then be written as
ion is produced, but two atoms are lost from the trap.
3
φTIMOT(t)=eReff K33n203(t)(πσ32)32 +K44n204(t)(πσ42)32 +K34n03(t)n04(t) σ2π2σ+32σσ422 2 +φbgr, (14)
" (cid:20) 3 4(cid:21) #
where n is the centraldensity,σ is the meanrmsradius measurementoftheratior =(φ −φ )/(φ −
0 TIMOT bgr MOT
(of a given cloud component), e is the electron charge, φ ) (where the time dependance of the measured sig-
bgr
and R is an effective resistance. nals has been omitted because of the short duration of
eff
TheexperimentisbasedaroundtheabilityofanMCP the switch-off period), we can derive an expression for
detector to measurethe ions producedinour metastable K34. It has been verified that under our experimental
isotopicmixturewithveryhighefficiency,andemploysa conditions the MCP signal varies linearly with the ion
method first used by Bardou et al. [5] to determine the productionrate,andallclouddensitiesandradiimaybe
ionization rate in the absence of light. To measure the derivedfromabsorptionimages,whilewehavepreviously
rate in the dark we perform an experiment in which we measuredK33andK44 [13]. Asthetrapparameters,and
loadtheTIMOT,switchofftheZeemanslowerbeamand therefore the distribution over the magnetic substates
allMOTbeamsusingthefrequencydetuningAOM’s(the of the atoms, have changed since the experiments de-
quadrupolefield remainson)for 100µs, before switching scribed in Ref. [13] were performed, we have used the
theslowingandtrappinglightbackonagain. Thison/off theorydescribedinSec.IIBtocorrectthemeasuredval-
cycleiseasilyrepeatedmanytimeswhile wemonitorthe ues of K33 and K44 for these effects, yielding: K33 =
ionsignalandaverageit(seeFig.6). Theswitch-offtime 1.6(3)×10−10cm3/s and K44=6.5(2)×10−11cm3/s.
isshortcomparedtothedynamicsoftheexpandingcloud
(weseenovariationintheionsignalduringtheswitchoff
V. RESULTS AND DISCUSSION
period) and we switch the light on long enough (200ms)
to recapture the cloud and allow it to equilibrate.
Performing the experiments described in the previ-
Equation(14) describes the ion productionrate in the
dark of our TIMOT; a similar equation describes the ous section, we obtain the result: K3(e4xp) = 2.5(8) ×
ion production rate of a single-isotope MOT, φ . By 10−10cm3/s, which compares well with the theoretical
MOT
combining the equations for φ and φ with a prediction, K(th) = 2.4 × 10−10cm3/s, obtained after
TIMOT MOT 34
7
dominant in the homonuclear case. In our TIMOT the
laser beams are, in contrast to most experiments per-
formed on heteronuclear collisions, far-detuned (25 nat-
ural linewidths) from resonance and the atomic excited
state population in the trap is therefore negligible. We
can only excite a molecular state if the correct light fre-
quencyispresentandtheatomshavereachedtheCondon
point for the transition. As all light frequencies in our
TIMOT are far detuned from any heteronuclear transi-
tionwe expect nocontributionto the traplossrate from
optically assisted heteronuclear collisions.
To summarize, we have measured the heteronuclear
loss rate coefficient K(exp) in the absence of light for a
34
FIG. 6: Averaged ion signals measured during the experi- trapped mixture of 3He* and 4He* atoms at T =1mK.
ments. The full line is the signal recorded whilst performing The measured value of K(exp) compares very well with
the experiment with a TIMOT, the dashed line is the corre- 34
the value predicted by our single channelmodel of ioniz-
sponding curve for a 3He* MOT (the analogous signal for a
4He* MOT can also be obtained), and the dotted line is the ing collisions in the He* system. Recently, both helium
background signal. The ion rate measured is then averaged isotopes were magnetically trapped in the multi-partial
overthe60µsintervalindicatedbytheshadedregioninorder wave regime using buffer-gas cooling, and a deep mag-
to obtain (φTIMOT−φbgr) and (φ3He*/4He*−φbgr). netic trap [38]. The probable observation of Penning
ionizationunder these conditions has beenreported[39],
and it would be interesting to extend our theory into
undertaking the calculation described in Sec. II. For the multi-partialwave regime and to highmagnetic field
future comparison with other theoretical models, the values. Withtheproductionofquantumdegeneratemix-
equivalent theoretical loss-rate coefficient for an unpo- tures of 3He* and 4He* [40], we also have the possibility
larized gas mixture at a temperature of T = 1mK is ofinvestigatingbothhomonuclearandheteronuclearHe*
K(unpol)=2.9×10−10cm3/s (see Fig. 3).These numbers collisionsatultracoldtemperatures ingreaterdetail. An
34
describe the total heteronuclear loss rate in the absence experiment of interest in this area would be the imple-
mentation of an optical dipole trap in which it would
of light; the only other potential loss process would be
be possible to prepare ultracold samples in well defined
hyperfine state changing collisions, however, due to the
inverted nature of the hyperfine structure in 3He* the magnetic substates. In particular, it would be possible
atoms occupythe lowesthyperfine levelofthe 23S mul- to prepare trapped ultracold samples of 3He* (4He*) in
1
the m =−3/2 (m =−1) states, for which (as in the
tiplet and so cannot relax to a lower level, while the en- F J
magnetically trapped m =+3/2 (m =+1) states used
dothermic collision necessary to reach the F=1/2 state F J
intheproductionofultracoldHe*gases)Penningioniza-
would require ≈ 200mK to be provided by the trap,
tion should be suppressed.
200 times more than the typical collision energy in the
TIMOT. The error in the experimental value is mainly
determined by errors in the absorption imaging, which
we find to be ≈ 30%, and by the error bars reported Acknowledgments
on our previous measurements of the homonuclear loss
rates [13]. We thank Jacques Bouma for technical support. This
With regard to optically assisted collisions, we note workwassupportedbythe“ColdAtoms”programofthe
that the excited state potentials in the case of heteronu- Dutch Foundation for Fundamental Research on Matter
clearcollisionsaregovernedatlong-rangebythevan-der- (FOM), the Space Research Organization Netherlands
Waalsinteraction(∝1/R6),havingamuchshorterrange (SRON), Grant No. MG-051, and the European Union,
than that of the resonant dipole interaction (∝ 1/R3) Grant No. HPRN-CT-2000-00125.
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