Cooling of Sr to high phase-space density by laser and sympathetic cooling in isotopic mixtures

0.2 MB·English

by  G. Ferrari

Cooling of Sr to high phase-space density by laser and sympathetic cooling in isotopic
mixtures
∗
G. Ferrari, R. E. Drullinger, N. Poli, F. Sorrentino, and G. M. Tino
Dipartimento di Fisica and LENS, Istituto Nazionale Fisica Nucleare, Istituto Nazionale Fisica della Materia,
Polo Scientifico-Universit`a di Firenze, 50019 Sesto Fiorentino, Italy
(Dated: February 2, 2008)
6 Based on an experimental study of two-body and three-body collisions in ultracold strontium
0 samples,anoveloptical-sympatheticcoolingmethodinisotopicmixturesisdemonstrated. Without
0 evaporative cooling, a phase-space density of 6×10−2 is obtained with a high spatial density that
2
should allow to overcome the difficulties encountered so far to reach quantum degeneracy for Sr

n atoms.
a
J PACSnumbers: 32.80.Pj,34.50.-s,05.30.Jp,32.80.-t.

2
1
The combination of laser cooling [1] and evaporative large interspecies elastic cross-section;this allowed us to

cooling allowed to reach ultra-low temperatures and to demonstrateanoptical-sympatheticcoolingmethodcon-
]
h observeBose-Einsteincondensation(BEC)andFermide- ceptually different from what was done so far on neutral
p
generacy for different atoms [2]. Laser cooling is indeed atoms [18, 19] and somehow analogous to the one used
-
m very effective to reach phase-space densities within few for trapped ions [20], achieving a phase-space density of
orders of magnitude of quantum degeneracy. The limits 6×10−2 in conditions suitable to further cooling of the
o
in cooling at high density are set by the optical depth of sample towards BEC.
t
a thesample,i.e. reabsorptionofscatteredlight,andlight- The experimental setup, based on the apparatus pre-
.
s assisted atom-atom collisions. Forced evaporative cool- viously described in [8, 21], allows to trap single-isotope
c ing [3] represents the common way to circumvent these samples or isotopic mixtures of 86Sr and 88Sr atoms in
i
s limits. However, this procedure does not work for all anopticaldipoletrap. Theloadingprocedurestartswith
hy atoms. In particular,among the atoms cooledwith opti- a magneto-opticaltrap on the 1S0-1P1 resonancetransi-
p calmethods,noneofthealkali-earthatomsreachedquan- tionat461nm. Duringthis phase,adecaychannelfrom
[ tum degeneracy so far, except ytterbium which has an the excited state results in the accumulation of atoms
alkali-earth-like electronic structure [4]. A phase-space in the magnetically trapped metastable 3P2 state [22].
1 density of∼10−1 was reportedfor Sr [5] but BEC could The isotopic mixture is produced in the magnetic trap
v
not be reached. Sr is of interest for several reasons: In a bysteppingthefrequencyofthetrappinglasertotheap-
6
8 naturalstrontiumsample,differentisotopescanbeinves- propriatevalues. After loadingthemagnetictrap,atoms
0 tigated with different statistics; 88Sr (82.6 %), 86Sr (9.8 are optically pumped back into the electronic ground
1 %), and 84Sr (0.6 %) are bosons with zero nuclear spin; state and a second cooling stage is applied based on a
0 87Sr(7%)isafermionwithnuclearspinI =9/2. ABEC magneto-optical trap operating on the narrow 1S0-3P1
6 ofSratoms wouldallowthe study of0-spincondensates, transition at 689 nm. At this point we typically obtain
0 fastopticalcoolingandcontinuouscoherentmatter-wave 107 88Sr atoms at 2 µK, and 106 86Sr atoms at 1 µK.
/
s sources, quantum devices both for frequency standards Theisotopicmixtureisthenloadedintoanopticaldipole
c and inertial sensors. Besides the studies towards quan- trap by superposing a focused 922 nm laser on the red
i
s tum degeneracy, Sr has recently been the subject of ac- magneto-optical trap, resulting in a 90 µK deep poten-
y tiveresearchinvariousfieldsspanningfromlasercooling tial with radial and axial frequencies of 2 kHz and 26
h
physics [6, 7], investigation of ultra-narrow transitions Hz,respectively. Tooptimizethetransferefficiencyfrom
p
: towardsfuture opticalclocks[8,9, 10,11], multiple scat- theredmagneto-opticaltrapintotheopticaldipoletrap,
v tering [12], and collisional physics [13] [14] [15] [16] [17]. the optical dipole beam waist is axially displaced from
i
X In this article, we present a novel scheme for the pro- the magneto-optical trap by 500 µm (corresponding to
r duction of a high phase-space density sample of atomic 2/3 of the dipole beam Rayleigh range and two times
a strontium. Since collisional processes play a crucial role the red magneto-optical trap radii) in order to increase
andrelevantparametersarenotwellknownforthisatom, themagneto-opticaltrap-dipoletrapspatialoverlap[23].
we studied 2-body and 3-body collisions both in pure Themeasured6slifetimeintheopticaltrapisconsistent
samples, and isotopic mixtures. Our results show that withtheresidualbackgroundgaspressureinourappara-
usual evaporative cooling methods are difficult to ap- tus. Theoff-resonantphotonscatteringinducesaheating
ply in a single species sample of 86Sr or 88Sr. The in- of0.4µK/s. Thepolarizationofthedipolebeamissetto
vestigation of an ultracold 86Sr-88Sr mixture revealed a nearlyfulfill the requirementsfortrappingatthe ”magic
wavelength” that cancels the differential Stark shift for
1 3
the S0- P1 transition [24]. The atom number and tem-
peraturearemeasuredindependentlyonthetwoisotopes
∗Electronicaddress: Guglielmo.Tino@fi.infn.it by absorption imaging with a resonant probe beam, and
2
thecontributionofthenon-resonantisotopeistakeninto
account. The spatial density is inferred from the mea-
sured temperature and the trapping potential.
Two-body and three-body collisions are studied by
loading single species or the isotopic mixture into the
optical dipole trap. For the investigation of 2-body elas-
ticcollisions,thegasisinitiallyputoutofequilibriumby
m(aptgσ[amp24uirlrsv5e2eere±fua,]seoev.)cdns)li1,σlo.uodoT)dno8ureWw×6eehrsns−ndiieesbn1spr8ty0gbie6rreetee−fynryaelast=1tarnunpua6etlwndhrnetimbs(dioictn1otagt2ehht.tgote.3eeoinadomtIpvms±eanhnaesrpteloe-aaotue0saclhfcere.isii5zeoalatsusei)hrttnsrcaurieaie×tgoernrvidsoneevgaptp1etlithσsoehlt0opael8in−eaci8betsdrsa1−ahclomei4elpt8netrrp8aopgofmecolporl=siosoatzre2cceoaas,oacnl(ttctpia3ihttaihncyotisenga±eencdd[rl,rt1peit1(owtn6isupσh)smgc,olsu8esr×--1e6reilisrb−e7seea1eon(]e8cst.sm0tgd8tauo−ttiNmilohphx1it=nnoe7ess-- tFrIaGp.pe1d: in tNhoeno-epxtpicoanlednitpiaolledtercaapyduofe ttohe3-nbuomdyberrecoomf b86inSar-, Please purchase docPrint product on www.verypdf.com site.
collisions. tion. Inset: the 3-body recombination rate constant is given
Westudiedthe3-bodyrecombinationrateK3 byload- by the slope of the natural log of the atom number with re-
ing a single isotope (either 86Sr or 88Sr) into the dipole spect to 0thn2(t′)idt′ where hn2(t′)i = N(1t′) V n3(~r,t′)d3r
trap and observing the evolution of the atom number (see thetRext). The term t/τ accounts for lossesRdueto back-
and temperature. With 88Sr we found no experimental ground collisions.
evidence for non-exponentialdecay and, giventhe initial
atom density at the trap center of 3×1013 cm−3, we set
an upper bound on K88 at 10−27 cm6/s. To determine
K86 we followed the a3nalysis described in [26]: the loss rate during the evaporation and by the 6 s background
3 limited lifetime.
ratedue to 3-bodyrecombinationis modeledby the rate
Theseresultsledtoanewall-opticalsympatheticcool-
equation
ing scheme. The basic idea of the new cooling method is
dN to use a mixture of isotopes trapped in the dipole trap:
=−K3 n3(~r,t)d3r (1) one isotope is laser cooled and by elastic collisions cools
dt ZV
the other isotope which is the one of interest. The ad-
or equivalently vantage,comparedtothe schemesusedsofarforneutral
atoms,is thatthe limitations oflasercoolingofspatially
N(t) t n3(~r,t′) denseandopticallythicksamplesaredrasticallyreduced.
lnN(0) =−K3Z0 dt′ZV N(t′) d3r, (2) Inthiswork,continuouslasercoolingof86Srleadstoheat
dissipation in a 88Sr sample by sympathetic cooling; the
where n is the density, and N(t) is the atom number small 86Sr optical depth does not limit the achievable
at time t. Figure 1 shows the data and the fit using minimum temperature. Sympathetic cooling with neu-
equation2fromwhichweobtaintherateconstantK86 = tralatomsnormallyrequiresathermalbathwitha large
3
(1.0±0.5)×10−24cm6/s. Thisrecombinationrateismore heat capacity with respect to that of the sample to be
than three orders of magnitude larger than the typical cooled. This is due to the fact that when the thermal
values for ultracold alkali vapors [27]. bath is cooled by evaporative cooling, each lost atom
The first consequence of these results is that evapora- carries an energy of the order of few times the temper-
tive cooling on pure samples of either 86Sr or 88Sr can- ature of the sample. In the case of optical-sympathetic
not be efficient. 86Sr presents an extremely large elastic cooling, each laser-cooled atom can subtract an energy
cross-section,agoodpointtoestablishafastthermaliza- of the order of the optical recoil in a time correspond-
tion,butthe3-bodyrecombinationrateintroducesaloss ing to a few lifetimes of the excited state (say 4, when
channel that is fatal with the typical geometries accessi- operating at 1/4 Isat), without being lost. Considering
blethroughopticaldipoletrapping. Anopticaltrapwith the 1S0-3P1 transition, the power subtracted per atom
a much larger trapping volume would partially suppress is of the order of 6 mK/s; if the inter-isotope thermal-
this loss channel[28]. 88Srinsteadturns outto be stable ization is fast enough, each 86Sr atom can cool about
against 3-body decay, but the small elastic cross-section 103 88Sr atoms down to µK temperatures in one sec-
results in a long thermalization time compared to typi- ond. Inthe86Sr-88Srisotopemixturetherelativelylarge
cal trap lifetime. Indeed, in our experiment evaporative inter-speciescross-sectionresultsinthermalizationtimes
cooling of 88Sr by reducing the dipole beam intensity al- typically of the order of few milliseconds. This thermal-
lowedto increasethe phase-spacedensity to a maximum ization is fast even on the time scale of laser cooling on
of2×10−1,limitedbythereductionofthethermalization the intercombination 1S0-3P1 transition. On the other
3
14
K)
16 106 m( 12
e
ur
mure(K)1124 110045number mperat 10
mperat10 103atom te 8
e
t
102 6
8
10 100 1000 10000
0,0 0,3 0,6 0,9 1,2 1,5
time(s) intensity(mW/cm2)
FIG.3: Asymptotictemperatureofthe88Sr cloudfordiffer-
ent intensities of the 86Sr laser cooling beam on the 1S -3P
FIG. 2: Dynamics of an optically trapped 88Sr cloud sym- 0 1
pathetically cooled with laser cooled 86Sr. Filled circles •: transition (Isat = 3 µW/cm2). The 88Sr atom number is
6×105.
88Sr atom number. Open circles ◦: 86Sr atom number. The
number of 88Sr atoms remains constant during the process,
while 86Sr decays exponentially with a 80 ms time constant.
Under optimized conditions, the temperature (triangles ▽)
sity. Figure 3 reports the asymptotic temperature as a
decreases with a 150 ms time constant and the mixture is
function of the overallcooling light intensity incident on
always at thermal equilibrium.
88
the sample, for a fixed amount of trapped Sr. At high
intensity, the 86Sr lifetime increases due to the reduced
spatial density and the final temperature is proportional
hand,the164MHz86Sr-88Srisotopicshiftandthe natu- to the intensity as expected from the usual Doppler the-
1 3
rallinewidthof7.6kHzforthe S0- P1 transition,makes ory. Byloweringthe intensity, the finaltemperatureand
lasercoolingononeisotopeinsensitivetothepresenceof the 86Sr lifetime decreaseto the point where 86Sr is lost
the other. too fast with respect to the cooling dynamics of 88Sr.
We implemented the optical-sympathetic cooling The optimum values are obtained when the overallcool-
scheme by extending the temporal overlap between the inglightincidentontheatomshasanintensity∼30Isat.
opticaldipoletrapandthe86Srredmagneto-opticaltrap For 6×105 88Sr atoms trapped in the dipole trap, the
afterswitchingoffthe88Srmagneto-opticaltrap. During finaltemperatureis6.7µKatapeakdensityof1.3×1014
thisphasetheparametersthatoptimizethe 88Sr cooling cm3; the corresponding phase-space density is 5×10−2.
are substantially the same as those typically employed This value is only a factor of two lower with respect to
in the second cooling stage (intensity 30-100 Isat with whatwaspreviouslyobtainedwithoutforcedevaporation
Isat = 3µW/cm2, -200 kHz frequency detuning, mag- [5], but it exhibits more favorableconditions for starting
netic field gradient 0.6 mT/cm). The horizontal dis- evaporative cooling, considering the higher spatial den-
placementbetweentheredmagneto-opticaltrapandthe sity (more than one order of magnitude higher) and the
dipole trap optimizes the spatial overlap and provides a largernumber of trapped atoms. By keeping the cooling
continuous flux of 86Sr atoms from the magneto-optical parameters on 86Sr fixed at the optimum value and by
88
trap to the optical dipole trap replacing the atoms that varying the number of trapped Sr, we determined the
are lost during the optical-sympathetic cooling due to dependence of the final temperature with respect to the
88 88
light assisted collisions. Figure 2 reports the dynamics Sr density. Figure4showsthedependenceof Sr tem-
of optical-sympathetic cooling, starting from an initial peraturefromthenumberofatomsinthetrap. Wedeter-
temperature of 15-20 µK, limited by density dependent minethedensity-dependentheatingdT/dn≃2µK/(1014
heating[21, 29]. Itcanbe observedthatthe coolingpro- cm−3), whichis20times lowerthanthe equivalentvalue
cess does not induce losses on 88Sr while the number of for pure laser cooled 88Sr [29]. This strong reduction
86Sr atoms exponentially decays with a 80 ms lifetime. is a direct consequence of the optical distinction of the
About 100 ms after switching off the 88Sr red magneto- twoisotopesonthe 1S0-3P1 transition. The limit onthe
opticaltrap,weobservethatthemixtureattainsthermal 86Sr temperature of 4 µK for zero 88Sr density can be
equilibrium. Fromthis point onthe equilibrium is main- attributed to the laser cooling dynamics in the tightly
tained, which is anessentialcondition for the implemen- confining potential of the dipole trap. Considering the
tation of this cooling scheme. Under optimized condi- power laws involved, reducing the optical dipole poten-
tions (overalloptical intensity 100 Isat) the temperature tial in the final stage of the optical-sympathetic cooling
decaysfromtheinitialvaluewitha150mstimeconstant. should lead to further cooling of the sample and consid-
The minimum attainable temperature depends both on erably increase the 88Sr phase-space density.
theintensityofthe86Sr coolingbeam,andthe88Sr den- Inconclusion,weinvestigatedthecollisionalproperties
4
measure a rather large inter-species elastic cross section.
0,06 We exploit the fast 86Sr-88Sr thermalization to demon-
7
strate an optical-sympathetic cooling scheme in which
y
mK) nsit heatdissipationforoneisotopeisobtainedbylasercool-
e( 6 0,04de ing; the sympathetically cooled component is more than
atur ace one order of magnitude more abundant than the laser
er p cooled one, reducing substantially the limitations asso-
temp 5 temperature 0,02phase-s cuipatteod7to×la1s0e5r 8c8oSorlinagtoamtshaigthasppaetaikalsdpeantsiaitly.deWnseitycooofl
4 phase-spacedensity 1.4×1014 cm−3 and 6×10−2 phase space density. The
0,00
combination of this cooling scheme to a final evapora-
0 2x105 4x105 6x105 tive cooling stage on pure 88Sr should allow to increase
88Sratomsnumber considerably the phase-space density opening the pos-
sibility to investigate quantum degenerate gases of Sr.
FIG. 4: Temperature and phase-space density of the 88Sr An interesting possibility is also the development of new
cloudsympatheticallycooledwithlasercooled86Sr,asafunc-
atomicsensorsbasedonultracoldSratomsexplotingthe
tion of the 88Sr atom number.
weak interatomic interaction and their small sensitivity
to magnetic and electric fields.
of ultracold Sr atoms of interest for the production of a
Bose-Einstein condensate. On pure 86Sr we find a very WeacknowledgefruitfuldiscussionswithM.Prevedelli
large3-bodyrecombinationratewhichsetsstringentlim- and A. Simoni. We thank R. Ballerini, M. De Pas, M.
itsontheevaporationefficiencyonthisisotope. For88Sr Giuntini, and A. Hajeb for technical assistance. This
we find that the small elastic cross-section results in a work was supported by Agenzia Spaziale Italiana, Ente
long thermalization time compared to typical trap life- Cassa di Risparmio di Firenze, MIUR-COFIN 2002, Is-
time. This can explain why BEC of Sr was not achieved tituto Nazionale Fisica della Materia, Istituto Nazionale
86 88
so far. On the other hand, for the Sr- Sr mixture we di Fisica Nucleare, and LENS.
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